(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 678989, 25966]*) (*NotebookOutlinePosition[ 680583, 26012]*) (* CellTagsIndexPosition[ 680539, 26008]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Intersections of Surfaces", "Title"], Cell["Revised 3/3/1999", "Text"], Cell[TextData[{ "This article presents an algorithm, along with a ", StyleBox["Mathematica", FontSlant->"Plain"], " package implementing it, that gives a parametrization for the \ intersection of two surfaces." }], "Text", FontSize->14, FontSlant->"Italic"], Cell[CellGroupData[{ Cell["by Steven Wilkinson", "Author"], Cell[TextData[{ "\tIf two surfaces in space intersect, their intersection is usually a \ curve or union of curves. How do you get your hands on a mathematical \ representation of those curves if you want to plot them or find out other \ information about them, such as their lengths? Sometimes, algebraic \ manipulation of the two surface equations provides an answer. For example, \ suppose we wish to find the intersection of the sphere centered at the origin \ of radius 1, given by ", Cell[BoxData[ \(TraditionalForm\`\(x\^2 + y\^2 + z\^2 = 1, \)\)]], " and the saddle surface, given by ", Cell[BoxData[ \(TraditionalForm\`z = x\^2 - y\^2\)]], "." }], "Text"], Cell[BoxData[ \(Needs["\"]\)], "Input", CellLabel->"In[41]:="], Cell[BoxData[ \(Block[{$DisplayFunction = Identity}, sphere\ = ContourPlot3D[ x\^2 + y\^2 + z\^2, {x, \(-1\), 1}, {y, \(-1\), 1}, {z, \(-1\), 1}, Contours \[Rule] {1}]; \n\t saddle = Plot3D[x\^2 - y\^2, {x, \(-1\), 1}, {y, \(-1\), 1}]; \n\t]\)], "Input", CellLabel->"In[42]:="], Cell[CellGroupData[{ Cell[BoxData[ \(\(intersectingSurfaces\ = Show[sphere, saddle]; \)\)], "Input", CellLabel->"In[43]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.0855 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics3D 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.70214 m .79851 .70357 L .80218 .70432 L .683 .142 0 r F .79104 .70203 m .78588 .69676 L p .78397 .69572 L .533 .026 0 r F P 0 g s .78152 .60188 m .76766 .62545 L .81323 .66082 L p .691 .248 .194 r F P 0 g s .79864 .67632 m .81323 .66082 L .76766 .62545 L p .695 .206 .08 r F P 0 g s .72684 .71024 m .71876 .64424 L .77325 .60815 L p .453 .311 .597 r F P 0 g s .76766 .62545 m .75222 .63966 L .79864 .67632 L p .695 .206 .08 r F P 0 g s .78234 .68124 m .79864 .67632 L .75222 .63966 L p .676 .135 0 r F P 0 g s .75222 .63966 m .73522 .64362 L .78234 .68124 L p .676 .135 0 r F P 0 g s .76437 .67478 m .78234 .68124 L .73522 .64362 L p .586 .02 0 r F P 0 g s .79051 .63983 m .8128 .68587 L p .77945 .6907 L .939 .87 .742 r F P 0 g s .75919 .69363 m .76747 .67942 L p .77945 .6907 L .939 .87 .742 r F P 0 g s .76437 .67478 m .76747 .67942 L .77793 .68927 L .533 .026 0 r F .76747 .67942 m .79051 .63983 L p .77945 .6907 L .939 .87 .742 r F P 0 g s .77325 .60815 m .71876 .64424 L p .75509 .57065 L .504 .402 .673 r F P 0 g s .71876 .64424 m .73459 .56154 L .74545 .56552 L .504 .402 .673 r F .75281 .54852 m .74545 .56552 L p .76857 .57781 L .634 .226 .252 r F P 0 g s .75509 .57065 m .74545 .56552 L .75576 .5693 L .504 .402 .673 r F .71876 .64424 m .74545 .56552 L .75509 .57065 L F .77325 .60815 m .76603 .57646 L p .78594 .59035 L .413 .342 .668 r F P 0 g s .76603 .57646 m .77325 .60815 L p .75509 .57065 L .504 .402 .673 r F P 0 g s .73951 .57923 m .78152 .60188 L p .76857 .57781 L .634 .226 .252 r F P 0 g s .74545 .56552 m .73951 .57923 L p .76857 .57781 L .634 .226 .252 r F P 0 g s .71876 .64424 m .70231 .56956 L .72097 .55654 L p .504 .402 .673 r F P 0 g s .70231 .56956 m .71876 .64424 L .65777 .66876 L p .58 .452 .671 r F P 0 g s .73522 .64362 m .71673 .63655 L .76437 .67478 L p .586 .02 0 r F P 0 g s .74483 .65626 m .76437 .67478 L .71673 .63655 L p 0 .126 .612 r F P 0 g s .76437 .67478 m .74483 .65626 L .76747 .67942 L p .533 .026 0 r F P 0 g s .76747 .67942 m .79629 .70889 L p .77793 .68927 L .533 .026 0 r F P 0 g s .77793 .68927 m .78397 .69572 L .78588 .69676 L .533 .026 0 r F .79629 .70889 m .81549 .72701 L .79104 .70203 L p F P 0 g s .78397 .69572 m .79629 .70889 L .79104 .70203 L .533 .026 0 r F .77542 .67773 m .79629 .70889 L .76747 .67942 L p 0 .093 .638 r F P 0 g s .76747 .67942 m .74483 .65626 L p .75792 .66545 L 0 .093 .638 r F P 0 g s .73522 .64362 m .75222 .63966 L .70849 .61505 L p .579 .011 0 r F P 0 g s .70849 .61505 m .69082 .61837 L .73522 .64362 L p .579 .011 0 r F P 0 g s .71673 .63655 m .73522 .64362 L .69082 .61837 L p .429 0 0 r F P 0 g s .71673 .63655 m .69686 .61784 L .74483 .65626 L p 0 .126 .612 r F P 0 g s .72386 .62528 m .74483 .65626 L .69686 .61784 L p 0 .239 .753 r F P 0 g s .75222 .63966 m .76766 .62545 L .72473 .60172 L p .626 .12 .027 r F P 0 g s .72473 .60172 m .70849 .61505 L .75222 .63966 L p .626 .12 .027 r F P 0 g s .79051 .63983 m .76747 .67942 L p .74555 .64735 L .888 .773 .729 r F P 0 g s .74555 .64735 m .72386 .62528 L p .7371 .62894 L 0 .178 .712 r F P 0 g s .73772 .6359 m .74039 .63609 L .74555 .64735 L .888 .773 .729 r F .74039 .63609 m .79051 .63983 L .74555 .64735 L F .74483 .65626 m .72386 .62528 L .74555 .64735 L p 0 .093 .638 r F P 0 g s .74555 .64735 m .77542 .67773 L p .75792 .66545 L 0 .093 .638 r F P 0 g s .74483 .65626 m .74555 .64735 L .75792 .66545 L 0 .093 .638 r F .76766 .62545 m .78152 .60188 L .73951 .57923 L p .636 .185 .165 r F P 0 g s .73951 .57923 m .72473 .60172 L .76766 .62545 L p .636 .185 .165 r F P 0 g s .69703 .55164 m .70231 .56956 L p .67882 .55165 L .6 .503 .716 r F P 0 g s .65777 .66876 m .64211 .59499 L .70231 .56956 L p .58 .452 .671 r F P 0 g s .69955 .56696 m .68389 .58876 L .72473 .60172 L p .562 .104 .123 r F P 0 g s .70849 .61505 m .72473 .60172 L .68389 .58876 L p .526 .003 0 r F P 0 g s .72386 .62528 m .70163 .58166 L .72548 .60562 L p 0 .178 .712 r F P 0 g s .72386 .62528 m .72548 .60562 L .727 .60846 L 0 .178 .712 r F .70231 .56956 m .69703 .55164 L p .70638 .55264 L .538 .465 .721 r F P 0 g s .71383 .53705 m .70697 .55142 L p .72097 .55654 L .575 .165 .227 r F P 0 g s .71383 .53705 m .72097 .55654 L .72662 .55806 L .575 .165 .227 r F .72097 .55654 m .70231 .56956 L p .70638 .55264 L .538 .465 .721 r F P 0 g s .72097 .55654 m .69955 .56696 L .72706 .55878 L .575 .165 .227 r F .70697 .55142 m .70638 .55264 L p .72097 .55654 L F P 0 g s .70638 .55264 m .69955 .56696 L p .72097 .55654 L .575 .165 .227 r F P 0 g s .69955 .56696 m .70686 .55164 L p .68846 .55164 L .5 .089 .192 r F P 0 g s .70638 .55264 m .69233 .53569 L .72387 .55452 L .538 .465 .721 r F .69703 .55164 m .69655 .55001 L p .70638 .55264 L F P 0 g s .69655 .55001 m .69233 .53569 L p .70638 .55264 L .538 .465 .721 r F P 0 g s .72387 .55452 m .72097 .55654 L p .70638 .55264 L .538 .465 .721 r F P 0 g s .72662 .55806 m .72097 .55654 L .72706 .55878 L .575 .165 .227 r F .72473 .60172 m .73951 .57923 L .69955 .56696 L p .562 .104 .123 r F P 0 g s .73184 .61745 m .74324 .5982 L .71762 .58555 L p .84 .698 .707 r F P 0 g s .72548 .60562 m .70163 .58166 L p .71464 .57892 L .048 .226 .725 r F P 0 g s .69955 .56696 m .73951 .57923 L p .72706 .55878 L .575 .165 .227 r F P 0 g s .74324 .5982 m .71762 .58555 L p .70633 .56041 L .859 .668 .643 r F P 0 g s .71464 .57892 m .715 .57885 L .71762 .58555 L .048 .226 .725 r F .71464 .57892 m .71762 .58555 L .72548 .60562 L F .69233 .53569 m .69703 .55164 L p .67882 .55165 L .6 .503 .716 r F P 0 g s .66118 .56449 m .69955 .56696 L p .68846 .55164 L .5 .089 .192 r F P 0 g s .6678 .55165 m .66118 .56449 L p .68846 .55164 L .5 .089 .192 r F P 0 g s .6678 .55165 m .6764 .53499 L p .6518 .55447 L .401 0 .144 r F P 0 g s .64211 .59499 m .57451 .60946 L p .60783 .56888 L .651 .534 .708 r F P 0 g s .60783 .56888 m .61485 .56565 L .64211 .59499 L .651 .534 .708 r F .60471 .55794 m .59503 .57476 L p .61536 .56542 L .272 0 .08 r F P 0 g s .63132 .55808 m .63182 .55718 L p .61778 .56313 L .272 0 .08 r F P 0 g s .61778 .56313 m .63182 .55718 L .61931 .56169 L .272 0 .08 r F .61536 .56542 m .63132 .55808 L .61778 .56313 L F .63132 .55808 m .64211 .59499 L p .61253 .56315 L .651 .534 .708 r F P 0 g s .57451 .60946 m .59503 .57476 L .60783 .56888 L .651 .534 .708 r F .58759 .58771 m .62398 .57146 L p .61536 .56542 L .272 0 .08 r F P 0 g s .59503 .57476 m .58759 .58771 L p .61536 .56542 L .272 0 .08 r F P 0 g s .60783 .56888 m .61253 .56315 L .61485 .56565 L .651 .534 .708 r F .62748 .54494 m .63132 .55808 L p .61253 .56315 L F P 0 g s .62398 .57146 m .66118 .56449 L p .65037 .55294 L .401 0 .144 r F P 0 g s .64014 .54201 m .63132 .55808 L p .65037 .55294 L .401 0 .144 r F P 0 g s .63132 .55808 m .62398 .57146 L p .65037 .55294 L .401 0 .144 r F P 0 g s .68075 .54937 m .63132 .55808 L .69233 .53569 L .6 .503 .716 r F .67211 .47821 m .69223 .53539 L p .62748 .54494 L .604 .534 .749 r F P 0 g s .69077 .53591 m .62748 .54494 L p .69223 .53539 L .604 .534 .749 r F P 0 g s .63132 .55808 m .62748 .54494 L .69077 .53591 L p .6 .503 .716 r F P 0 g s .69077 .53591 m .69233 .53569 L p .63132 .55808 L .6 .503 .716 r F P 0 g s .68389 .58876 m .69955 .56696 L .66118 .56449 L p .46 0 .065 r F P 0 g s .66118 .56449 m .6678 .55165 L p .6518 .55447 L .401 0 .144 r F P 0 g s .67836 .5255 m .70163 .58166 L .65361 .54419 L p .182 .316 .766 r F P 0 g s .73951 .57923 m .74545 .56552 L p .72706 .55878 L .575 .165 .227 r F P 0 g s .72097 .55654 m .73779 .5448 L p .73459 .56154 L .504 .402 .673 r F P 0 g s .69233 .53569 m .73779 .5448 L .72387 .55452 L p .538 .465 .721 r F P 0 g s .73779 .5448 m .69233 .53569 L .67211 .47821 L p .527 .489 .757 r F P 0 g s .67211 .47821 m .70367 .44738 L p .73779 .5448 L .527 .489 .757 r F P 0 g s .74324 .5982 m .70633 .56041 L .70124 .47846 L .859 .668 .643 r F .70163 .58166 m .67836 .5255 L .7004 .54722 L p .048 .226 .725 r F P 0 g s .70163 .58166 m .7004 .54722 L .70371 .55458 L .048 .226 .725 r F .70633 .56041 m .7004 .54722 L .70124 .47846 L .859 .668 .643 r F .69223 .53539 m .69233 .53569 L .69077 .53591 L p .604 .534 .749 r F P 0 g s .7004 .54722 m .67836 .5255 L p .68974 .51691 L .148 .251 .715 r F P 0 g s .68826 .5127 m .70124 .47846 L p .7004 .54722 L .859 .668 .643 r F P 0 g s .62748 .54494 m .61412 .50727 L .67211 .47821 L p .604 .534 .749 r F P 0 g s .65886 .44612 m .67211 .47821 L .61412 .50727 L p .619 .571 .779 r F P 0 g s .67211 .47821 m .65886 .44612 L .70367 .44738 L closepath p .557 .537 .789 r F P 0 g s .70367 .44738 m .65886 .44612 L .62584 .38056 L p .546 .575 .835 r F P 0 g s .62584 .38056 m .69385 .38111 L p .70367 .44738 L .546 .575 .835 r F P 0 g s .70124 .47846 m .66991 .46856 L p .65136 .38685 L .816 .556 .546 r F P 0 g s .66991 .46856 m .66905 .46669 L .65136 .38685 L .816 .556 .546 r F .61412 .50727 m .59422 .45998 L .65886 .44612 L p .619 .571 .779 r F P 0 g s .65886 .44612 m .59422 .45998 L .56076 .39561 L p .624 .615 .821 r F P 0 g s .56076 .39561 m .62584 .38056 L .65886 .44612 L p .624 .615 .821 r F P 0 g s .6543 .45721 m .63633 .39892 L p .66072 .44854 L .215 .265 .699 r F P 0 g s .62808 .38222 m .65136 .38685 L .65888 .44144 L p .772 .525 .562 r F P 0 g s .65888 .44144 m .65948 .44583 L p .63633 .39892 L .772 .525 .562 r F P 0 g s .63633 .39892 m .62808 .38222 L .65888 .44144 L .772 .525 .562 r F .6543 .45721 m .60704 .42255 L p .6274 .38208 L .306 .324 .716 r F P 0 g s .63633 .39892 m .6543 .45721 L p .6274 .38208 L .306 .324 .716 r F P 0 g s .67836 .5255 m .6543 .45721 L .6718 .47398 L p .148 .251 .715 r F P 0 g s .68826 .5127 m .70124 .47846 L .66991 .46856 L p .81 .608 .629 r F P 0 g s .6718 .47398 m .6543 .45721 L p .66072 .44854 L .215 .265 .699 r F P 0 g s .66072 .44854 m .66991 .46856 L .6718 .47398 L .215 .265 .699 r F .63633 .39892 m .65948 .44583 L .66072 .44854 L F .66013 .45055 m .65948 .44583 L p .66943 .46841 L .816 .556 .546 r F P 0 g s .65948 .44583 m .65136 .38685 L p .66905 .46669 L .816 .556 .546 r F P 0 g s .66943 .46841 m .65948 .44583 L .66905 .46669 L .816 .556 .546 r F .66072 .44854 m .66222 .44651 L .66991 .46856 L .215 .265 .699 r F .66991 .46856 m .66943 .46841 L p .6718 .47398 L .81 .608 .629 r F P 0 g s .68826 .5127 m .66991 .46856 L .6718 .47398 L .81 .608 .629 r F .70367 .44738 m .72676 .45128 L p .73779 .5448 L .527 .489 .757 r F P 0 g s .72676 .45128 m .70367 .44738 L .71575 .42594 L closepath p .506 .525 .81 r F P 0 g s .69385 .38111 m .71575 .42594 L .70367 .44738 L p .546 .575 .835 r F P 0 g s .71575 .42594 m .69385 .38111 L .7223 .38787 L closepath p .452 .523 .84 r F P 0 g s .65136 .38685 m .70869 .40575 L .70124 .47846 L p .816 .556 .546 r F P 0 g s .67937 .42333 m .70477 .50557 L .6718 .47398 L p .215 .265 .699 r F P 0 g s .66222 .44651 m .67937 .42333 L .6718 .47398 L .215 .265 .699 r F .6718 .47398 m .67287 .47501 L p .67309 .47701 L .148 .251 .715 r F P 0 g s .67836 .5255 m .6718 .47398 L .67309 .47701 L .148 .251 .715 r F .67836 .5255 m .67287 .47501 L .67625 .48149 L F .67836 .5255 m .67608 .47808 L .68974 .51691 L F .65361 .54419 m .63062 .48921 L .67836 .5255 L p .182 .316 .766 r F P 0 g s .6543 .45721 m .67836 .5255 L .63062 .48921 L p .257 .324 .741 r F P 0 g s .66228 .46614 m .68028 .53375 L .68826 .5127 L p .81 .608 .629 r F P 0 g s .66943 .46841 m .66228 .46614 L p .68826 .5127 L .81 .608 .629 r F P 0 g s .62584 .38056 m .56076 .39561 L .52632 .34495 L p .627 .674 .875 r F P 0 g s .69385 .38111 m .62584 .38056 L .5922 .32881 L p .526 .627 .894 r F P 0 g s .52632 .34495 m .5922 .32881 L .62584 .38056 L p .627 .674 .875 r F P 0 g s .60704 .42255 m .58313 .34486 L .61694 .36853 L p .306 .324 .716 r F P 0 g s .5922 .32881 m .66092 .32826 L .69385 .38111 L p .526 .627 .894 r F P 0 g s .66092 .32826 m .5922 .32881 L .55733 .29085 L p .479 .692 .961 r F P 0 g s .65136 .38685 m .6274 .38208 L p .58594 .31693 L .758 .423 .417 r F P 0 g s .5922 .32881 m .52632 .34495 L .49024 .30801 L p .62 .753 .941 r F P 0 g s .49024 .30801 m .55733 .29085 L .5922 .32881 L p .62 .753 .941 r F P 0 g s .6274 .38208 m .61694 .36853 L .58594 .31693 L .758 .423 .417 r F .59025 .33189 m .58594 .31693 L p .61694 .36853 L F P 0 g s .55733 .29085 m .62716 .28945 L .66092 .32826 L p .479 .692 .961 r F P 0 g s .55733 .29085 m .62716 .28945 L .60391 .27345 L p .369 .742 .989 r F P 0 g s .7042 .3378 m .66092 .32826 L .62716 .28945 L p .296 .591 .945 r F P 0 g s .52049 .26717 m .55733 .29085 L p .60391 .27345 L .369 .742 .989 r F P 0 g s .62716 .28945 m .65627 .29551 L .7042 .3378 L p .296 .591 .945 r F P 0 g s .65627 .29551 m .60391 .27345 L .62716 .28945 L closepath p .112 .579 .915 r F P 0 g s .56227 .27579 m .6528 .2947 L p .65613 .33132 L .692 .233 .158 r F P 0 g s .55457 .28599 m .56227 .27579 L p .65613 .33132 L .692 .233 .158 r F P 0 g s .65613 .33132 m .58594 .31693 L .55457 .28599 L p .692 .233 .158 r F P 0 g s .58594 .31693 m .65613 .33132 L .65136 .38685 L p .758 .423 .417 r F P 0 g s .60489 .28723 m .62972 .37747 L .61694 .36853 L p .339 .322 .694 r F P 0 g s .61694 .36853 m .58313 .34486 L p .58873 .33001 L .339 .322 .694 r F P 0 g s .57764 .31622 m .58594 .31693 L .59025 .33189 L p .71 .394 .442 r F P 0 g s .58313 .34486 m .57462 .3137 L p .58878 .32988 L .339 .322 .694 r F P 0 g s .55457 .28599 m .58594 .31693 L .57816 .31626 L p .662 .254 .261 r F P 0 g s .57816 .31626 m .57764 .31622 L p .57708 .31547 L .662 .254 .261 r F P 0 g s .57816 .31626 m .57708 .31547 L .55457 .28599 L .662 .254 .261 r F .58313 .34486 m .53887 .32415 L p .54769 .29495 L .41 .369 .702 r F P 0 g s .42466 .34049 m .49024 .30801 L .52632 .34495 L p .718 .782 .903 r F P 0 g s .49024 .30801 m .42466 .34049 L .38443 .31905 L p .718 .877 .955 r F P 0 g s .55733 .29085 m .49024 .30801 L .45177 .28528 L p .578 .839 .994 r F P 0 g s .38443 .31905 m .45177 .28528 L .49024 .30801 L p .718 .877 .955 r F P 0 g s .39834 .42275 m .46206 .37624 L .49744 .4258 L p .756 .719 .818 r F P 0 g s .46206 .37624 m .39834 .42275 L .35943 .38837 L p .783 .792 .861 r F P 0 g s .52632 .34495 m .46206 .37624 L .42466 .34049 L p .718 .782 .903 r F P 0 g s .35943 .38837 m .42466 .34049 L .46206 .37624 L p .783 .792 .861 r F P 0 g s .33162 .37532 m .35943 .38837 L .42466 .34049 L p .803 .88 .902 r F P 0 g s .42466 .34049 m .38443 .31905 L p .33162 .37532 L .803 .88 .902 r F P 0 g s .43662 .39836 m .41432 .32534 L .45498 .31492 L p .589 .502 .725 r F P 0 g s .56076 .39561 m .49744 .4258 L .46206 .37624 L p .702 .703 .848 r F P 0 g s .46206 .37624 m .52632 .34495 L .56076 .39561 L p .702 .703 .848 r F P 0 g s .45498 .31492 m .47755 .38865 L .43662 .39836 L p .589 .502 .725 r F P 0 g s .47755 .38865 m .45498 .31492 L .49634 .31439 L p .532 .468 .729 r F P 0 g s .45177 .28528 m .52049 .26717 L .55733 .29085 L p .578 .839 .994 r F P 0 g s .42709 .28086 m .45177 .28528 L .52049 .26717 L p .448 .864 .951 r F P 0 g s .52049 .26717 m .505 .26391 L .42709 .28086 L p .448 .864 .951 r F P 0 g s .40968 .28458 m .42709 .28086 L .505 .26391 L p .153 .689 .694 r F P 0 g s .60391 .27345 m .56773 .26585 L .52049 .26717 L p .369 .742 .989 r F P 0 g s .56773 .26585 m .505 .26391 L .52049 .26717 L closepath p .16 .689 .863 r F P 0 g s .505 .26391 m .48063 .26911 L .40968 .28458 L p .153 .689 .694 r F P 0 g s .48063 .26911 m .505 .26391 L p .56227 .27579 L .233 0 0 r F P 0 g s .49634 .31439 m .45498 .31492 L p .4636 .27574 L .532 .447 .705 r F P 0 g s .45177 .28528 m .42709 .28086 L .36722 .31669 L p .663 .948 .957 r F P 0 g s .33969 .32321 m .36722 .31669 L .42709 .28086 L p .548 .929 .835 r F P 0 g s .42709 .28086 m .40968 .28458 L .33969 .32321 L p .548 .929 .835 r F P 0 g s .40968 .28458 m .48063 .26911 L p .46 .27594 L .122 0 0 r F P 0 g s .45654 .27709 m .45074 .27801 L .46 .27594 L .122 0 0 r F .45074 .27801 m .40968 .28458 L .46 .27594 L F .36722 .31669 m .38443 .31905 L .45177 .28528 L p .663 .948 .957 r F P 0 g s .41432 .32534 m .40455 .28836 L p .4224 .28436 L .582 .479 .702 r F P 0 g s .40455 .28836 m .41432 .32534 L p .3873 .29783 L .626 .506 .697 r F P 0 g s .33969 .32321 m .40968 .28458 L p .38654 .29801 L 0 0 0 r F P 0 g s .37873 .30254 m .37376 .30518 L .38654 .29801 L 0 0 0 r F .37376 .30518 m .33969 .32321 L .38654 .29801 L F .31702 .3719 m .33958 .35212 L .33162 .37532 L closepath p .844 .925 .885 r F P 0 g s .38443 .31905 m .33958 .35212 L .33162 .37532 L p .803 .88 .902 r F P 0 g s .27885 .38253 m .31702 .3719 L .33958 .35212 L p .788 .998 .846 r F P 0 g s .33958 .35212 m .36722 .31669 L p .27885 .38253 L .788 .998 .846 r F P 0 g s .36722 .31669 m .33969 .32321 L p .27885 .38253 L .788 .998 .846 r F P 0 g s .33969 .32321 m .29246 .36463 L .27885 .38253 L p .788 .998 .846 r F P 0 g s .33969 .32321 m .29246 .36463 L .3052 .3526 L p .567 .893 .633 r F P 0 g s .3052 .3526 m .3233 .33662 L .33969 .32321 L .567 .893 .633 r F .33309 .32797 m .33377 .32748 L p .3233 .33662 L F P 0 g s .33377 .32748 m .33969 .32321 L p .3233 .33662 L .567 .893 .633 r F P 0 g s .33307 .4139 m .33162 .37532 L .35943 .38837 L closepath p .853 .869 .852 r F P 0 g s .33307 .4139 m .33162 .37532 L p .26271 .45745 L .897 .897 .818 r F P 0 g s .33162 .37532 m .31702 .3719 L p .26271 .45745 L .897 .897 .818 r F P 0 g s .31702 .3719 m .26122 .43829 L .26271 .45745 L p .897 .897 .818 r F P 0 g s .26122 .43829 m .27885 .38253 L .31702 .3719 L closepath p .896 .981 .805 r F P 0 g s .33333 .37535 m .29216 .4152 L p .30163 .35732 L .693 .547 .684 r F P 0 g s .30163 .35732 m .3029 .35584 L .33333 .37535 L .693 .547 .684 r F .31209 .29334 m .3233 .33662 L p .30197 .35524 L F P 0 g s .3233 .33662 m .32258 .33386 L p .33309 .32797 L .662 .528 .69 r F P 0 g s .3052 .3526 m .32555 .33339 L .33309 .32797 L p .567 .893 .633 r F P 0 g s .26122 .43829 m .27885 .38253 L p .22455 .48651 L .883 .96 .625 r F P 0 g s .29246 .36463 m .30485 .35294 L p .27788 .38479 L 0 0 0 r F P 0 g s .30485 .35294 m .3079 .35006 L p .28288 .379 L 0 0 0 r F P 0 g s .27788 .38479 m .30485 .35294 L .28288 .379 L 0 0 0 r F .24642 .46304 m .26271 .45745 L p .24037 .56159 L .968 .873 .688 r F P 0 g s .24642 .46304 m .26122 .43829 L .26271 .45745 L closepath p .954 .92 .736 r F P 0 g s .22455 .48651 m .24642 .46304 L .26122 .43829 L p .883 .96 .625 r F P 0 g s .26815 .39347 m .23718 .44496 L .22455 .48651 L p .883 .96 .625 r F P 0 g s .27885 .38253 m .26815 .39347 L p .22455 .48651 L .883 .96 .625 r F P 0 g s .26815 .39347 m .23718 .44496 L .23973 .44073 L p 0 0 0 r F P 0 g s .29216 .4152 m .24996 .46546 L p .25902 .40866 L .72 .563 .676 r F P 0 g s .25902 .40866 m .25992 .40716 L .29216 .4152 L .72 .563 .676 r F .23973 .44073 m .24253 .43608 L .26815 .39347 L 0 0 0 r F .26185 .40395 m .26308 .40191 L p .24253 .43608 L F P 0 g s .26308 .40191 m .26815 .39347 L p .24253 .43608 L 0 0 0 r F P 0 g s .24037 .56159 m .22388 .51053 L .24642 .46304 L p .968 .873 .688 r F P 0 g s .22388 .51053 m .22455 .48651 L .24642 .46304 L closepath p .963 .937 .631 r F P 0 g s .22455 .48651 m .22388 .51053 L .20808 .57708 L p .897 .822 .352 r F P 0 g s .20808 .57708 m .20877 .54153 L .22455 .48651 L p .897 .822 .352 r F P 0 g s .23718 .44496 m .22455 .48651 L .20877 .54153 L p 0 0 0 r F P 0 g s .22388 .51053 m .24037 .56159 L .22534 .62709 L p .999 .837 .522 r F P 0 g s .22534 .62709 m .20808 .57708 L .22388 .51053 L p .999 .837 .522 r F P 0 g s .22846 .60033 m .21225 .54658 L p .24996 .46546 L .759 .6 .681 r F P 0 g s .21225 .54658 m .21272 .53321 L .24996 .46546 L .759 .6 .681 r F .20808 .57708 m .22534 .62709 L .22853 .68907 L p .927 .674 .189 r F P 0 g s .22853 .68907 m .21097 .63986 L .20808 .57708 L p .927 .674 .189 r F P 0 g s .20877 .54153 m .21063 .59329 L p .21225 .54658 L 0 0 .336 r F P 0 g s .2129 .52797 m .21278 .52836 L p .21225 .54658 L 0 0 .336 r F P 0 g s .21278 .52836 m .20877 .54153 L p .21225 .54658 L 0 0 .336 r F P 0 g s .20877 .54153 m .2129 .52797 L p .23718 .44496 L 0 0 0 r F P 0 g s .20877 .54153 m .20808 .57708 L .21097 .63986 L p 0 0 .085 r F P 0 g s .21097 .63986 m .21137 .62124 L p .20877 .54153 L 0 0 .085 r F P 0 g s .21078 .59744 m .20877 .54153 L p .21137 .62124 L 0 0 .085 r F P 0 g s .21225 .54658 m .22846 .60033 L .21251 .6264 L p .777 .611 .673 r F P 0 g s .21097 .63986 m .21137 .62124 L p .21251 .6264 L 0 0 .459 r F P 0 g s .22534 .62709 m .25961 .66843 L .26347 .7297 L p .973 .672 .383 r F P 0 g s .25961 .66843 m .22534 .62709 L .24037 .56159 L p .96 .756 .585 r F P 0 g s .26347 .7297 m .22853 .68907 L .22534 .62709 L p .973 .672 .383 r F P 0 g s .22853 .68907 m .26347 .7297 L .28649 .78816 L p .877 .462 .032 r F P 0 g s .28649 .78816 m .25124 .74803 L .22853 .68907 L p .877 .462 .032 r F P 0 g s .21097 .63986 m .22853 .68907 L .25124 .74803 L p 0 0 .273 r F P 0 g s .21918 .65858 m .22846 .60033 L .2282 .68526 L .796 .637 .684 r F .25124 .74803 m .23655 .70775 L .21097 .63986 L 0 0 .273 r F .23655 .70775 m .23493 .70337 L .21097 .63986 L F .23199 .69545 m .25165 .66282 L p .24193 .72225 L .818 .667 .696 r F P 0 g s .22033 .66412 m .21097 .63986 L p .23575 .70555 L 0 0 .273 r F P 0 g s .23107 .78863 m .20658 .73761 L .23199 .69545 L p .818 .667 .696 r F P 0 g s .25124 .74803 m .28649 .78816 L p .27348 .77509 L .604 .127 0 r F P 0 g s .26347 .7297 m .31484 .76285 L .33867 .82085 L p .886 .482 .25 r F P 0 g s .31484 .76285 m .26347 .7297 L .25961 .66843 L p .908 .609 .468 r F P 0 g s .33867 .82085 m .28649 .78816 L .26347 .7297 L p .886 .482 .25 r F P 0 g s .28142 .78442 m .27699 .79195 L p .26652 .76692 L .842 .703 .709 r F P 0 g s .27699 .79195 m .25622 .82733 L p .26592 .77047 L .842 .703 .709 r F P 0 g s .26592 .77047 m .26652 .76692 L .27699 .79195 L .842 .703 .709 r F .28174 .85365 m .25622 .82733 L .28142 .78442 L p .87 .745 .722 r F P 0 g s .28174 .85365 m .28142 .78442 L .29206 .79677 L .87 .745 .722 r F .30432 .81481 m .30563 .81254 L p .30576 .81661 L .901 .795 .734 r F P 0 g s .40603 .81392 m .38236 .84239 L .40413 .80401 L p .869 .95 .595 r F P 0 g s .38236 .84239 m .40603 .81392 L .36741 .89191 L p .928 .948 .611 r F P 0 g s .41809 .78326 m .41861 .78016 L p .4365 .75629 L .753 .48 .518 r F P 0 g s .41861 .78016 m .42512 .74181 L p .43646 .75623 L .753 .48 .518 r F P 0 g s .4365 .75629 m .41861 .78016 L .43646 .75623 L .753 .48 .518 r F .50013 .66005 m .46482 .71325 L p .47496 .69955 L 0 0 0 r F P 0 g s .47496 .69955 m .47585 .69835 L .47809 .69482 L 0 0 0 r F .47496 .69955 m .47809 .69482 L .50013 .66005 L F .48478 .68469 m .51262 .68661 L .5067 .65614 L p .727 .549 .65 r F P 0 g s .53501 .61672 m .50013 .66005 L p .50872 .65356 L 0 0 0 r F P 0 g s .5067 .65614 m .48719 .68105 L .48478 .68469 L .727 .549 .65 r F .51262 .68661 m .5067 .65614 L p .51956 .64017 L .689 .524 .658 r F P 0 g s .50872 .65356 m .50886 .65346 L .52605 .63145 L 0 0 0 r F .51262 .68661 m .51956 .64017 L .57451 .60946 L .689 .524 .658 r F .52441 .63414 m .54669 .61182 L .57451 .60946 L F .56977 .58279 m .53501 .61672 L p .54139 .61538 L 0 0 0 r F P 0 g s .54139 .61538 m .54339 .61496 L .54842 .609 L 0 0 0 r F .54339 .61496 m .5436 .61492 L .5442 .61418 L F .54339 .61496 m .5442 .61418 L .54842 .609 L F .54139 .61538 m .54842 .609 L .56977 .58279 L F .56107 .59742 m .56977 .58279 L p .5436 .61492 L F P 0 g s .56491 .57635 m .52374 .61217 L .54761 .61089 L p .693 .558 .698 r F P 0 g s .54761 .61089 m .57451 .60946 L .56943 .59194 L p .693 .558 .698 r F P 0 g s .55553 .61047 m .57451 .60946 L p .55458 .61115 L .689 .524 .658 r F P 0 g s .54206 .61221 m .55553 .61047 L .55458 .61115 L .689 .524 .658 r F .54347 .61111 m .55553 .61047 L p .54206 .61221 L F P 0 g s .57451 .60946 m .56943 .59194 L p .59503 .57476 L .651 .534 .708 r F P 0 g s .55166 .61322 m .58759 .58771 L p .57854 .58521 L .107 0 0 r F P 0 g s .57721 .58485 m .5736 .58886 L .57854 .58521 L .107 0 0 r F .5736 .58886 m .55166 .61322 L .57854 .58521 L F .56977 .58279 m .56107 .59742 L p .57721 .58485 L F P 0 g s .56943 .59194 m .56032 .59867 L .54761 .61089 L .693 .558 .698 r F .56107 .59742 m .56032 .59867 L p .57721 .58485 L .107 0 0 r F P 0 g s .56032 .59867 m .55166 .61322 L p .5736 .58886 L .107 0 0 r F P 0 g s .56032 .59867 m .5736 .58886 L .57721 .58485 L .107 0 0 r F .56897 .59035 m .56491 .57635 L p .54987 .60639 L .693 .558 .698 r F P 0 g s .55166 .61322 m .56107 .59742 L p .5436 .61492 L 0 0 0 r F P 0 g s .56032 .59867 m .54987 .60639 L .54761 .61089 L .693 .558 .698 r F .56897 .59035 m .54987 .60639 L .56032 .59867 L F .56943 .59194 m .56897 .59035 L p .56032 .59867 L F P 0 g s .56943 .59194 m .56897 .59035 L p .61277 .56286 L .651 .534 .708 r F P 0 g s .56897 .59035 m .56491 .57635 L p .59317 .56838 L .651 .534 .708 r F P 0 g s .56897 .59035 m .59317 .56838 L .61277 .56286 L .651 .534 .708 r F .51956 .64017 m .52441 .63414 L .57451 .60946 L .689 .524 .658 r F .51587 .64817 m .55166 .61322 L p .5436 .61492 L 0 0 0 r F P 0 g s .53501 .61672 m .52441 .63414 L p .5436 .61492 L 0 0 0 r F P 0 g s .52441 .63414 m .51587 .64817 L p .5436 .61492 L 0 0 0 r F P 0 g s .52441 .63414 m .52605 .63145 L p .50886 .65346 L 0 0 0 r F P 0 g s .52605 .63145 m .53501 .61672 L p .50872 .65356 L 0 0 0 r F P 0 g s .52374 .61217 m .54292 .61114 L p .52441 .63414 L .689 .524 .658 r F P 0 g s .51956 .64017 m .51976 .63879 L .52441 .63414 L .689 .524 .658 r F .51976 .63879 m .52374 .61217 L .52441 .63414 L F .52441 .63414 m .54206 .61221 L .54669 .61182 L F .54292 .61114 m .54347 .61111 L p .54206 .61221 L F P 0 g s .51587 .64817 m .52441 .63414 L p .50886 .65346 L 0 0 0 r F P 0 g s .50313 .63774 m .52374 .61217 L p .51956 .64017 L .689 .524 .658 r F P 0 g s .50872 .65356 m .50816 .65433 L .50886 .65346 L 0 0 0 r F .50013 .66005 m .48719 .68105 L p .50872 .65356 L F P 0 g s .47585 .69835 m .47588 .6983 L .4884 .67909 L 0 0 0 r F .51262 .68661 m .51729 .7515 L p .48136 .68993 L .725 .509 .598 r F P 0 g s .48478 .68469 m .51262 .68661 L p .48136 .68993 L .725 .509 .598 r F P 0 g s .48762 .68035 m .4884 .67909 L p .47588 .6983 L 0 0 0 r F P 0 g s .4884 .67909 m .50013 .66005 L p .47585 .69835 L 0 0 0 r F P 0 g s .47394 .70363 m .47467 .70015 L p .47559 .70126 L .725 .509 .598 r F P 0 g s .4434 .74789 m .46482 .71325 L .42874 .77702 L p .693 .844 .419 r F P 0 g s .46482 .71325 m .44834 .74044 L .47467 .70015 L 0 0 0 r F .47585 .69835 m .47467 .70015 L .47588 .6983 L F .46482 .71325 m .47467 .70015 L .47585 .69835 L F .46482 .71325 m .4434 .74789 L .44834 .74044 L p F P 0 g s .46458 .74801 m .44546 .745 L p .45327 .73301 L .757 .542 .605 r F P 0 g s .45442 .73138 m .45327 .73301 L .45438 .73131 L .757 .542 .605 r F .46458 .74801 m .45327 .73301 L .45442 .73138 L F .51729 .7515 m .47467 .70015 L .48136 .68993 L .725 .509 .598 r F .47467 .70015 m .46458 .74801 L p .45438 .73131 L .757 .542 .605 r F P 0 g s .47588 .6983 m .45335 .73277 L .47989 .69288 L 0 0 0 r F .45335 .73277 m .44834 .74044 L .47989 .69288 L F .42512 .74181 m .41976 .67466 L p .45438 .73131 L .757 .542 .605 r F P 0 g s .45327 .73301 m .44834 .74044 L p .44887 .73926 L .766 .924 .559 r F P 0 g s .44834 .74044 m .4434 .74789 L p .44402 .74665 L .766 .924 .559 r F P 0 g s .45327 .73301 m .42512 .74181 L .45438 .73131 L .757 .542 .605 r F .44402 .74665 m .44489 .74492 L .44834 .74044 L .766 .924 .559 r F .44489 .74492 m .44887 .73926 L .44834 .74044 L F .44546 .745 m .44489 .74492 L p .45327 .73301 L .757 .542 .605 r F P 0 g s .44489 .74492 m .42512 .74181 L p .45327 .73301 L .757 .542 .605 r F P 0 g s .45438 .73131 m .41976 .67466 L .47467 .70015 L .757 .542 .605 r F .44489 .74492 m .45864 .71759 L .44887 .73926 L .766 .924 .559 r F .47467 .70015 m .47501 .69856 L p .47795 .69515 L .725 .509 .598 r F P 0 g s .47501 .69856 m .47803 .68423 L p .47795 .69515 L .725 .509 .598 r F P 0 g s .48136 .68993 m .47795 .69515 L .47803 .68423 L .725 .509 .598 r F .47989 .69288 m .48762 .68035 L p .47588 .6983 L 0 0 0 r F P 0 g s .41976 .67466 m .47803 .68423 L .47467 .70015 L p .757 .542 .605 r F P 0 g s .45864 .71759 m .47989 .69288 L .45327 .73301 L p .766 .924 .559 r F P 0 g s .44887 .73926 m .45864 .71759 L .45327 .73301 L .766 .924 .559 r F .51729 .7515 m .46458 .74801 L .47394 .70363 L p .725 .509 .598 r F P 0 g s .51729 .7515 m .47394 .70363 L .47559 .70126 L .725 .509 .598 r F .47803 .68423 m .48478 .68469 L p .48136 .68993 L F P 0 g s .48719 .68105 m .47989 .69288 L p .50872 .65356 L 0 0 0 r F P 0 g s .5067 .65614 m .50313 .63774 L p .51956 .64017 L .689 .524 .658 r F P 0 g s .47989 .69288 m .51587 .64817 L p .50886 .65346 L 0 0 0 r F P 0 g s .50816 .65433 m .47989 .69288 L .50886 .65346 L 0 0 0 r F .50601 .65257 m .50313 .63774 L p .48523 .68356 L .727 .549 .65 r F P 0 g s .48719 .68105 m .48523 .68356 L .48478 .68469 L .727 .549 .65 r F .50601 .65257 m .48523 .68356 L .48719 .68105 L F .5067 .65614 m .50601 .65257 L p .48719 .68105 L F P 0 g s .50313 .63774 m .47803 .68423 L .48478 .68469 L p .727 .549 .65 r F P 0 g s .4434 .74789 m .43748 .75486 L p .44489 .74492 L .766 .924 .559 r F P 0 g s .42874 .77702 m .40603 .81392 L .4434 .74789 L p .693 .844 .419 r F P 0 g s .4434 .74789 m .40603 .81392 L p .41699 .78487 L .869 .95 .595 r F P 0 g s .41699 .78487 m .41809 .78326 L .4434 .74789 L .869 .95 .595 r F .43748 .75486 m .44045 .75136 L p .41809 .78326 L F P 0 g s .44045 .75136 m .4434 .74789 L p .41809 .78326 L .869 .95 .595 r F P 0 g s .37596 .7292 m .42512 .74181 L .41809 .78326 L p .791 .517 .522 r F P 0 g s .4122 .79167 m .37596 .7292 L .41809 .78326 L .791 .517 .522 r F .42512 .74181 m .44433 .74483 L p .4365 .75629 L .753 .48 .518 r F P 0 g s .42099 .77427 m .43748 .75486 L p .41699 .78487 L .869 .95 .595 r F P 0 g s .40413 .80401 m .38236 .84239 L p .3908 .81444 L .947 .959 .696 r F P 0 g s .3908 .81444 m .39094 .81399 L .39239 .81289 L .947 .959 .696 r F .3908 .81444 m .39239 .81289 L .40413 .80401 L F .38213 .78935 m .40915 .79602 L p .40742 .7982 L .782 .446 .418 r F P 0 g s .39239 .81289 m .38213 .78935 L p .40742 .7982 L .782 .446 .418 r F P 0 g s .38213 .78935 m .37596 .7292 L p .4122 .79167 L .791 .517 .522 r F P 0 g s .40915 .79602 m .38213 .78935 L p .4122 .79167 L .791 .517 .522 r F P 0 g s .39775 .79144 m .42099 .77427 L .40742 .7982 L p .947 .959 .696 r F P 0 g s .40742 .7982 m .40413 .80401 L p .40325 .80228 L .947 .959 .696 r F P 0 g s .40325 .80228 m .39775 .79144 L .40742 .7982 L .947 .959 .696 r F .40513 .80224 m .4066 .79965 L p .40921 .79593 L .869 .95 .595 r F P 0 g s .41087 .79384 m .40513 .80224 L .40921 .79593 L .869 .95 .595 r F .4066 .79965 m .42099 .77427 L p .41703 .78477 L F P 0 g s .41699 .78487 m .4066 .79965 L .41703 .78477 L .869 .95 .595 r F .38213 .78935 m .39239 .81289 L p .38369 .81948 L .831 .464 .36 r F P 0 g s .39094 .81399 m .39775 .79144 L .40413 .80401 L .947 .959 .696 r F .40413 .80401 m .40513 .80224 L p .40518 .80284 L .869 .95 .595 r F P 0 g s .40603 .81392 m .40413 .80401 L .40518 .80284 L .869 .95 .595 r F .40603 .81392 m .40513 .80224 L .41699 .78487 L F .39361 .81569 m .40742 .7982 L .41565 .79762 L .782 .446 .418 r F .40915 .79602 m .40956 .79612 L p .40742 .7982 L F P 0 g s .40956 .79612 m .41565 .79762 L p .40742 .7982 L .782 .446 .418 r F P 0 g s .39361 .81569 m .39239 .81289 L p .40742 .7982 L .782 .446 .418 r F P 0 g s .41465 .80504 m .39156 .85224 L .42874 .77702 L p 0 0 0 r F P 0 g s .40603 .81392 m .42874 .77702 L .39156 .85224 L p .813 .897 .482 r F P 0 g s .39156 .85224 m .36741 .89191 L .40603 .81392 L p .813 .897 .482 r F P 0 g s .41565 .79762 m .39873 .82744 L .39361 .81569 L p .782 .446 .418 r F P 0 g s .41699 .78487 m .41087 .79384 L .40921 .79593 L .869 .95 .595 r F .41565 .79762 m .40915 .79602 L p .4122 .79167 L .791 .517 .522 r F P 0 g s .41809 .78326 m .41565 .79762 L p .4122 .79167 L .791 .517 .522 r F P 0 g s .46458 .74801 m .47618 .80678 L p .4365 .75629 L .753 .48 .518 r F P 0 g s .44433 .74483 m .46458 .74801 L p .4365 .75629 L .753 .48 .518 r F P 0 g s .42099 .77427 m .45864 .71759 L p .44489 .74492 L .766 .924 .559 r F P 0 g s .43748 .75486 m .42099 .77427 L p .44489 .74492 L .766 .924 .559 r F P 0 g s .38036 .822 m .37755 .82694 L p .36618 .82874 L .955 .913 .735 r F P 0 g s .37755 .82694 m .3579 .86145 L p .36598 .82954 L .955 .913 .735 r F P 0 g s .36598 .82954 m .36618 .82874 L .37755 .82694 L .955 .913 .735 r F .38236 .84239 m .3579 .86145 L .38036 .822 L p .947 .959 .696 r F P 0 g s .38236 .84239 m .38036 .822 L .39094 .81399 L .947 .959 .696 r F .33867 .82085 m .36316 .83018 L p .35462 .8321 L .782 .323 .154 r F P 0 g s .33283 .87018 m .34109 .83265 L .34789 .83238 L .932 .853 .741 r F .35462 .8321 m .35324 .83451 L p .34789 .83238 L F P 0 g s .35324 .83451 m .33283 .87018 L p .34789 .83238 L .932 .853 .741 r F P 0 g s .3579 .86145 m .33283 .87018 L .35324 .83451 L p .955 .913 .735 r F P 0 g s .31484 .76285 m .38213 .78935 L p .38374 .82039 L .831 .464 .36 r F P 0 g s .38467 .83837 m .37284 .82558 L .38374 .82039 L .831 .464 .36 r F .37284 .82558 m .31484 .76285 L .38374 .82039 L F .33867 .82085 m .31484 .76285 L p .37284 .82558 L F P 0 g s .37121 .82635 m .33867 .82085 L .37284 .82558 L .831 .464 .36 r F .36406 .83711 m .35378 .83464 L .36618 .82874 L .955 .913 .735 r F .36741 .8318 m .33867 .82085 L p .37399 .82682 L .831 .464 .36 r F P 0 g s .35324 .83451 m .37382 .79854 L p .36618 .82874 L .955 .913 .735 r F P 0 g s .35378 .83464 m .35324 .83451 L .36618 .82874 L .955 .913 .735 r F .3579 .86145 m .35324 .83451 L .36406 .83711 L F .31594 .82431 m .30563 .81254 L .3171 .81843 L .901 .795 .734 r F .30737 .86779 m .30563 .81254 L .31594 .82431 L F .28649 .78816 m .33867 .82085 L p .32247 .82119 L .773 .264 0 r F P 0 g s .33153 .82584 m .30737 .86779 L p .3171 .81843 L .901 .795 .734 r F P 0 g s .33867 .82085 m .34789 .83238 L p .32001 .82124 L .773 .264 0 r F P 0 g s .32474 .77966 m .34941 .79481 L .33153 .82584 L p .901 .795 .734 r F P 0 g s .31723 .81849 m .28649 .78816 L .32247 .82119 L .773 .264 0 r F .30902 .81685 m .30563 .81254 L p .32001 .82124 L F P 0 g s .30563 .81254 m .28649 .78816 L p .31982 .82105 L .773 .264 0 r F P 0 g s .30563 .81254 m .31982 .82105 L .32001 .82124 L .773 .264 0 r F .30005 .75268 m .32474 .77966 L .30563 .81254 L p .87 .745 .722 r F P 0 g s .30563 .81254 m .28174 .85365 L p .29081 .80364 L .87 .745 .722 r F P 0 g s .28649 .78816 m .30563 .81254 L p .27348 .77509 L .604 .127 0 r F P 0 g s .29081 .80364 m .29206 .79677 L .30563 .81254 L .87 .745 .722 r F .30563 .81254 m .30902 .81685 L p .28142 .78442 L .604 .127 0 r F P 0 g s .27348 .77509 m .30563 .81254 L .28142 .78442 L .604 .127 0 r F .29206 .79677 m .30005 .75268 L .30563 .81254 L .87 .745 .722 r F .3171 .81843 m .32474 .77966 L .33153 .82584 L .901 .795 .734 r F .32001 .82124 m .31723 .81849 L .32247 .82119 L .773 .264 0 r F .31258 .82139 m .30902 .81685 L p .32001 .82124 L F P 0 g s .33283 .87018 m .30737 .86779 L .33153 .82584 L p .932 .853 .741 r F P 0 g s .34789 .83238 m .33867 .82085 L p .35462 .8321 L .782 .323 .154 r F P 0 g s .33153 .82584 m .34941 .79481 L p .34169 .8299 L .932 .853 .741 r F P 0 g s .33283 .87018 m .33153 .82584 L .34169 .8299 L .932 .853 .741 r F .30563 .81254 m .32474 .77966 L p .3171 .81843 L .901 .795 .734 r F P 0 g s .31258 .82139 m .32001 .82124 L .33493 .83011 L .773 .264 0 r F .3562 .84277 m .32601 .82797 L p .33493 .83011 L F P 0 g s .32601 .82797 m .31258 .82139 L p .33493 .83011 L .773 .264 0 r F P 0 g s .34109 .83265 m .34941 .79481 L .35462 .8321 L .932 .853 .741 r F .34789 .83238 m .3562 .84277 L p .32001 .82124 L .773 .264 0 r F P 0 g s .34873 .83343 m .34789 .83238 L p .35462 .8321 L .782 .323 .154 r F P 0 g s .34941 .79481 m .37382 .79854 L .35462 .8321 L p .932 .853 .741 r F P 0 g s .38467 .83837 m .3562 .84277 L .34873 .83343 L p .782 .323 .154 r F P 0 g s .36316 .83018 m .38467 .83837 L p .34873 .83343 L .782 .323 .154 r F P 0 g s .37382 .79854 m .39775 .79144 L .38036 .822 L p .955 .913 .735 r F P 0 g s .36618 .82874 m .37382 .79854 L .38036 .822 L .955 .913 .735 r F .37399 .82682 m .37121 .82635 L .37284 .82558 L .831 .464 .36 r F .38467 .83837 m .36741 .8318 L p .37399 .82682 L F P 0 g s .38036 .822 m .39775 .79144 L p .39094 .81399 L .947 .959 .696 r F P 0 g s .38404 .82632 m .38369 .81948 L .39361 .81569 L .831 .464 .36 r F .39239 .81289 m .39361 .81569 L p .38369 .81948 L F P 0 g s .39873 .82744 m .38467 .83837 L p .38404 .82632 L .831 .464 .36 r F P 0 g s .39361 .81569 m .39873 .82744 L p .38404 .82632 L .831 .464 .36 r F P 0 g s .47618 .80678 m .41565 .79762 L .41809 .78326 L p .753 .48 .518 r F P 0 g s .47618 .80678 m .41809 .78326 L .4365 .75629 L .753 .48 .518 r F .26856 .77016 m .27348 .77509 L .29053 .79528 L .604 .127 0 r F .31258 .82139 m .26963 .7714 L p .29053 .79528 L F P 0 g s .26963 .7714 m .26856 .77016 L p .29053 .79528 L .604 .127 0 r F P 0 g s .30902 .81685 m .31258 .82139 L p .27348 .77509 L .604 .127 0 r F P 0 g s .27034 .7714 m .25124 .74803 L .27348 .77509 L .604 .127 0 r F .27112 .77246 m .26849 .76923 L .27278 .77439 L F .26849 .76923 m .25124 .74803 L .27034 .7714 L F .26849 .76923 m .27034 .7714 L .27278 .77439 L F .25622 .82733 m .23107 .78863 L .25325 .75132 L p .842 .703 .709 r F P 0 g s .25622 .82733 m .25325 .75132 L .26652 .76692 L .842 .703 .709 r F .26118 .76073 m .25124 .74803 L p .27228 .77389 L .604 .127 0 r F P 0 g s .26034 .75966 m .25124 .74803 L .24525 .7312 L p 0 .041 .609 r F P 0 g s .24193 .72225 m .25165 .66282 L .25282 .74524 L .818 .667 .696 r F .24193 .72225 m .25282 .74524 L .24562 .73188 L F .26034 .75966 m .24525 .7312 L .25475 .7488 L 0 .041 .609 r F .24525 .7312 m .25291 .75092 L .25229 .75019 L .818 .667 .696 r F .24193 .72225 m .24562 .73188 L .24525 .7312 L F .24562 .73188 m .25291 .75092 L .24525 .7312 L F .25325 .75132 m .2756 .71372 L p .26652 .76692 L .842 .703 .709 r F P 0 g s .25165 .66282 m .2756 .71372 L .25475 .7488 L p .818 .667 .696 r F P 0 g s .25475 .7488 m .25292 .75188 L p .25282 .74524 L .818 .667 .696 r F P 0 g s .25282 .74524 m .25165 .66282 L .25475 .7488 L .818 .667 .696 r F .26652 .76692 m .2666 .76646 L .26738 .76793 L .842 .703 .709 r F .2666 .76646 m .2756 .71372 L .26738 .76793 L F .26738 .76793 m .2756 .71372 L .28142 .78442 L F .26856 .77016 m .26118 .76073 L p .27228 .77389 L .604 .127 0 r F P 0 g s .23981 .71592 m .26856 .77016 L .26118 .76073 L p 0 .041 .609 r F P 0 g s .26118 .76073 m .26034 .75966 L p .25861 .75596 L 0 .041 .609 r F P 0 g s .26118 .76073 m .25861 .75596 L .23981 .71592 L 0 .041 .609 r F .24431 .72857 m .23981 .71592 L p .25861 .75596 L F P 0 g s .26034 .75966 m .25475 .7488 L .25861 .75596 L 0 .041 .609 r F .25475 .7488 m .24431 .72857 L .25861 .75596 L F .24525 .7312 m .24431 .72857 L p .25475 .7488 L F P 0 g s .24562 .73188 m .25282 .74524 L .25291 .75092 L .818 .667 .696 r F .2756 .71372 m .30005 .75268 L .28142 .78442 L p .842 .703 .709 r F P 0 g s .28142 .78442 m .30005 .75268 L p .29206 .79677 L .87 .745 .722 r F P 0 g s .36741 .89191 m .34234 .92295 L .38236 .84239 L p .928 .948 .611 r F P 0 g s .3579 .86145 m .38236 .84239 L .34234 .92295 L p .968 .934 .681 r F P 0 g s .39506 .87345 m .3562 .84277 L .31258 .82139 L p .582 .015 0 r F P 0 g s .31258 .82139 m .33847 .84201 L .39506 .87345 L p .582 .015 0 r F P 0 g s .33847 .84201 m .31258 .82139 L .26963 .7714 L p 0 .204 .717 r F P 0 g s .26963 .7714 m .26856 .77016 L p .26898 .77059 L 0 .204 .717 r F P 0 g s .33847 .84201 m .26963 .7714 L .26898 .77059 L 0 .204 .717 r F .30737 .86779 m .28174 .85365 L .30432 .81481 L p .901 .795 .734 r F P 0 g s .30737 .86779 m .30432 .81481 L .30576 .81661 L .901 .795 .734 r F .27278 .77439 m .27034 .7714 L .27348 .77509 L .604 .127 0 r F .27228 .77389 m .27112 .77246 L .27278 .77439 L F .25229 .75019 m .25291 .75092 L .25292 .75188 L .818 .667 .696 r F .21918 .65858 m .2282 .68526 L .22033 .66412 L .796 .637 .684 r F .22846 .60033 m .25165 .66282 L .23199 .69545 L p F P 0 g s .2282 .68526 m .22846 .60033 L .23199 .69545 L .796 .637 .684 r F .23981 .71592 m .22612 .67915 L p .23575 .70555 L 0 0 .273 r F P 0 g s .25124 .74803 m .24419 .72822 L p .23575 .70555 L 0 0 .273 r F P 0 g s .24419 .72822 m .23981 .71592 L p .23575 .70555 L 0 0 .273 r F P 0 g s .23199 .69545 m .22814 .70183 L p .2282 .68526 L .796 .637 .684 r F P 0 g s .23107 .78863 m .23199 .69545 L .24193 .72225 L .818 .667 .696 r F .22612 .67915 m .22144 .66702 L p .23575 .70555 L 0 0 .273 r F P 0 g s .22144 .66702 m .22033 .66412 L p .23199 .69545 L 0 0 .273 r F P 0 g s .23575 .70555 m .22144 .66702 L .23199 .69545 L 0 0 .273 r F .23655 .70775 m .23575 .70555 L .23493 .70337 L F .25292 .75188 m .23107 .78863 L p .24193 .72225 L .818 .667 .696 r F P 0 g s .22033 .66412 m .2282 .68526 L .22814 .70183 L .796 .637 .684 r F .22033 .66412 m .21097 .63986 L p .21251 .6264 L 0 0 .459 r F P 0 g s .20658 .73761 m .18301 .67459 L .21251 .6264 L p .796 .637 .684 r F P 0 g s .21251 .6264 m .22846 .60033 L p .21918 .65858 L .796 .637 .684 r F P 0 g s .20658 .73761 m .21251 .6264 L .21918 .65858 L .796 .637 .684 r F .21024 .6161 m .21225 .54658 L .21251 .6264 L .777 .611 .673 r F .22144 .66702 m .21251 .6264 L .21147 .61667 L 0 0 .459 r F .21137 .62124 m .21138 .62095 L p .21251 .6264 L F P 0 g s .21138 .62095 m .21147 .61667 L p .21251 .6264 L 0 0 .459 r F P 0 g s .22144 .66702 m .22033 .66412 L p .21251 .6264 L 0 0 .459 r F P 0 g s .22814 .70183 m .20658 .73761 L p .21918 .65858 L .796 .637 .684 r F P 0 g s .21251 .6264 m .20982 .6308 L p .21024 .6161 L .777 .611 .673 r F P 0 g s .21147 .61667 m .22612 .67915 L .22144 .66702 L p 0 0 .459 r F P 0 g s .21137 .62124 m .21147 .61667 L .21078 .59744 L p 0 0 .085 r F P 0 g s .20629 .5268 m .20927 .53669 L p .18301 .67459 L .777 .611 .673 r F P 0 g s .20927 .53669 m .21225 .54658 L p .20979 .55739 L .777 .611 .673 r F P 0 g s .18301 .67459 m .20927 .53669 L .20979 .55739 L .777 .611 .673 r F .21811 .5102 m .24996 .46546 L p .21272 .53321 L .759 .6 .681 r F P 0 g s .20981 .53849 m .2129 .52797 L .21272 .53321 L .759 .6 .681 r F .2129 .52797 m .21811 .5102 L .21272 .53321 L F .21063 .59329 m .21147 .61667 L p .2129 .52797 L 0 0 .336 r F P 0 g s .20982 .6308 m .18301 .67459 L p .21225 .54658 L .777 .611 .673 r F P 0 g s .2171 .51419 m .2129 .52797 L p .21147 .61667 L 0 0 .336 r F P 0 g s .21225 .54658 m .20981 .53849 L p .21272 .53321 L .759 .6 .681 r F P 0 g s .2129 .52797 m .21449 .52253 L .23718 .44496 L 0 0 0 r F .23218 .46222 m .23718 .44496 L p .21302 .52758 L F P 0 g s .20981 .53849 m .20629 .5268 L .21811 .5102 L p .759 .6 .681 r F P 0 g s .2129 .52797 m .21302 .52758 L p .21449 .52253 L 0 0 0 r F P 0 g s .24996 .46546 m .21811 .5102 L p .2277 .47748 L .742 .577 .67 r F P 0 g s .24253 .43608 m .24996 .46546 L p .22654 .47811 L .742 .577 .67 r F P 0 g s .2399 .44045 m .23718 .44496 L .23218 .46222 L p 0 0 .092 r F P 0 g s .21279 .48553 m .2399 .44045 L .22654 .47811 L .742 .577 .67 r F .2399 .44045 m .24253 .43608 L .22654 .47811 L F .229 .38263 m .27109 .33295 L p .25928 .407 L .72 .563 .676 r F P 0 g s .24996 .46546 m .24073 .42901 L p .25928 .407 L .72 .563 .676 r F P 0 g s .24073 .42901 m .229 .38263 L p .25928 .407 L .72 .563 .676 r F P 0 g s .27712 .38583 m .26143 .40753 L p .25928 .407 L .72 .563 .676 r F P 0 g s .27712 .38583 m .28288 .379 L .283 .37946 L .72 .563 .676 r F .28388 .38287 m .29216 .4152 L p .26281 .40788 L F P 0 g s .3233 .33662 m .33333 .37535 L p .3029 .35584 L .693 .547 .684 r F P 0 g s .30197 .35524 m .3079 .35006 L .3029 .35584 L .693 .547 .684 r F .3079 .35006 m .3233 .33662 L .3029 .35584 L F .26815 .39347 m .29246 .36463 L .27885 .38253 L closepath p .644 .891 .554 r F P 0 g s .27109 .33295 m .31209 .29334 L p .30163 .35732 L .693 .547 .684 r F P 0 g s .29216 .4152 m .28288 .379 L p .30163 .35732 L .693 .547 .684 r F P 0 g s .26815 .39347 m .29246 .36463 L p .27788 .38479 L 0 0 0 r F P 0 g s .28288 .379 m .27109 .33295 L p .30163 .35732 L .693 .547 .684 r F P 0 g s .25128 .42156 m .26308 .40191 L p .27788 .38479 L 0 0 0 r F P 0 g s .26308 .40191 m .26815 .39347 L p .27788 .38479 L 0 0 0 r F P 0 g s .25128 .42156 m .27712 .38583 L .32555 .33339 L 0 0 0 r F .27712 .38583 m .27788 .38479 L .27925 .38331 L F .27712 .38583 m .27925 .38331 L .32555 .33339 L F .25128 .42156 m .2399 .44045 L p .2171 .51419 L 0 0 .092 r F P 0 g s .23218 .46222 m .2171 .51419 L p .2399 .44045 L 0 0 .092 r F P 0 g s .21302 .52758 m .2171 .51419 L .23218 .46222 L p 0 0 0 r F P 0 g s .20629 .5268 m .21279 .48553 L .2277 .47748 L .742 .577 .67 r F .21811 .5102 m .20629 .5268 L p .2277 .47748 L F P 0 g s .229 .38263 m .24253 .43608 L p .21279 .48553 L .742 .577 .67 r F P 0 g s .23973 .44073 m .25128 .42156 L .26185 .40395 L p 0 0 0 r F P 0 g s .25902 .40866 m .25928 .407 L .25992 .40716 L .72 .563 .676 r F .3079 .35006 m .32555 .33339 L p .27788 .38479 L 0 0 0 r F P 0 g s .27109 .33295 m .28288 .379 L p .25928 .407 L .72 .563 .676 r F P 0 g s .30163 .35732 m .30197 .35524 L .3029 .35584 L .693 .547 .684 r F .33333 .37535 m .3233 .33662 L p .34229 .32281 L .662 .528 .69 r F P 0 g s .3233 .33662 m .33309 .32797 L .34229 .32281 L .662 .528 .69 r F .33512 .32651 m .33969 .32321 L p .37376 .30518 L 0 0 0 r F P 0 g s .36469 .31026 m .37376 .30518 L .37873 .30254 L 0 0 0 r F .33512 .32651 m .37376 .30518 L .36469 .31026 L F .33958 .35212 m .36722 .31669 L .38443 .31905 L closepath p .793 .963 .917 r F P 0 g s .37391 .34547 m .33333 .37535 L p .34229 .32281 L .662 .528 .69 r F P 0 g s .36469 .31026 m .37391 .34547 L p .34229 .32281 L .662 .528 .69 r F P 0 g s .37391 .34547 m .36469 .31026 L p .38202 .30073 L .626 .506 .697 r F P 0 g s .41432 .32534 m .37391 .34547 L p .38202 .30073 L .626 .506 .697 r F P 0 g s .38202 .30073 m .3873 .29783 L .41432 .32534 L .626 .506 .697 r F .38979 .29919 m .32555 .33339 L p .37873 .30254 L 0 0 0 r F P 0 g s .40968 .28458 m .40455 .28836 L p .38616 .29823 L 0 0 0 r F P 0 g s .40455 .28836 m .40706 .28651 L p .42614 .28288 L .122 0 0 r F P 0 g s .40706 .28651 m .40968 .28458 L p .45074 .27801 L .122 0 0 r F P 0 g s .44546 .2792 m .45074 .27801 L .45654 .27709 L .122 0 0 r F .40706 .28651 m .45074 .27801 L .44546 .2792 L F .45498 .31492 m .41432 .32534 L p .4224 .28436 L .582 .479 .702 r F P 0 g s .44546 .2792 m .45498 .31492 L p .4224 .28436 L .582 .479 .702 r F P 0 g s .48063 .26911 m .47491 .27359 L p .45654 .27709 L .122 0 0 r F P 0 g s .43279 .23165 m .47366 .23 L p .4636 .27574 L .532 .447 .705 r F P 0 g s .45498 .31492 m .44546 .2792 L p .4636 .27574 L .532 .447 .705 r F P 0 g s .44546 .2792 m .43279 .23165 L p .4636 .27574 L .532 .447 .705 r F P 0 g s .4636 .27574 m .47491 .27359 L .49634 .31439 L .532 .447 .705 r F .50566 .2763 m .48563 .27453 L .48063 .26911 L .378 0 0 r F .47491 .27359 m .4755 .27313 L p .48563 .27453 L F P 0 g s .4755 .27313 m .48063 .26911 L p .48563 .27453 L .378 0 0 r F P 0 g s .48063 .26911 m .52942 .27477 L .50566 .2763 L p .378 0 0 r F P 0 g s .49634 .31439 m .48563 .27453 L p .50067 .27662 L .475 .411 .705 r F P 0 g s .50067 .27662 m .52942 .27477 L p .51623 .28203 L .558 .147 .218 r F P 0 g s .50547 .27829 m .50067 .27662 L .50572 .27732 L .475 .411 .705 r F .49634 .31439 m .50067 .27662 L .50547 .27829 L F .48563 .27453 m .49634 .31439 L p .47491 .27359 L .532 .447 .705 r F P 0 g s .44856 .31925 m .46839 .2787 L .50067 .27662 L p .558 .147 .218 r F P 0 g s .505 .26391 m .56773 .26585 L p .56227 .27579 L .233 0 0 r F P 0 g s .56227 .27579 m .52942 .27477 L .48063 .26911 L p .233 0 0 r F P 0 g s .53887 .32415 m .49634 .31439 L p .50547 .27829 L .475 .411 .705 r F P 0 g s .52863 .28634 m .52942 .27477 L .54041 .29043 L .558 .147 .218 r F .51623 .28203 m .51752 .28132 L .52863 .28634 L F .51752 .28132 m .52942 .27477 L .52863 .28634 L F .52942 .27477 m .55457 .28599 L p .54041 .29043 L F P 0 g s .55457 .28599 m .55037 .29616 L p .53881 .29094 L .558 .147 .218 r F P 0 g s .55457 .28599 m .52942 .27477 L .56227 .27579 L closepath p .556 .077 .074 r F P 0 g s .5156 .23826 m .55914 .25703 L p .54769 .29495 L .41 .369 .702 r F P 0 g s .53887 .32415 m .52863 .28634 L p .54769 .29495 L .41 .369 .702 r F P 0 g s .52863 .28634 m .53887 .32415 L p .50547 .27829 L .475 .411 .705 r F P 0 g s .44856 .31925 m .51623 .28203 L .54041 .29043 L .558 .147 .218 r F .52863 .28634 m .5156 .23826 L p .54769 .29495 L .41 .369 .702 r F P 0 g s .5156 .23826 m .52863 .28634 L p .50547 .27829 L .475 .411 .705 r F P 0 g s .44856 .31925 m .50067 .27662 L .51623 .28203 L .558 .147 .218 r F .50566 .2763 m .46839 .2787 L .47491 .27359 L p .378 0 0 r F P 0 g s .47366 .23 m .5156 .23826 L p .50572 .27732 L .475 .411 .705 r F P 0 g s .48563 .27453 m .47366 .23 L p .50572 .27732 L .475 .411 .705 r F P 0 g s .48486 .27169 m .48563 .27453 L p .47491 .27359 L .532 .447 .705 r F P 0 g s .46839 .2787 m .38979 .29919 L p .45654 .27709 L .122 0 0 r F P 0 g s .47491 .27359 m .46839 .2787 L p .45654 .27709 L .122 0 0 r F P 0 g s .40455 .28836 m .42614 .28288 L .45654 .27709 L .122 0 0 r F .43279 .23165 m .44546 .2792 L p .4224 .28436 L .582 .479 .702 r F P 0 g s .40455 .28836 m .39252 .24283 L p .4195 .28033 L .582 .479 .702 r F P 0 g s .40455 .28836 m .4195 .28033 L .4224 .28436 L .582 .479 .702 r F .37873 .30254 m .38616 .29823 L .40455 .28836 L 0 0 0 r F .40455 .28836 m .38979 .29919 L p .37873 .30254 L F P 0 g s .38202 .30073 m .38329 .29375 L .3873 .29783 L .626 .506 .697 r F .35243 .26338 m .39252 .24283 L p .38202 .30073 L F P 0 g s .36469 .31026 m .35243 .26338 L p .38202 .30073 L .626 .506 .697 r F P 0 g s .32555 .33339 m .33309 .32797 L p .37873 .30254 L 0 0 0 r F P 0 g s .33309 .32797 m .33512 .32651 L p .36469 .31026 L 0 0 0 r F P 0 g s .33309 .32797 m .36469 .31026 L .37873 .30254 L 0 0 0 r F .35243 .26338 m .36469 .31026 L p .34229 .32281 L .662 .528 .69 r F P 0 g s .31209 .29334 m .35243 .26338 L p .34229 .32281 L .662 .528 .69 r F P 0 g s .32258 .33386 m .31209 .29334 L p .34229 .32281 L .662 .528 .69 r F P 0 g s .38329 .29375 m .40455 .28836 L .3873 .29783 L .626 .506 .697 r F .38979 .29919 m .40455 .28836 L p .45654 .27709 L .122 0 0 r F P 0 g s .39252 .24283 m .40455 .28836 L p .38329 .29375 L .626 .506 .697 r F P 0 g s .39252 .24283 m .43279 .23165 L p .4224 .28436 L .582 .479 .702 r F P 0 g s .47366 .23 m .48486 .27169 L p .4636 .27574 L .532 .447 .705 r F P 0 g s .49634 .31439 m .51925 .38911 L .47755 .38865 L p .532 .468 .729 r F P 0 g s .51925 .38911 m .49634 .31439 L .53887 .32415 L p .466 .427 .73 r F P 0 g s .54329 .31328 m .44856 .31925 L p .53881 .29094 L .558 .147 .218 r F P 0 g s .54769 .29495 m .54856 .29535 L .58313 .34486 L .41 .369 .702 r F .57462 .3137 m .58313 .34486 L p .54787 .29436 L F P 0 g s .55037 .29616 m .54329 .31328 L p .53881 .29094 L .558 .147 .218 r F P 0 g s .54769 .29495 m .54787 .29436 L .54856 .29535 L .41 .369 .702 r F .57462 .3137 m .58067 .31874 L .58878 .32988 L .339 .322 .694 r F .57764 .31622 m .54329 .31328 L .55119 .29418 L p .662 .254 .261 r F P 0 g s .55119 .29418 m .55457 .28599 L p .57764 .31622 L .662 .254 .261 r F P 0 g s .59197 .26855 m .56773 .26585 L .60391 .27345 L closepath p .081 .609 .871 r F P 0 g s .56773 .26585 m .59197 .26855 L .56227 .27579 L p .233 0 0 r F P 0 g s .6528 .2947 m .56227 .27579 L .59197 .26855 L closepath p .486 0 0 r F P 0 g s .55914 .25703 m .57462 .3137 L p .54787 .29436 L .41 .369 .702 r F P 0 g s .57462 .3137 m .57319 .30848 L p .58067 .31874 L .339 .322 .694 r F P 0 g s .49744 .4258 m .56076 .39561 L .59422 .45998 L p .685 .643 .802 r F P 0 g s .56224 .40018 m .53887 .32415 L .58313 .34486 L p .39 .379 .726 r F P 0 g s .58313 .34486 m .60704 .42255 L .56224 .40018 L p .39 .379 .726 r F P 0 g s .54329 .31328 m .57764 .31622 L p .60331 .37728 L .71 .394 .442 r F P 0 g s .58873 .33001 m .59025 .33189 L .61694 .36853 L .339 .322 .694 r F .59025 .33189 m .60331 .37728 L p .57764 .31622 L .71 .394 .442 r F P 0 g s .58873 .33001 m .58878 .32988 L .59025 .33189 L .339 .322 .694 r F .58878 .32988 m .60489 .28723 L .61694 .36853 L F .60331 .37728 m .59119 .33516 L p .61694 .36853 L .758 .423 .417 r F P 0 g s .60704 .42255 m .61694 .36853 L .62147 .3744 L .306 .324 .716 r F .60704 .42255 m .62214 .37217 L .6274 .38208 L F .6274 .38208 m .62671 .38194 L p .61694 .36853 L .758 .423 .417 r F P 0 g s .62671 .38194 m .60331 .37728 L p .61694 .36853 L .758 .423 .417 r F P 0 g s .59119 .33516 m .59025 .33189 L p .61694 .36853 L .758 .423 .417 r F P 0 g s .55914 .25703 m .60489 .28723 L p .58878 .32988 L .339 .322 .694 r F P 0 g s .57319 .30848 m .55914 .25703 L p .58878 .32988 L .339 .322 .694 r F P 0 g s .61694 .36853 m .62214 .37217 L p .62147 .3744 L .306 .324 .716 r F P 0 g s .60331 .37728 m .6274 .38208 L p .66228 .46614 L .772 .525 .562 r F P 0 g s .6274 .38208 m .62808 .38222 L p .63012 .38721 L .772 .525 .562 r F P 0 g s .66228 .46614 m .6274 .38208 L .63012 .38721 L .772 .525 .562 r F .62214 .37217 m .62972 .37747 L p .6274 .38208 L .306 .324 .716 r F P 0 g s .65948 .44583 m .66228 .46614 L p .62808 .38222 L .772 .525 .562 r F P 0 g s .62972 .37747 m .63633 .39892 L p .6274 .38208 L .306 .324 .716 r F P 0 g s .63633 .39892 m .63302 .3882 L p .65948 .44583 L .215 .265 .699 r F P 0 g s .62972 .37747 m .67937 .42333 L p .66072 .44854 L .215 .265 .699 r F P 0 g s .63302 .3882 m .62972 .37747 L p .66072 .44854 L .215 .265 .699 r F P 0 g s .66991 .46856 m .66943 .46841 L p .66905 .46669 L .816 .556 .546 r F P 0 g s .66943 .46841 m .66228 .46614 L .66013 .45055 L p .816 .556 .546 r F P 0 g s .67287 .47501 m .67608 .47808 L p .67625 .48149 L .148 .251 .715 r F P 0 g s .67608 .47808 m .70477 .50557 L p .68974 .51691 L .148 .251 .715 r F P 0 g s .68028 .53375 m .68672 .51676 L p .7004 .54722 L .859 .668 .643 r F P 0 g s .71464 .57892 m .704 .55076 L .715 .57885 L .048 .226 .725 r F .70163 .58166 m .70371 .55458 L .71464 .57892 L F .70371 .55458 m .704 .55076 L .71464 .57892 L F .70633 .56041 m .70432 .55835 L .7004 .54722 L .859 .668 .643 r F .70432 .55835 m .68028 .53375 L .7004 .54722 L F .68672 .51676 m .68826 .5127 L p .7004 .54722 L F P 0 g s .70477 .50557 m .72943 .57581 L .7004 .54722 L p .148 .251 .715 r F P 0 g s .68974 .51691 m .70477 .50557 L .7004 .54722 L .148 .251 .715 r F .7004 .54722 m .704 .55076 L p .70371 .55458 L .048 .226 .725 r F P 0 g s .704 .55076 m .72943 .57581 L p .715 .57885 L .048 .226 .725 r F P 0 g s .72386 .62528 m .727 .60846 L .7371 .62894 L 0 .178 .712 r F .73184 .61745 m .71762 .58555 L .72548 .60562 L .84 .698 .707 r F .727 .60846 m .72721 .60736 L .73184 .61745 L 0 .178 .712 r F .727 .60846 m .73184 .61745 L .7371 .62894 L F .66118 .56449 m .64464 .58596 L .68389 .58876 L p .46 0 .065 r F P 0 g s .66686 .60156 m .68389 .58876 L .64464 .58596 L p .377 0 0 r F P 0 g s .68389 .58876 m .66686 .60156 L .70849 .61505 L p .526 .003 0 r F P 0 g s .70163 .58166 m .72386 .62528 L .67576 .58711 L p .062 .295 .782 r F P 0 g s .67576 .58711 m .65361 .54419 L .70163 .58166 L p .062 .295 .782 r F P 0 g s .71363 .58358 m .69452 .57415 L p .72867 .61378 L .84 .698 .707 r F P 0 g s .73184 .61745 m .72548 .60562 L .72867 .61378 L .84 .698 .707 r F .72548 .60562 m .71363 .58358 L .72867 .61378 L F .69452 .57415 m .68028 .53375 L p .70633 .56041 L .859 .668 .643 r F P 0 g s .71762 .58555 m .69452 .57415 L p .70633 .56041 L .859 .668 .643 r F P 0 g s .71762 .58555 m .71363 .58358 L p .72548 .60562 L .84 .698 .707 r F P 0 g s .74324 .5982 m .79051 .63983 L p .74039 .63609 L .888 .773 .729 r F P 0 g s .73834 .63164 m .74324 .5982 L .74039 .63609 L .888 .773 .729 r F .72872 .62272 m .74324 .5982 L p .73772 .6359 L F P 0 g s .72943 .57581 m .75306 .63334 L .72548 .60562 L p .048 .226 .725 r F P 0 g s .715 .57885 m .72943 .57581 L .72548 .60562 L .048 .226 .725 r F .69082 .61837 m .70849 .61505 L .66686 .60156 L p .425 0 0 r F P 0 g s .69686 .61784 m .67576 .58711 L .72386 .62528 L p 0 .239 .753 r F P 0 g s .69452 .57415 m .72163 .63469 L .73184 .61745 L p .84 .698 .707 r F P 0 g s .72548 .60562 m .72721 .60736 L p .727 .60846 L 0 .178 .712 r F P 0 g s .72721 .60736 m .75306 .63334 L p .7371 .62894 L 0 .178 .712 r F P 0 g s .73772 .6359 m .73834 .63164 L .74039 .63609 L .888 .773 .729 r F .72163 .63469 m .72872 .62272 L p .73772 .6359 L F P 0 g s .75306 .63334 m .77542 .67773 L .74555 .64735 L p 0 .178 .712 r F P 0 g s .7371 .62894 m .75306 .63334 L .74555 .64735 L 0 .178 .712 r F .75919 .69363 m .72163 .63469 L p .73772 .6359 L .888 .773 .729 r F P 0 g s .76747 .67942 m .75919 .69363 L p .73772 .6359 L .888 .773 .729 r F P 0 g s .75792 .66545 m .75996 .66688 L .76747 .67942 L 0 .093 .638 r F .75996 .66688 m .77542 .67773 L .76747 .67942 L F .7919 .72021 m .75919 .69363 L p .77464 .69139 L .939 .87 .742 r F P 0 g s .80717 .70479 m .81248 .70372 L .81352 .70293 L .739 .222 0 r F .83986 .60656 m .8128 .68587 L .81243 .70643 L p .933 .893 .487 r F P 0 g s .81243 .70643 m .8122 .71924 L p .81546 .70594 L .933 .893 .487 r F P 0 g s .81546 .70594 m .83986 .60656 L .81243 .70643 L .933 .893 .487 r F .81549 .72701 m .8329 .73258 L .80788 .70718 L p .683 .142 0 r F P 0 g s .80788 .70718 m .80581 .70507 L p .80681 .70735 L .683 .142 0 r F P 0 g s .80681 .70735 m .81549 .72701 L .80788 .70718 L .683 .142 0 r F .80121 .706 m .8128 .68587 L .81248 .70372 L p .948 .958 .701 r F P 0 g s .79851 .70357 m .81549 .72701 L .80581 .70507 L .683 .142 0 r F .80717 .70479 m .80788 .70718 L .81248 .70372 L .739 .222 0 r F .81443 .70224 m .82643 .726 L .82657 .72218 L F .81352 .70293 m .82643 .726 L .81443 .70224 L F .82168 .69678 m .82217 .69564 L .82147 .69694 L .933 .893 .487 r F .82217 .69564 m .83815 .6578 L .81971 .69845 L F .82609 .69346 m .82737 .68969 L p .82421 .69488 L F P 0 g s .82254 .69521 m .82442 .70218 L .82737 .68969 L .744 .269 .117 r F .82254 .69521 m .82737 .68969 L .82779 .68788 L F .82017 .69792 m .82442 .70218 L p .82254 .69521 L F P 0 g s .82442 .70218 m .84845 .72628 L p .82779 .68788 L .744 .269 .117 r F P 0 g s .83815 .6578 m .83073 .6756 L p .83022 .67758 L 0 0 0 r F P 0 g s .83125 .6786 m .83022 .67758 L p .82823 .6887 L .744 .269 .117 r F P 0 g s .82779 .68788 m .82823 .6887 L .83022 .67758 L .744 .269 .117 r F .82737 .68969 m .83815 .6578 L p .83022 .67758 L 0 0 0 r F P 0 g s .82442 .70218 m .82017 .69792 L p .82202 .71471 L .739 .222 0 r F P 0 g s .81443 .70224 m .82202 .71471 L .82017 .69792 L .739 .222 0 r F .82737 .68969 m .83815 .6578 L p .82217 .69564 L .933 .893 .487 r F P 0 g s .82823 .6887 m .8376 .70611 L .83246 .68385 L .744 .269 .117 r F .82823 .6887 m .83246 .68385 L .83125 .6786 L F .8376 .70611 m .84845 .72628 L .83125 .6786 L F .80788 .70718 m .82643 .726 L p .81352 .70293 L .739 .222 0 r F P 0 g s .82643 .726 m .8329 .73258 L p .82657 .72218 L .739 .222 0 r F P 0 g s .82202 .71471 m .8329 .73258 L .82442 .70218 L .739 .222 0 r F .84278 .66969 m .84173 .67119 L .8621 .70903 L .733 .296 .215 r F .82301 .64348 m .82304 .64339 L .82299 .6434 L .004 0 .348 r F .82878 .62258 m .82028 .63469 L p .82304 .64339 L F P 0 g s .81686 .552 m .79238 .58882 L .79723 .60319 L p .224 .166 .578 r F P 0 g s .81303 .62525 m .81686 .552 L .79723 .60319 L .224 .166 .578 r F .79238 .58882 m .78861 .59262 L p .79153 .59619 L .336 .229 .582 r F P 0 g s .7862 .58967 m .78594 .59035 L p .78861 .59262 L .68 .274 .27 r F P 0 g s .78885 .59238 m .78861 .59262 L p .78594 .59035 L .413 .342 .668 r F P 0 g s .76167 .55732 m .79238 .58882 L .78885 .59238 L p .413 .342 .668 r F P 0 g s .76603 .57646 m .76167 .55732 L p .78885 .59238 L .413 .342 .668 r F P 0 g s .78152 .60188 m .78594 .59035 L p .76893 .57849 L .634 .226 .252 r F P 0 g s .76167 .55732 m .76603 .57646 L p .75509 .57065 L .504 .402 .673 r F P 0 g s .73779 .5448 m .76167 .55732 L p .75576 .5693 L .504 .402 .673 r F P 0 g s .73459 .56154 m .73779 .5448 L .75576 .5693 L .504 .402 .673 r F .62398 .57146 m .63132 .55808 L p .61536 .56542 L .272 0 .08 r F P 0 g s .60783 .56888 m .59503 .57476 L .61277 .56286 L .651 .534 .708 r F .56491 .57635 m .62748 .54494 L p .61277 .56286 L F P 0 g s .58759 .58771 m .59503 .57476 L p .57919 .58539 L .107 0 0 r F P 0 g s .79378 .56993 m .80448 .53063 L .76463 .51058 L p .63 .253 .311 r F P 0 g s .76463 .51058 m .75281 .54852 L .79378 .56993 L p .63 .253 .311 r F P 0 g s .50313 .63774 m .52374 .61217 L .49648 .61147 L closepath p .714 .559 .678 r F P 0 g s .54488 .52033 m .56491 .57635 L .52374 .61217 L p .713 .594 .721 r F P 0 g s .49019 .51885 m .54488 .52033 L p .52374 .61217 L .713 .594 .721 r F P 0 g s .46956 .53684 m .49019 .51885 L p .52374 .61217 L .713 .594 .721 r F P 0 g s .52374 .61217 m .49648 .61147 L .46956 .53684 L p .713 .594 .721 r F P 0 g s .49648 .61147 m .50313 .63774 L .47803 .68423 L p .755 .584 .664 r F P 0 g s .41948 .59821 m .49648 .61147 L p .47803 .68423 L .755 .584 .664 r F P 0 g s .49648 .61147 m .46956 .53684 L .41948 .59821 L closepath p .749 .612 .706 r F P 0 g s .61412 .50727 m .62748 .54494 L .56491 .57635 L p .666 .568 .736 r F P 0 g s .56491 .57635 m .54488 .52033 L .61412 .50727 L p .666 .568 .736 r F P 0 g s .58942 .6827 m .57451 .60946 L .64211 .59499 L p .641 .492 .665 r F P 0 g s .57451 .60946 m .58942 .6827 L .51262 .68661 L p .689 .524 .658 r F P 0 g s .59422 .45998 m .61412 .50727 L .54488 .52033 L p .67 .598 .766 r F P 0 g s .54488 .52033 m .53149 .48915 L .59422 .45998 L p .67 .598 .766 r F P 0 g s .54488 .52033 m .53149 .48915 L .49019 .51885 L closepath p .711 .618 .751 r F P 0 g s .46956 .53684 m .49019 .51885 L .45813 .51303 L closepath p .74 .643 .752 r F P 0 g s .45813 .51303 m .46956 .53684 L .41948 .59821 L p .779 .658 .73 r F P 0 g s .49744 .4258 m .53149 .48915 L .49019 .51885 L p .731 .662 .781 r F P 0 g s .43483 .4712 m .49744 .4258 L p .49019 .51885 L .731 .662 .781 r F P 0 g s .49019 .51885 m .45813 .51303 L .43483 .4712 L p .731 .662 .781 r F P 0 g s .59422 .45998 m .53149 .48915 L .49744 .4258 L p .685 .643 .802 r F P 0 g s .40968 .49563 m .45813 .51303 L p .41948 .59821 L .779 .658 .73 r F P 0 g s .45813 .51303 m .43483 .4712 L .40968 .49563 L closepath p .767 .674 .76 r F P 0 g s .51729 .7515 m .51262 .68661 L .58942 .6827 L p .681 .476 .602 r F P 0 g s .40659 .62137 m .41948 .59821 L p .47803 .68423 L .755 .584 .664 r F P 0 g s .40659 .62137 m .41948 .59821 L .39515 .58997 L closepath p .792 .633 .684 r F P 0 g s .37142 .54207 m .40968 .49563 L p .41948 .59821 L .779 .658 .73 r F P 0 g s .41948 .59821 m .39515 .58997 L .37142 .54207 L p .779 .658 .73 r F P 0 g s .47803 .68423 m .41976 .67466 L .40659 .62137 L p .755 .584 .664 r F P 0 g s .64211 .59499 m .65777 .66876 L .58942 .6827 L p .641 .492 .665 r F P 0 g s .5953 .74769 m .58942 .6827 L .65777 .66876 L p .624 .434 .605 r F P 0 g s .58942 .6827 m .5953 .74769 L .51729 .7515 L p .681 .476 .602 r F P 0 g s .41976 .67466 m .40659 .62137 L .38751 .66602 L closepath p .785 .602 .652 r F P 0 g s .38751 .66602 m .40659 .62137 L .39515 .58997 L p .821 .646 .666 r F P 0 g s .39515 .58997 m .35272 .57091 L p .38751 .66602 L .821 .646 .666 r F P 0 g s .39515 .58997 m .37142 .54207 L .35272 .57091 L closepath p .807 .668 .71 r F P 0 g s .56929 .60951 m .58759 .58771 L .55166 .61322 L p 0 0 0 r F P 0 g s .55166 .61322 m .53244 .63566 L .56929 .60951 L p 0 0 0 r F P 0 g s .53244 .63566 m .55166 .61322 L .51587 .64817 L p 0 0 0 r F P 0 g s .49567 .67157 m .51587 .64817 L .47989 .69288 L p .601 .851 .491 r F P 0 g s .51587 .64817 m .49567 .67157 L .53244 .63566 L p 0 0 0 r F P 0 g s .38751 .66602 m .41976 .67466 L .42512 .74181 L p .79 .567 .598 r F P 0 g s .49744 .4258 m .43483 .4712 L .39834 .42275 L p .756 .719 .818 r F P 0 g s .40968 .49563 m .43483 .4712 L .39834 .42275 L p .794 .727 .789 r F P 0 g s .40968 .49563 m .37142 .54207 L .3337 .49157 L p .816 .72 .759 r F P 0 g s .3337 .49157 m .35982 .46011 L .40968 .49563 L p .816 .72 .759 r F P 0 g s .39834 .42275 m .35982 .46011 L .40968 .49563 L p .794 .727 .789 r F P 0 g s .60657 .59294 m .62398 .57146 L .58759 .58771 L p .129 0 0 r F P 0 g s .58759 .58771 m .56929 .60951 L .60657 .59294 L p .129 0 0 r F P 0 g s .47989 .69288 m .45864 .71759 L .49567 .67157 L p .601 .851 .491 r F P 0 g s .66477 .73412 m .65777 .66876 L .71876 .64424 L p .549 .379 .604 r F P 0 g s .65777 .66876 m .66477 .73412 L .5953 .74769 L p .624 .434 .605 r F P 0 g s .35272 .57091 m .37142 .54207 L .3337 .49157 L p .842 .722 .731 r F P 0 g s .42512 .74181 m .37596 .7292 L .38751 .66602 L p .79 .567 .598 r F P 0 g s .32286 .63837 m .38751 .66602 L .37596 .7292 L p .834 .611 .601 r F P 0 g s .35272 .57091 m .32286 .63837 L .38751 .66602 L p .821 .646 .666 r F P 0 g s .64464 .58596 m .66118 .56449 L .62398 .57146 L p .32 0 0 r F P 0 g s .62398 .57146 m .60657 .59294 L .64464 .58596 L p .32 0 0 r F P 0 g s .51209 .80906 m .51729 .7515 L .5953 .74769 L p .666 .411 .524 r F P 0 g s .46458 .74801 m .51729 .7515 L .51209 .80906 L p .717 .456 .529 r F P 0 g s .30483 .53542 m .35272 .57091 L .32286 .63837 L p .867 .706 .68 r F P 0 g s .3337 .49157 m .30483 .53542 L .35272 .57091 L p .842 .722 .731 r F P 0 g s .51209 .80906 m .47618 .80678 L .46458 .74801 L p .717 .456 .529 r F P 0 g s .59184 .80532 m .5953 .74769 L .66477 .73412 L p .596 .351 .516 r F P 0 g s .5953 .74769 m .59184 .80532 L .51209 .80906 L p .666 .411 .524 r F P 0 g s .88378 .64585 m .89193 .60219 L .84673 .56086 L p .703 .325 .33 r F P 0 g s .71876 .64424 m .72684 .71024 L .66477 .73412 L p .549 .379 .604 r F P 0 g s .66285 .79197 m .66477 .73412 L .72684 .71024 L p .5 .274 .502 r F P 0 g s .66477 .73412 m .66285 .79197 L .59184 .80532 L p .596 .351 .516 r F P 0 g s .35982 .46011 m .39834 .42275 L .35943 .38837 L p .825 .792 .821 r F P 0 g s .35982 .46011 m .3337 .49157 L .29271 .46218 L p .858 .8 .792 r F P 0 g s .29271 .46218 m .33307 .4139 L .35982 .46011 L p .858 .8 .792 r F P 0 g s .35943 .38837 m .33307 .4139 L .35982 .46011 L p .825 .792 .821 r F P 0 g s .30998 .70218 m .37596 .7292 L .38213 .78935 L p .842 .555 .504 r F P 0 g s .37596 .7292 m .30998 .70218 L .32286 .63837 L p .834 .611 .601 r F P 0 g s .27366 .60384 m .32286 .63837 L .30998 .70218 L p .892 .674 .6 r F P 0 g s .32286 .63837 m .27366 .60384 L .30483 .53542 L p .867 .706 .68 r F P 0 g s .30483 .53542 m .3337 .49157 L .29271 .46218 L p .883 .789 .752 r F P 0 g s .76167 .55732 m .73779 .5448 L .75423 .52989 L closepath p .48 .414 .705 r F P 0 g s .72676 .45128 m .75423 .52989 L .73779 .5448 L p .527 .489 .757 r F P 0 g s .5499 .62248 m .56929 .60951 L .53244 .63566 L p .437 .828 .605 r F P 0 g s .53244 .63566 m .5122 .64923 L .5499 .62248 L p .437 .828 .605 r F P 0 g s .5122 .64923 m .53244 .63566 L .49567 .67157 L p .677 .947 .686 r F P 0 g s .49567 .67157 m .47451 .68603 L .5122 .64923 L p .677 .947 .686 r F P 0 g s .47451 .68603 m .49567 .67157 L .45864 .71759 L p .825 .985 .711 r F P 0 g s .588 .60557 m .60657 .59294 L .56929 .60951 L p 0 0 0 r F P 0 g s .56929 .60951 m .5499 .62248 L .588 .60557 L p 0 0 0 r F P 0 g s .51209 .80906 m .59184 .80532 L .57831 .85624 L p .637 .319 .415 r F P 0 g s .50162 .84266 m .51209 .80906 L p .57831 .85624 L .637 .319 .415 r F P 0 g s .50162 .84266 m .47618 .80678 L .51209 .80906 L closepath p .7 .383 .437 r F P 0 g s .2728 .49204 m .30483 .53542 L .27366 .60384 L p .92 .783 .693 r F P 0 g s .29271 .46218 m .2728 .49204 L .30483 .53542 L p .883 .789 .752 r F P 0 g s .45864 .71759 m .43649 .73324 L .47451 .68603 L p .825 .985 .711 r F P 0 g s .43649 .73324 m .45864 .71759 L .42099 .77427 L p .905 .98 .708 r F P 0 g s .47618 .80678 m .50162 .84266 L .49413 .85808 L p .734 .386 .391 r F P 0 g s .41565 .79762 m .47618 .80678 L p .49413 .85808 L .734 .386 .391 r F P 0 g s .57831 .85624 m .59184 .80532 L .66285 .79197 L p .547 .232 .386 r F P 0 g s .75423 .52989 m .78534 .47971 L p .79238 .58882 L .354 .332 .696 r F P 0 g s .79238 .58882 m .76167 .55732 L .75423 .52989 L p .354 .332 .696 r F P 0 g s .75423 .52989 m .72676 .45128 L .78534 .47971 L closepath p .432 .432 .758 r F P 0 g s .62685 .59853 m .64464 .58596 L .60657 .59294 L p .158 0 0 r F P 0 g s .60657 .59294 m .588 .60557 L .62685 .59853 L p .158 0 0 r F P 0 g s .72684 .71024 m .72632 .76848 L .66285 .79197 L p .5 .274 .502 r F P 0 g s .78534 .47971 m .72676 .45128 L .71575 .42594 L p .376 .448 .808 r F P 0 g s .42099 .77427 m .39775 .79144 L .43649 .73324 L p .905 .98 .708 r F P 0 g s .39873 .82744 m .41565 .79762 L p .49413 .85808 L .734 .386 .391 r F P 0 g s .38213 .78935 m .31484 .76285 L .30998 .70218 L p .842 .555 .504 r F P 0 g s .25961 .66843 m .30998 .70218 L .31484 .76285 L p .908 .609 .468 r F P 0 g s .30998 .70218 m .25961 .66843 L .27366 .60384 L p .892 .674 .6 r F P 0 g s .71575 .42594 m .7223 .38787 L p .78534 .47971 L .376 .448 .808 r F P 0 g s .93412 .70275 m .94075 .65586 L .89193 .60219 L p .731 .353 .335 r F P 0 g s .89193 .60219 m .88378 .64585 L .93412 .70275 L p .731 .353 .335 r F P 0 g s .65134 .84298 m .66285 .79197 L .72632 .76848 L p .42 .119 .346 r F P 0 g s .66285 .79197 m .65134 .84298 L .57831 .85624 L p .547 .232 .386 r F P 0 g s .64464 .58596 m .62685 .59853 L .66686 .60156 L p .377 0 0 r F P 0 g s .24037 .56159 m .27366 .60384 L .25961 .66843 L p .96 .756 .585 r F P 0 g s .27366 .60384 m .24037 .56159 L .2728 .49204 L p .92 .783 .693 r F P 0 g s .26271 .45745 m .29271 .46218 L .33307 .4139 L p .897 .897 .818 r F P 0 g s .57831 .85624 m .52354 .85872 L .50162 .84266 L p .637 .319 .415 r F P 0 g s .52354 .85872 m .49413 .85808 L .50162 .84266 L closepath p .657 .299 .354 r F P 0 g s .52953 .62581 m .5499 .62248 L .5122 .64923 L p .713 .986 .872 r F P 0 g s .5122 .64923 m .49105 .65315 L .52953 .62581 L p .713 .986 .872 r F P 0 g s .49105 .65315 m .5122 .64923 L .47451 .68603 L p .841 .994 .844 r F P 0 g s .7223 .38787 m .69385 .38111 L .66092 .32826 L p .397 .558 .897 r F P 0 g s .47451 .68603 m .45253 .69075 L .49105 .65315 L p .841 .994 .844 r F P 0 g s .45253 .69075 m .47451 .68603 L .43649 .73324 L p .906 .971 .804 r F P 0 g s .2728 .49204 m .26271 .45745 L .29271 .46218 L closepath p .922 .867 .768 r F P 0 g s .56834 .60856 m .588 .60557 L .5499 .62248 L p .479 .898 .846 r F P 0 g s .5499 .62248 m .52953 .62581 L .56834 .60856 L p .479 .898 .846 r F P 0 g s .8012 .49503 m .81686 .552 L .79238 .58882 L p .354 .332 .696 r F P 0 g s .78534 .47971 m .8012 .49503 L p .79238 .58882 L .354 .332 .696 r F P 0 g s .43649 .73324 m .41358 .73901 L .45253 .69075 L p .906 .971 .804 r F P 0 g s .41358 .73901 m .43649 .73324 L .39775 .79144 L p .939 .942 .766 r F P 0 g s .26271 .45745 m .2728 .49204 L .24037 .56159 L p .968 .873 .688 r F P 0 g s .78319 .73385 m .72632 .76848 L .71656 .81961 L p .251 0 .292 r F P 0 g s .72632 .76848 m .71656 .81961 L .65134 .84298 L p .42 .119 .346 r F P 0 g s .60787 .60139 m .62685 .59853 L .588 .60557 L p .146 .688 .72 r F P 0 g s .588 .60557 m .56834 .60856 L .60787 .60139 L p .146 .688 .72 r F P 0 g s .56861 .87371 m .52354 .85872 L .57831 .85624 L closepath p .586 .193 .265 r F P 0 g s .52354 .85872 m .56861 .87371 L .54717 .89521 L p .57 .108 .117 r F P 0 g s .49413 .85808 m .52354 .85872 L p .54717 .89521 L .57 .108 .117 r F P 0 g s .49413 .85808 m .41099 .84593 L .39873 .82744 L p .734 .386 .391 r F P 0 g s .41099 .84593 m .38467 .83837 L .39873 .82744 L closepath p .783 .389 .308 r F P 0 g s .46308 .88598 m .49413 .85808 L p .54717 .89521 L .57 .108 .117 r F P 0 g s .46308 .88598 m .41099 .84593 L .49413 .85808 L closepath p .685 .25 .212 r F P 0 g s .34234 .92295 m .31653 .94432 L .3579 .86145 L p .968 .934 .681 r F P 0 g s .7223 .38787 m .76697 .40834 L p .78534 .47971 L .376 .448 .808 r F P 0 g s .7223 .38787 m .76697 .40834 L .73435 .35104 L p .267 .464 .867 r F P 0 g s .73435 .35104 m .7042 .3378 L .7223 .38787 L p .267 .464 .867 r F P 0 g s .66092 .32826 m .7042 .3378 L .7223 .38787 L p .397 .558 .897 r F P 0 g s .39775 .79144 m .37382 .79854 L .41358 .73901 L p .939 .942 .766 r F P 0 g s .56861 .87371 m .57831 .85624 L .65134 .84298 L p .465 .068 .201 r F P 0 g s .8012 .49503 m .78534 .47971 L .78939 .46103 L closepath p .242 .31 .734 r F P 0 g s .76697 .40834 m .78939 .46103 L .78534 .47971 L p .376 .448 .808 r F P 0 g s .64855 .60452 m .66686 .60156 L .62685 .59853 L p .184 0 0 r F P 0 g s .62685 .59853 m .60787 .60139 L .64855 .60452 L p .184 0 0 r F P 0 g s .41099 .84593 m .46308 .88598 L .44968 .88879 L p .688 .178 .018 r F P 0 g s .38467 .83837 m .41099 .84593 L p .44968 .88879 L .688 .178 .018 r F P 0 g s .81686 .552 m .8012 .49503 L .82551 .52913 L closepath p .208 .235 .67 r F P 0 g s .82551 .52913 m .8012 .49503 L .78939 .46103 L p .02 .161 .671 r F P 0 g s .6382 .86934 m .65134 .84298 L .71656 .81961 L p .295 0 .119 r F P 0 g s .65134 .84298 m .6382 .86934 L .56861 .87371 L p .465 .068 .201 r F P 0 g s .5083 .61885 m .52953 .62581 L .49105 .65315 L p .797 .931 .921 r F P 0 g s .49105 .65315 m .46916 .64671 L .5083 .61885 L p .797 .931 .921 r F P 0 g s .46916 .64671 m .49105 .65315 L .45253 .69075 L p .864 .917 .863 r F P 0 g s .33283 .87018 m .3579 .86145 L .31653 .94432 L p .962 .888 .71 r F P 0 g s .45253 .69075 m .42989 .68502 L .46916 .64671 L p .864 .917 .863 r F P 0 g s .42989 .68502 m .45253 .69075 L .41358 .73901 L p .901 .895 .813 r F P 0 g s .78939 .46103 m .78948 .4252 L p .82551 .52913 L .02 .161 .671 r F P 0 g s .78939 .46103 m .76697 .40834 L .78948 .4252 L closepath p .224 .351 .784 r F P 0 g s .54773 .60122 m .56834 .60856 L .52953 .62581 L p .672 .919 .975 r F P 0 g s .52953 .62581 m .5083 .61885 L .54773 .60122 L p .672 .919 .975 r F P 0 g s .3562 .84277 m .38467 .83837 L p .44968 .88879 L .688 .178 .018 r F P 0 g s .82551 .52913 m .81686 .552 L .82878 .62258 L p .024 .028 .522 r F P 0 g s .92559 .74177 m .93412 .70275 L .88378 .64585 L p .748 .346 .29 r F P 0 g s .88378 .64585 m .87386 .68185 L .92559 .74177 L p .748 .346 .29 r F P 0 g s .41358 .73901 m .39011 .73418 L .42989 .68502 L p .901 .895 .813 r F P 0 g s .39011 .73418 m .41358 .73901 L .37382 .79854 L p .921 .873 .773 r F P 0 g s .54717 .89521 m .56861 .87371 L .6382 .86934 L p .374 0 0 r F P 0 g s .66686 .60156 m .64855 .60452 L .69082 .61837 L p .425 0 0 r F P 0 g s .58783 .59385 m .60787 .60139 L .56834 .60856 L p .453 .839 .985 r F P 0 g s .56834 .60856 m .54773 .60122 L .58783 .59385 L p .453 .839 .985 r F P 0 g s .78948 .4252 m .76697 .40834 L .73435 .35104 L p .045 .316 .802 r F P 0 g s .37382 .79854 m .34941 .79481 L .39011 .73418 L p .921 .873 .773 r F P 0 g s .31653 .94432 m .29016 .95505 L .33283 .87018 L p .962 .888 .71 r F P 0 g s .7042 .3378 m .73435 .35104 L .70183 .31508 L p .043 .445 .875 r F P 0 g s .70183 .31508 m .65627 .29551 L .7042 .3378 L p .043 .445 .875 r F P 0 g s .71656 .81961 m .70872 .83699 L .6382 .86934 L p .295 0 .119 r F P 0 g s .82878 .62258 m .84229 .58895 L .82551 .52913 L p .024 .028 .522 r F P 0 g s .82677 .47606 m .82551 .52913 L .84229 .58895 L p 0 0 .406 r F P 0 g s .78948 .4252 m .82677 .47606 L .82551 .52913 L p .02 .161 .671 r F P 0 g s .62904 .59694 m .64855 .60452 L .60787 .60139 L p .138 .651 .896 r F P 0 g s .60787 .60139 m .58783 .59385 L .62904 .59694 L p .138 .651 .896 r F P 0 g s .4864 .60105 m .5083 .61885 L .46916 .64671 L p .789 .827 .882 r F P 0 g s .46916 .64671 m .44668 .62941 L .4864 .60105 L p .789 .827 .882 r F P 0 g s .44668 .62941 m .46916 .64671 L .42989 .68502 L p .838 .824 .834 r F P 0 g s .42989 .68502 m .40678 .66831 L .44668 .62941 L p .838 .824 .834 r F P 0 g s .40678 .66831 m .42989 .68502 L .39011 .73418 L p .869 .815 .794 r F P 0 g s .76843 .37596 m .78948 .4252 L .82677 .47606 L p 0 .008 .582 r F P 0 g s .73435 .35104 m .76843 .37596 L .78948 .4252 L p .045 .316 .802 r F P 0 g s .52632 .58304 m .54773 .60122 L .5083 .61885 L p .708 .816 .933 r F P 0 g s .5083 .61885 m .4864 .60105 L .52632 .58304 L p .708 .816 .933 r F P 0 g s .62505 .88371 m .6382 .86934 L .70872 .83699 L p .067 0 0 r F P 0 g s .6382 .86934 m .62505 .88371 L .54717 .89521 L p .374 0 0 r F P 0 g s .30737 .86779 m .33283 .87018 L .29016 .95505 L p .938 .835 .716 r F P 0 g s .39011 .73418 m .36627 .71817 L .40678 .66831 L p .869 .815 .794 r F P 0 g s .36627 .71817 m .39011 .73418 L .34941 .79481 L p .889 .805 .761 r F P 0 g s .54717 .89521 m .48573 .89391 L .46308 .88598 L p .57 .108 .117 r F P 0 g s .48573 .89391 m .44968 .88879 L .46308 .88598 L closepath p .491 0 0 r F P 0 g s .56686 .57537 m .58783 .59385 L .54773 .60122 L p .576 .776 .974 r F P 0 g s .54773 .60122 m .52632 .58304 L .56686 .57537 L p .576 .776 .974 r F P 0 g s .44968 .88879 m .39506 .87345 L .3562 .84277 L p .688 .178 .018 r F P 0 g s .76843 .37596 m .73435 .35104 L .70183 .31508 L p 0 .217 .711 r F P 0 g s .67182 .61094 m .69082 .61837 L .64855 .60452 L p 0 .393 .712 r F P 0 g s .64855 .60452 m .62904 .59694 L .67182 .61094 L p 0 .393 .712 r F P 0 g s .34941 .79481 m .32474 .77966 L .36627 .71817 L p .889 .805 .761 r F P 0 g s .70872 .83699 m .69059 .85806 L .62505 .88371 L p .067 0 0 r F P 0 g s .5322 .90202 m .54717 .89521 L .62505 .88371 L p .141 0 0 r F P 0 g s .5322 .90202 m .48573 .89391 L .54717 .89521 L closepath p .414 0 0 r F P 0 g s .48573 .89391 m .5322 .90202 L p .42212 .88638 L .183 0 0 r F P 0 g s .42212 .88638 m .44968 .88879 L .48573 .89391 L p .183 0 0 r F P 0 g s .46399 .57209 m .4864 .60105 L .44668 .62941 L p .761 .739 .833 r F P 0 g s .44668 .62941 m .42384 .60088 L .46399 .57209 L p .761 .739 .833 r F P 0 g s .42384 .60088 m .44668 .62941 L .40678 .66831 L p .805 .747 .799 r F P 0 g s .40678 .66831 m .38341 .64025 L .42384 .60088 L p .805 .747 .799 r F P 0 g s .38341 .64025 m .40678 .66831 L .36627 .71817 L p .835 .749 .769 r F P 0 g s .60846 .57827 m .62904 .59694 L .58783 .59385 L p .374 .682 .978 r F P 0 g s .58783 .59385 m .56686 .57537 L .60846 .57827 L p .374 .682 .978 r F P 0 g s .91508 .77167 m .92559 .74177 L .87386 .68185 L p .765 .335 .229 r F P 0 g s .87386 .68185 m .8621 .70903 L .91508 .77167 L p .765 .335 .229 r F P 0 g s .42212 .88638 m .39506 .87345 L .44968 .88879 L closepath p .494 0 0 r F P 0 g s .29016 .95505 m .26349 .95429 L .30737 .86779 L p .938 .835 .716 r F P 0 g s .50429 .55367 m .52632 .58304 L .4864 .60105 L p .697 .722 .869 r F P 0 g s .4864 .60105 m .46399 .57209 L .50429 .55367 L p .697 .722 .869 r F P 0 g s .65627 .29551 m .70183 .31508 L .67994 .30613 L p .288 0 0 r F P 0 g s .60391 .27345 m .65627 .29551 L p .67994 .30613 L .288 0 0 r F P 0 g s .36627 .71817 m .3423 .69063 L .38341 .64025 L p .835 .749 .769 r F P 0 g s .3423 .69063 m .36627 .71817 L .32474 .77966 L p .856 .748 .743 r F P 0 g s .84229 .58895 m .84411 .53653 L .82677 .47606 L p 0 0 .406 r F P 0 g s .84411 .53653 m .84229 .58895 L .83815 .6578 L p .736 .631 .067 r F P 0 g s .60412 .89382 m .62505 .88371 L .69059 .85806 L p 0 0 0 r F P 0 g s .62505 .88371 m .60412 .89382 L .5322 .90202 L p .141 0 0 r F P 0 g s .77316 .78305 m .75096 .80965 L p .69059 .85806 L 0 0 0 r F P 0 g s .75096 .80965 m .80754 .7366 L .77316 .78305 L closepath p .597 .839 .468 r F P 0 g s .28174 .85365 m .30737 .86779 L .26349 .95429 L p .91 .786 .712 r F P 0 g s .54514 .54562 m .56686 .57537 L .52632 .58304 L p .604 .687 .901 r F P 0 g s .52632 .58304 m .50429 .55367 L .54514 .54562 L p .604 .687 .901 r F P 0 g s .69082 .61837 m .67182 .61094 L .71673 .63655 L p .429 0 0 r F P 0 g s .32474 .77966 m .30005 .75268 L .3423 .69063 L p .856 .748 .743 r F P 0 g s .44131 .53183 m .46399 .57209 L .42384 .60088 L p .734 .673 .791 r F P 0 g s .42384 .60088 m .40085 .56099 L .44131 .53183 L p .734 .673 .791 r F P 0 g s .40085 .56099 m .42384 .60088 L .38341 .64025 L p .774 .687 .767 r F P 0 g s .82677 .47606 m .80617 .42688 L .76843 .37596 L p 0 .008 .582 r F P 0 g s .80617 .42688 m .82677 .47606 L .84411 .53653 L p .792 .464 0 r F P 0 g s .38341 .64025 m .36003 .6007 L .40085 .56099 L p .774 .687 .767 r F P 0 g s .36003 .6007 m .38341 .64025 L .3423 .69063 L p .804 .695 .745 r F P 0 g s .70183 .31508 m .72468 .33164 L .76843 .37596 L p 0 .217 .711 r F P 0 g s .72468 .33164 m .76843 .37596 L .80617 .42688 L p .694 .201 0 r F P 0 g s .5322 .90202 m .4928 .89879 L .42212 .88638 L p .183 0 0 r F P 0 g s .60412 .89382 m .5322 .90202 L .4928 .89879 L p .226 .742 .859 r F P 0 g s .39506 .87345 m .42212 .88638 L .37924 .86141 L p 0 .316 .71 r F P 0 g s .37924 .86141 m .33847 .84201 L .39506 .87345 L p 0 .316 .71 r F P 0 g s .59197 .26855 m .60391 .27345 L p .67994 .30613 L .288 0 0 r F P 0 g s .65161 .59219 m .67182 .61094 L .62904 .59694 L p .111 .521 .911 r F P 0 g s .62904 .59694 m .60846 .57827 L .65161 .59219 L p .111 .521 .911 r F P 0 g s .48184 .51299 m .50429 .55367 L .46399 .57209 L p .68 .652 .815 r F P 0 g s .46399 .57209 m .44131 .53183 L .48184 .51299 L p .68 .652 .815 r F P 0 g s .31209 .29334 m .29185 .20272 L .33182 .17276 L p .65 .507 .675 r F P 0 g s .29185 .20272 m .31209 .29334 L .27109 .33295 L p .68 .526 .67 r F P 0 g s .27109 .33295 m .25115 .24195 L .29185 .20272 L p .68 .526 .67 r F P 0 g s .25115 .24195 m .27109 .33295 L .229 .38263 L p .705 .542 .664 r F P 0 g s .229 .38263 m .20931 .29086 L .25115 .24195 L p .705 .542 .664 r F P 0 g s .3423 .69063 m .31843 .65138 L .36003 .6007 L p .804 .695 .745 r F P 0 g s .31843 .65138 m .3423 .69063 L .30005 .75268 L p .826 .7 .726 r F P 0 g s .58699 .54816 m .60846 .57827 L .56686 .57537 L p .47 .625 .919 r F P 0 g s .56686 .57537 m .54514 .54562 L .58699 .54816 L p .47 .625 .919 r F P 0 g s .35243 .26338 m .33182 .17276 L .37146 .15181 L p .616 .485 .679 r F P 0 g s .33182 .17276 m .35243 .26338 L .31209 .29334 L p .65 .507 .675 r F P 0 g s .52286 .50447 m .54514 .54562 L .50429 .55367 L p .606 .619 .838 r F P 0 g s .50429 .55367 m .48184 .51299 L .52286 .50447 L p .606 .619 .838 r F P 0 g s .20931 .29086 m .229 .38263 L .18536 .44305 L p .727 .556 .659 r F P 0 g s .18536 .44305 m .16587 .35009 L .20931 .29086 L p .727 .556 .659 r F P 0 g s .41858 .48038 m .44131 .53183 L .40085 .56099 L p .711 .624 .758 r F P 0 g s .40085 .56099 m .37794 .50985 L .41858 .48038 L p .711 .624 .758 r F P 0 g s .37794 .50985 m .40085 .56099 L .36003 .6007 L p .749 .64 .74 r F P 0 g s .26349 .95429 m .23676 .94137 L .28174 .85365 L p .91 .786 .712 r F P 0 g s .36003 .6007 m .33686 .54975 L .37794 .50985 L p .749 .64 .74 r F P 0 g s .33686 .54975 m .36003 .6007 L .31843 .65138 L p .778 .652 .724 r F P 0 g s .25622 .82733 m .28174 .85365 L .23676 .94137 L p .881 .742 .704 r F P 0 g s .83815 .6578 m .83986 .60656 L .84411 .53653 L p .736 .631 .067 r F P 0 g s .72468 .33164 m .67994 .30613 L .70183 .31508 L closepath p .521 0 0 r F P 0 g s .45921 .46111 m .48184 .51299 L .44131 .53183 L p .663 .6 .775 r F P 0 g s .44131 .53183 m .41858 .48038 L .45921 .46111 L p .663 .6 .775 r F P 0 g s .75096 .80965 m .7266 .83071 L .69059 .85806 L p 0 0 0 r F P 0 g s .69059 .85806 m .67756 .86444 L .60412 .89382 L p 0 0 0 r F P 0 g s .67756 .86444 m .7266 .83071 L .69059 .85806 L closepath p .516 .892 .702 r F P 0 g s .4928 .89879 m .42212 .88638 L .37924 .86141 L p .165 .616 .936 r F P 0 g s .30005 .75268 m .2756 .71372 L .31843 .65138 L p .826 .7 .726 r F P 0 g s .39252 .24283 m .37146 .15181 L .4112 .13985 L p .577 .459 .683 r F P 0 g s .37146 .15181 m .39252 .24283 L .35243 .26338 L p .616 .485 .679 r F P 0 g s .31843 .65138 m .29491 .60052 L .33686 .54975 L p .778 .652 .724 r F P 0 g s .29491 .60052 m .31843 .65138 L .2756 .71372 L p .8 .661 .709 r F P 0 g s .67994 .30613 m .6528 .2947 L .59197 .26855 L p .288 0 0 r F P 0 g s .39603 .41807 m .41858 .48038 L .37794 .50985 L p .692 .585 .731 r F P 0 g s .37794 .50985 m .35535 .44778 L .39603 .41807 L p .692 .585 .731 r F P 0 g s .35535 .44778 m .37794 .50985 L .33686 .54975 L p .727 .603 .718 r F P 0 g s .33686 .54975 m .31416 .48773 L .35535 .44778 L p .727 .603 .718 r F P 0 g s .31416 .48773 m .33686 .54975 L .29491 .60052 L p .755 .617 .706 r F P 0 g s .35535 .44778 m .33333 .37535 L .37391 .34547 L p .676 .554 .709 r F P 0 g s .33333 .37535 m .35535 .44778 L .31416 .48773 L p .709 .573 .7 r F P 0 g s .31416 .48773 m .29216 .4152 L .33333 .37535 L p .709 .573 .7 r F P 0 g s .16587 .35009 m .18536 .44305 L .13967 .5151 L p .746 .568 .654 r F P 0 g s .13967 .5151 m .12033 .4205 L .16587 .35009 L p .746 .568 .654 r F P 0 g s .20629 .5268 m .18536 .44305 L .229 .38263 L p .742 .577 .67 r F P 0 g s .29216 .4152 m .31416 .48773 L .27201 .53835 L p .736 .588 .69 r F P 0 g s .27201 .53835 m .24996 .46546 L .29216 .4152 L p .736 .588 .69 r F P 0 g s .37391 .34547 m .39603 .41807 L .35535 .44778 L p .676 .554 .709 r F P 0 g s .67756 .86444 m .60412 .89382 L .56661 .89023 L p .563 .925 .943 r F P 0 g s .4928 .89879 m .56661 .89023 L .60412 .89382 L p .226 .742 .859 r F P 0 g s .43662 .39836 m .45921 .46111 L .41858 .48038 L p .649 .561 .743 r F P 0 g s .41858 .48038 m .39603 .41807 L .43662 .39836 L p .649 .561 .743 r F P 0 g s .50025 .45203 m .52286 .50447 L .48184 .51299 L p .601 .569 .79 r F P 0 g s .48184 .51299 m .45921 .46111 L .50025 .45203 L p .601 .569 .79 r F P 0 g s .56482 .50648 m .58699 .54816 L .54514 .54562 L p .507 .569 .852 r F P 0 g s .54514 .54562 m .52286 .50447 L .56482 .50648 L p .507 .569 .852 r F P 0 g s .29491 .60052 m .27201 .53835 L .31416 .48773 L p .755 .617 .706 r F P 0 g s .63035 .56175 m .65161 .59219 L .60846 .57827 L p .292 .526 .906 r F P 0 g s .60846 .57827 m .58699 .54816 L .63035 .56175 L p .292 .526 .906 r F P 0 g s .69686 .61784 m .71673 .63655 L .67182 .61094 L p 0 .319 .774 r F P 0 g s .67182 .61094 m .65161 .59219 L .69686 .61784 L p 0 .319 .774 r F P 0 g s .39603 .41807 m .37391 .34547 L .41432 .32534 L p .636 .531 .717 r F P 0 g s .90249 .79126 m .91508 .77167 L .8621 .70903 L p .78 .317 .143 r F P 0 g s .8621 .70903 m .84845 .72628 L .90249 .79126 L p .78 .317 .143 r F P 0 g s .2756 .71372 m .25165 .66282 L .29491 .60052 L p .8 .661 .709 r F P 0 g s .27201 .53835 m .29491 .60052 L .25165 .66282 L p .778 .628 .695 r F P 0 g s .41432 .32534 m .43662 .39836 L .39603 .41807 L p .636 .531 .717 r F P 0 g s .4112 .13985 m .43279 .23165 L .39252 .24283 L p .577 .459 .683 r F P 0 g s .24996 .46546 m .27201 .53835 L .22846 .60033 L p .759 .6 .681 r F P 0 g s .43279 .23165 m .4112 .13985 L .45145 .13699 L p .532 .43 .685 r F P 0 g s .25165 .66282 m .22846 .60033 L .27201 .53835 L p .778 .628 .695 r F P 0 g s .30151 .37461 m .32555 .33339 L .38979 .29919 L p .131 0 .012 r F P 0 g s .32555 .33339 m .30151 .37461 L .25128 .42156 L p 0 0 0 r F P 0 g s .82351 .48789 m .84411 .53653 L .83986 .60656 L p .992 .766 .39 r F P 0 g s .84411 .53653 m .82351 .48789 L .80617 .42688 L p .792 .464 0 r F P 0 g s .33847 .84201 m .37924 .86141 L .33501 .81362 L p .069 .432 .873 r F P 0 g s .33501 .81362 m .30756 .80088 L .33847 .84201 L p .069 .432 .873 r F P 0 g s .26856 .77016 m .30756 .80088 L .33847 .84201 L p 0 .204 .717 r F P 0 g s .23676 .94137 m .21027 .9158 L .25622 .82733 L p .881 .742 .704 r F P 0 g s .23107 .78863 m .25622 .82733 L .21027 .9158 L p .855 .704 .694 r F P 0 g s .47755 .38865 m .50025 .45203 L .45921 .46111 L p .595 .531 .753 r F P 0 g s .45921 .46111 m .43662 .39836 L .47755 .38865 L p .595 .531 .753 r F P 0 g s .80617 .42688 m .76211 .38255 L .72468 .33164 L p .694 .201 0 r F P 0 g s .67994 .30613 m .72468 .33164 L .76211 .38255 L p .794 .304 .038 r F P 0 g s .18536 .44305 m .20629 .5268 L .16063 .60014 L p .761 .588 .663 r F P 0 g s .16063 .60014 m .13967 .5151 L .18536 .44305 L p .761 .588 .663 r F P 0 g s .74057 .81162 m .75096 .80965 L .80754 .7366 L p .89 .99 .764 r F P 0 g s .54216 .45335 m .56482 .50648 L .52286 .50447 L p .523 .526 .8 r F P 0 g s .52286 .50447 m .50025 .45203 L .54216 .45335 L p .523 .526 .8 r F P 0 g s .76211 .38255 m .80617 .42688 L .82351 .48789 L p .93 .548 .225 r F P 0 g s .12033 .4205 m .13967 .5151 L .09138 .59995 L p .762 .578 .649 r F P 0 g s .09138 .59995 m .07214 .50323 L .12033 .4205 L p .762 .578 .649 r F P 0 g s .7266 .83071 m .67756 .86444 L .6423 .85976 L p .758 .978 .917 r F P 0 g s .56661 .89023 m .6423 .85976 L .67756 .86444 L p .563 .925 .943 r F P 0 g s .18301 .67459 m .16063 .60014 L .20629 .5268 L p .777 .611 .673 r F P 0 g s .45145 .13699 m .47366 .23 L .43279 .23165 L p .532 .43 .685 r F P 0 g s .23838 .47956 m .25128 .42156 L .30151 .37461 L p .095 0 .261 r F P 0 g s .2171 .51419 m .23838 .47956 L .25128 .42156 L p 0 0 .092 r F P 0 g s .30756 .80088 m .26856 .77016 L .23981 .71592 L p .092 .3 .779 r F P 0 g s .60822 .51948 m .63035 .56175 L .58699 .54816 L p .381 .498 .852 r F P 0 g s .58699 .54816 m .56482 .50648 L .60822 .51948 L p .381 .498 .852 r F P 0 g s .74057 .81162 m .7266 .83071 L p .6423 .85976 L .758 .978 .917 r F P 0 g s .7266 .83071 m .74057 .81162 L .75096 .80965 L closepath p .752 .994 .818 r F P 0 g s .21027 .9158 m .1843 .87737 L .23107 .78863 L p .855 .704 .694 r F P 0 g s .20658 .73761 m .23107 .78863 L .1843 .87737 L p .832 .671 .684 r F P 0 g s .51925 .38911 m .54216 .45335 L .50025 .45203 L p .529 .493 .76 r F P 0 g s .50025 .45203 m .47755 .38865 L .51925 .38911 L p .529 .493 .76 r F P 0 g s .67576 .58711 m .69686 .61784 L .65161 .59219 L p .083 .391 .85 r F P 0 g s .65161 .59219 m .63035 .56175 L .67576 .58711 L p .083 .391 .85 r F P 0 g s .56661 .89023 m .4928 .89879 L .45101 .8736 L p .488 .791 .998 r F P 0 g s .37924 .86141 m .45101 .8736 L .4928 .89879 L p .165 .616 .936 r F P 0 g s .47366 .23 m .45145 .13699 L .49267 .14358 L p .48 .397 .684 r F P 0 g s .13967 .5151 m .16063 .60014 L .11243 .68668 L p .776 .597 .657 r F P 0 g s .11243 .68668 m .09138 .59995 L .13967 .5151 L p .776 .597 .657 r F P 0 g s .21147 .61667 m .22435 .57648 L .2171 .51419 L p 0 0 .336 r F P 0 g s .23838 .47956 m .2171 .51419 L .22435 .57648 L p .032 0 .424 r F P 0 g s .21147 .61667 m .22435 .57648 L p .23792 .69808 L .077 .131 .617 r F P 0 g s .23792 .69808 m .22612 .67915 L .21147 .61667 L p .077 .131 .617 r F P 0 g s .66898 .30975 m .67994 .30613 L p .76211 .38255 L .794 .304 .038 r F P 0 g s .66898 .30975 m .6528 .2947 L .67994 .30613 L closepath p .697 .164 0 r F P 0 g s .1843 .87737 m .15915 .82612 L .20658 .73761 L p .832 .671 .684 r F P 0 g s .18301 .67459 m .20658 .73761 L .15915 .82612 L p .811 .643 .674 r F P 0 g s .23981 .71592 m .23792 .69808 L p .30756 .80088 L .092 .3 .779 r F P 0 g s .23981 .71592 m .22612 .67915 L .23792 .69808 L closepath p 0 .004 .575 r F P 0 g s .16063 .60014 m .18301 .67459 L .1351 .76235 L p .793 .619 .665 r F P 0 g s .1351 .76235 m .11243 .68668 L .16063 .60014 L p .793 .619 .665 r F P 0 g s .58544 .4655 m .60822 .51948 L .56482 .50648 L p .426 .47 .802 r F P 0 g s .56482 .50648 m .54216 .45335 L .58544 .4655 L p .426 .47 .802 r F P 0 g s .3675 .34 m .38979 .29919 L .46839 .2787 L p .394 0 .142 r F P 0 g s .38979 .29919 m .3675 .34 L .30151 .37461 L p .131 0 .012 r F P 0 g s .45101 .8736 m .37924 .86141 L .33501 .81362 L p .368 .608 .942 r F P 0 g s .15915 .82612 m .1351 .76235 L .18301 .67459 L p .811 .643 .674 r F P 0 g s .81872 .55897 m .83986 .60656 L .8128 .68587 L p .984 .853 .63 r F P 0 g s .83986 .60656 m .81872 .55897 L .82351 .48789 L p .992 .766 .39 r F P 0 g s .6528 .2947 m .66898 .30975 L .65613 .33132 L p .692 .233 .158 r F P 0 g s .49267 .14358 m .5156 .23826 L .47366 .23 L p .48 .397 .684 r F P 0 g s .71847 .8072 m .74859 .77759 L .74057 .81162 L closepath p .86 .977 .859 r F P 0 g s .79267 .72084 m .74859 .77759 L .74057 .81162 L p .89 .99 .764 r F P 0 g s .6423 .85976 m .71847 .8072 L .74057 .81162 L p .758 .978 .917 r F P 0 g s .88779 .79941 m .90249 .79126 L .84845 .72628 L p .781 .285 .02 r F P 0 g s .84845 .72628 m .8329 .73258 L .88779 .79941 L p .781 .285 .02 r F P 0 g s .56224 .40018 m .58544 .4655 L .54216 .45335 L p .451 .446 .762 r F P 0 g s .54216 .45335 m .51925 .38911 L .56224 .40018 L p .451 .446 .762 r F P 0 g s .65361 .54419 m .67576 .58711 L .63035 .56175 L p .229 .405 .83 r F P 0 g s .63035 .56175 m .60822 .51948 L .65361 .54419 L p .229 .405 .83 r F P 0 g s .53887 .32415 m .56224 .40018 L .51925 .38911 L p .466 .427 .73 r F P 0 g s .23792 .69808 m .29049 .73806 L p .30756 .80088 L .092 .3 .779 r F P 0 g s .29049 .73806 m .23792 .69808 L .25637 .64599 L closepath p .243 .319 .743 r F P 0 g s .24864 .61338 m .25637 .64599 L .23792 .69808 L p .077 .131 .617 r F P 0 g s .22435 .57648 m .24864 .61338 L p .23792 .69808 L .077 .131 .617 r F P 0 g s .46839 .2787 m .44856 .31925 L .3675 .34 L p .394 0 .142 r F P 0 g s .77879 .44399 m .82351 .48789 L .81872 .55897 L p .952 .695 .51 r F P 0 g s .82351 .48789 m .77879 .44399 L .76211 .38255 L p .93 .548 .225 r F P 0 g s .69338 .34398 m .76211 .38255 L .77879 .44399 L p .874 .514 .362 r F P 0 g s .76211 .38255 m .69338 .34398 L .66898 .30975 L p .794 .304 .038 r F P 0 g s .33501 .81362 m .30756 .80088 L .3053 .76633 L closepath p .247 .443 .856 r F P 0 g s .29049 .73806 m .3053 .76633 L .30756 .80088 L p .092 .3 .779 r F P 0 g s .5156 .23826 m .49267 .14358 L .53536 .16018 L p .424 .36 .681 r F P 0 g s .6423 .85976 m .56661 .89023 L .52632 .86433 L p .683 .858 .966 r F P 0 g s .45101 .8736 m .52632 .86433 L .56661 .89023 L p .488 .791 .998 r F P 0 g s .69338 .34398 m .65613 .33132 L .66898 .30975 L closepath p .769 .327 .202 r F P 0 g s .28962 .43289 m .30151 .37461 L .3675 .34 L p .358 .088 .361 r F P 0 g s .30151 .37461 m .28962 .43289 L .23838 .47956 L p .095 0 .261 r F P 0 g s .2389 .55381 m .23838 .47956 L .28962 .43289 L p .292 .15 .51 r F P 0 g s .22435 .57648 m .2389 .55381 L .23838 .47956 L p .032 0 .424 r F P 0 g s .63062 .48921 m .65361 .54419 L .60822 .51948 L p .311 .399 .792 r F P 0 g s .60822 .51948 m .58544 .4655 L .63062 .48921 L p .311 .399 .792 r F P 0 g s .8128 .68587 m .79051 .63983 L .81872 .55897 L p .984 .853 .63 r F P 0 g s .53536 .16018 m .55914 .25703 L .5156 .23826 L p .424 .36 .681 r F P 0 g s .24864 .61338 m .22435 .57648 L .2389 .55381 L closepath p .212 .181 .604 r F P 0 g s .74859 .77759 m .79267 .72084 L .75919 .69363 L p .904 .887 .804 r F P 0 g s .71847 .8072 m .6423 .85976 L .60386 .83261 L p .792 .876 .908 r F P 0 g s .52632 .86433 m .60386 .83261 L .6423 .85976 L p .683 .858 .966 r F P 0 g s .60704 .42255 m .63062 .48921 L .58544 .4655 L p .36 .389 .756 r F P 0 g s .58544 .4655 m .56224 .40018 L .60704 .42255 L p .36 .389 .756 r F P 0 g s .33501 .81362 m .40742 .82492 L .45101 .8736 L p .368 .608 .942 r F P 0 g s .36277 .75199 m .40742 .82492 L .33501 .81362 L p .446 .555 .873 r F P 0 g s .31398 .74546 m .36277 .75199 L p .33501 .81362 L .446 .555 .873 r F P 0 g s .33501 .81362 m .3053 .76633 L .31398 .74546 L p .446 .555 .873 r F P 0 g s .52632 .86433 m .45101 .8736 L .40742 .82492 L p .565 .701 .933 r F P 0 g s .74859 .77759 m .71847 .8072 L .68221 .77829 L p .857 .876 .852 r F P 0 g s .68221 .77829 m .72879 .73254 L .74859 .77759 L p .857 .876 .852 r F P 0 g s .75919 .69363 m .72879 .73254 L .74859 .77759 L p .904 .887 .804 r F P 0 g s .60386 .83261 m .68221 .77829 L .71847 .8072 L p .792 .876 .908 r F P 0 g s .871 .79513 m .88779 .79941 L .8329 .73258 L p .744 .228 0 r F P 0 g s .8329 .73258 m .81549 .72701 L .871 .79513 L p .744 .228 0 r F P 0 g s .77296 .51596 m .81872 .55897 L .79051 .63983 L p .922 .75 .651 r F P 0 g s .81872 .55897 m .77296 .51596 L .77879 .44399 L p .952 .695 .51 r F P 0 g s .77879 .44399 m .70869 .40575 L .69338 .34398 L p .874 .514 .362 r F P 0 g s .65613 .33132 m .69338 .34398 L .70869 .40575 L p .811 .473 .417 r F P 0 g s .55914 .25703 m .53536 .16018 L .5801 .18765 L p .362 .319 .675 r F P 0 g s .35716 .39846 m .3675 .34 L .44856 .31925 L p .527 .233 .411 r F P 0 g s .3675 .34 m .35716 .39846 L .28962 .43289 L p .358 .088 .361 r F P 0 g s .2389 .55381 m .29113 .50825 L p .271 .6292 L .397 .311 .641 r F P 0 g s .271 .6292 m .24864 .61338 L .2389 .55381 L p .397 .311 .641 r F P 0 g s .28962 .43289 m .29113 .50825 L .2389 .55381 L p .292 .15 .51 r F P 0 g s .3053 .76633 m .29049 .73806 L .31398 .74546 L closepath p .378 .476 .833 r F P 0 g s .70869 .40575 m .77879 .44399 L .77296 .51596 L p .876 .615 .541 r F P 0 g s .70869 .40575 m .65136 .38685 L .65613 .33132 L p .811 .473 .417 r F P 0 g s .31398 .74546 m .29049 .73806 L .25637 .64599 L p .433 .438 .765 r F P 0 g s .25637 .64599 m .24864 .61338 L .271 .6292 L closepath p .349 .317 .681 r F P 0 g s .5801 .18765 m .60489 .28723 L .55914 .25703 L p .362 .319 .675 r F P 0 g s .29113 .50825 m .28962 .43289 L .35716 .39846 L p .469 .285 .548 r F P 0 g s .60386 .83261 m .52632 .86433 L .48377 .81452 L p .689 .747 .896 r F P 0 g s .40742 .82492 m .48377 .81452 L .52632 .86433 L p .565 .701 .933 r F P 0 g s .25637 .64599 m .271 .6292 L p .31398 .74546 L .433 .438 .765 r F P 0 g s .44032 .37778 m .44856 .31925 L .54329 .31328 L p .636 .329 .434 r F P 0 g s .44856 .31925 m .44032 .37778 L .35716 .39846 L p .527 .233 .411 r F P 0 g s .63062 .48921 m .60704 .42255 L .6543 .45721 L p .257 .324 .741 r F P 0 g s .79051 .63983 m .74324 .5982 L .77296 .51596 L p .922 .75 .651 r F P 0 g s .60331 .37728 m .53763 .37184 L .54329 .31328 L p .71 .394 .442 r F P 0 g s .54329 .31328 m .53763 .37184 L .44032 .37778 L p .636 .329 .434 r F P 0 g s .48377 .81452 m .40742 .82492 L .36277 .75199 L p .581 .622 .858 r F P 0 g s .36277 .75199 m .31398 .74546 L .34495 .71345 L closepath p .478 .509 .812 r F P 0 g s .31874 .64224 m .34495 .71345 L .31398 .74546 L p .433 .438 .765 r F P 0 g s .271 .6292 m .31874 .64224 L p .31398 .74546 L .433 .438 .765 r F P 0 g s .85216 .77764 m .871 .79513 L .81549 .72701 L p .635 .138 0 r F P 0 g s .81549 .72701 m .79629 .70889 L .85216 .77764 L p .635 .138 0 r F P 0 g s .68221 .77829 m .60386 .83261 L .56274 .78142 L p .768 .769 .854 r F P 0 g s .48377 .81452 m .56274 .78142 L .60386 .83261 L p .689 .747 .896 r F P 0 g s .31874 .64224 m .271 .6292 L .30679 .59985 L closepath p .456 .409 .717 r F P 0 g s .29113 .50825 m .30679 .59985 L .271 .6292 L p .397 .311 .641 r F P 0 g s .72879 .73254 m .75919 .69363 L .72163 .63469 L p .851 .77 .772 r F P 0 g s .70124 .47846 m .77296 .51596 L .74324 .5982 L p .859 .668 .643 r F P 0 g s .77296 .51596 m .70124 .47846 L .70869 .40575 L p .876 .615 .541 r F P 0 g s .72879 .73254 m .68221 .77829 L .64283 .72547 L p .821 .78 .814 r F P 0 g s .64283 .72547 m .67469 .69424 L .72879 .73254 L p .821 .78 .814 r F P 0 g s .72163 .63469 m .67469 .69424 L .72879 .73254 L p .851 .77 .772 r F P 0 g s .60489 .28723 m .5801 .18765 L .62757 .22715 L p .295 .275 .666 r F P 0 g s .56274 .78142 m .64283 .72547 L .68221 .77829 L p .768 .769 .854 r F P 0 g s .36001 .4746 m .35716 .39846 L .44032 .37778 L p .587 .375 .56 r F P 0 g s .35716 .39846 m .36001 .4746 L .29113 .50825 L p .469 .285 .548 r F P 0 g s .30679 .59985 m .29113 .50825 L .36001 .4746 L p .526 .4 .652 r F P 0 g s .36277 .75199 m .43968 .74004 L .48377 .81452 L p .581 .622 .858 r F P 0 g s .4129 .68091 m .43968 .74004 L .36277 .75199 L p .581 .565 .801 r F P 0 g s .36277 .75199 m .34495 .71345 L .4129 .68091 L p .581 .565 .801 r F P 0 g s .56274 .78142 m .48377 .81452 L .43968 .74004 L p .673 .663 .832 r F P 0 g s .62972 .37747 m .60489 .28723 L .65354 .33011 L p .262 .272 .682 r F P 0 g s .62757 .22715 m .65354 .33011 L .60489 .28723 L p .295 .275 .666 r F P 0 g s .83139 .7464 m .85216 .77764 L .79629 .70889 L p 0 0 .526 r F P 0 g s .79629 .70889 m .77542 .67773 L .83139 .7464 L p 0 0 .526 r F P 0 g s .39521 .63242 m .4129 .68091 L .34495 .71345 L p .562 .515 .76 r F P 0 g s .34495 .71345 m .31874 .64224 L .39521 .63242 L p .562 .515 .76 r F P 0 g s .44485 .45438 m .44032 .37778 L .53763 .37184 L p .669 .437 .561 r F P 0 g s .44032 .37778 m .44485 .45438 L .36001 .4746 L p .587 .375 .56 r F P 0 g s .65354 .33011 m .67937 .42333 L .62972 .37747 L p .262 .272 .682 r F P 0 g s .66228 .46614 m .58879 .45212 L .60331 .37728 L p .772 .525 .562 r F P 0 g s .53763 .37184 m .60331 .37728 L .58879 .45212 L p .727 .481 .554 r F P 0 g s .31874 .64224 m .30679 .59985 L .37678 .5676 L p .557 .473 .715 r F P 0 g s .36001 .4746 m .37678 .5676 L .30679 .59985 L p .526 .4 .652 r F P 0 g s .37678 .5676 m .39521 .63242 L .31874 .64224 L p .557 .473 .715 r F P 0 g s .58879 .45212 m .5441 .44857 L .53763 .37184 L p .727 .481 .554 r F P 0 g s .53763 .37184 m .5441 .44857 L .44485 .45438 L p .669 .437 .561 r F P 0 g s .69452 .57415 m .72163 .63469 L .67469 .69424 L p .802 .685 .736 r F P 0 g s .64283 .72547 m .56274 .78142 L .51957 .70542 L p .738 .689 .804 r F P 0 g s .43968 .74004 m .51957 .70542 L .56274 .78142 L p .673 .663 .832 r F P 0 g s .37678 .5676 m .36001 .4746 L .44485 .45438 L p .617 .462 .649 r F P 0 g s .64283 .72547 m .67469 .69424 L .61505 .67416 L closepath p .785 .706 .777 r F P 0 g s .66489 .56336 m .69452 .57415 L p .67469 .69424 L .802 .685 .736 r F P 0 g s .60081 .64368 m .66489 .56336 L p .67469 .69424 L .802 .685 .736 r F P 0 g s .67469 .69424 m .61505 .67416 L .60081 .64368 L p .802 .685 .736 r F P 0 g s .80885 .70118 m .83139 .7464 L .77542 .67773 L p 0 .066 .63 r F P 0 g s .77542 .67773 m .75306 .63334 L .80885 .70118 L p 0 .066 .63 r F P 0 g s .61505 .67416 m .64283 .72547 L p .51957 .70542 L .738 .689 .804 r F P 0 g s .50192 .66545 m .51957 .70542 L .43968 .74004 L p .655 .603 .784 r F P 0 g s .43968 .74004 m .4129 .68091 L .50192 .66545 L p .655 .603 .784 r F P 0 g s .66228 .46614 m .68028 .53375 L .66489 .56336 L p .769 .585 .649 r F P 0 g s .58879 .45212 m .66228 .46614 L p .66489 .56336 L .769 .585 .649 r F P 0 g s .69452 .57415 m .68028 .53375 L .66489 .56336 L closepath p .82 .651 .673 r F P 0 g s .65354 .33011 m .62757 .22715 L .6786 .28029 L p .226 .228 .652 r F P 0 g s .44485 .45438 m .5441 .44857 L p .52972 .54451 L .683 .505 .641 r F P 0 g s .52972 .54451 m .46281 .54822 L .44485 .45438 L p .683 .505 .641 r F P 0 g s .44485 .45438 m .46281 .54822 L .37678 .5676 L p .617 .462 .649 r F P 0 g s .39521 .63242 m .37678 .5676 L .46281 .54822 L p .632 .518 .707 r F P 0 g s .47534 .59188 m .50192 .66545 L .4129 .68091 L p .651 .565 .745 r F P 0 g s .4129 .68091 m .39521 .63242 L .47534 .59188 L p .651 .565 .745 r F P 0 g s .55684 .51104 m .58879 .45212 L p .66489 .56336 L .769 .585 .649 r F P 0 g s .55684 .51104 m .58879 .45212 L .5441 .44857 L closepath p .732 .538 .629 r F P 0 g s .46281 .54822 m .47534 .59188 L .39521 .63242 L p .632 .518 .707 r F P 0 g s .78475 .64208 m .80885 .70118 L .75306 .63334 L p 0 .134 .672 r F P 0 g s .75306 .63334 m .72943 .57581 L .78475 .64208 L p 0 .134 .672 r F P 0 g s .60081 .64368 m .66489 .56336 L .56575 .54547 L closepath p .763 .623 .705 r F P 0 g s .66489 .56336 m .56575 .54547 L .55684 .51104 L p .769 .585 .649 r F P 0 g s .5441 .44857 m .55684 .51104 L .52972 .54451 L p .683 .505 .641 r F P 0 g s .51957 .70542 m .5737 .66723 L .61505 .67416 L p .738 .689 .804 r F P 0 g s .61505 .67416 m .60081 .64368 L .5737 .66723 L closepath p .75 .664 .766 r F P 0 g s .51957 .70542 m .5737 .66723 L .50192 .66545 L closepath p .712 .63 .765 r F P 0 g s .67937 .42333 m .65354 .33011 L .70596 .3874 L p .182 .218 .664 r F P 0 g s .6786 .28029 m .70596 .3874 L .65354 .33011 L p .226 .228 .652 r F P 0 g s .56575 .54547 m .60081 .64368 L .5737 .66723 L p .715 .599 .725 r F P 0 g s .52972 .54451 m .56575 .54547 L p .5737 .66723 L .715 .599 .725 r F P 0 g s .47534 .59188 m .52972 .54451 L p .5737 .66723 L .715 .599 .725 r F P 0 g s .5737 .66723 m .50192 .66545 L .47534 .59188 L p .715 .599 .725 r F P 0 g s .75937 .56951 m .78475 .64208 L .72943 .57581 L p .037 .176 .68 r F P 0 g s .72943 .57581 m .70477 .50557 L .75937 .56951 L p .037 .176 .68 r F P 0 g s .70477 .50557 m .67937 .42333 L .733 .48426 L p .122 .202 .675 r F P 0 g s .70596 .3874 m .733 .48426 L .67937 .42333 L p .182 .218 .664 r F P 0 g s .56575 .54547 m .55684 .51104 L .52972 .54451 L closepath p .716 .553 .668 r F P 0 g s .47534 .59188 m .52972 .54451 L .46281 .54822 L closepath p .688 .552 .695 r F P 0 g s .733 .48426 m .75937 .56951 L .70477 .50557 L p .122 .202 .675 r F P 0 g s .25 Mabswid .67245 0 m .92713 .41497 L s .92713 .41497 m 1 .94814 L s 1 .94814 m .70644 .58546 L s .70644 .58546 m .67245 0 L s .08846 .24555 m 0 .80374 L s 0 .80374 m .70644 .58546 L s .70644 .58546 m .67245 0 L s .67245 0 m .08846 .24555 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[43]:=", ImageSize->{144.3125, 156.625}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg?oo0`009ooo00<00?ooool01Ooo00<00?ooool09?oo000fool2000Zool00`00oooo o`06ool00`00ooooo`0Sool003Coo`8002coo`03003ooooo00Ooo`03003ooooo02;oo`00G[003002G[9N/00>G[0030026[8J/00>6[003001f [7J/00Af[003001U[6F/009U[004001E[000000Aool00`00ooooo`0:ool00`00ooooo`0Oool002?o o`8000Woo`8000JG[003002G[9N/00:G[0030026[8J/00>6[003001f[7J/00Af[003001U[6F/009U 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o`05003oooooool00001ool001Ooo`8000Goo`03003[]>^d00;[]003003/]>bd00;/]005003m]?fd oK@00002o[@01000oZcn[0001ooo00<00?ooool0Cooo00@00?ooool0007oo`006Ooo00<00?ooool0 0_oo00<00>^djk@00^^d00<00>bdk;@00^bd00D00?fdoKCm]00000;n]0<000Soo`03003ooooo04oo o`04003ooooo0001ool001[oo`03003ooooo00;oo`04003[]>^d0004k;@01@00oKCm]?fd00000_jd 0P002_oo00<00?ooool0D?oo00<00?ooool00@00000Kool20003ool00`00jk@00004k;@01@00oKCm ]?fd00000_jd00<00?ooool02Ooo00<00?ooool0DOoo0@000Ooo0@00000Mool01000oooooooo0P00 0nbd00H00?fdoKCm]000o[@2000_oo000bool20005ool00`00ooooo`0Bool5 000nool003Coo`03003ooooo00;oo`03003ooooo00koo`@004?oo`00=Ooo00D00?ooooooo`0000[o o`H004Ooo`00=_oo0P0000?oo`00ool01Ooo1000COoo000hool200000ooo00000003001Aool003Wo o`8005Koo`00\ \>"], ImageRangeCache->{{{0, 143.3125}, {155.625, 0}} -> {0.04864, -0.000182, 0.005984, 0.005984}}] }, Open ]], Cell["\<\ To determine a representation for the curve of intersection we can \ simultaneously solve the equations that represent these two surfaces.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(solution = Solve[{x\^2 + y\^2 + z\^2 == 1, z == x\^2 - y\^2}, {x, z}]\)], "Input", CellLabel->"In[44]:="], Cell[BoxData[ \({{z \[Rule] 1\/2\ \((\(-1\) - \@\(5 - 8\ y\^2\))\), x \[Rule] \(-\(\@\(\(-1\) + 2\ y\^2 - \@\(5 - 8\ y\^2\)\)\/\@2\)\)}, { z \[Rule] 1\/2\ \((\(-1\) - \@\(5 - 8\ y\^2\))\), x \[Rule] \@\(\(-1\) + 2\ y\^2 - \@\(5 - 8\ y\^2\)\)\/\@2}, { z \[Rule] 1\/2\ \((\(-1\) + \@\(5 - 8\ y\^2\))\), x \[Rule] \(-\(\@\(\(-1\) + 2\ y\^2 + \@\(5 - 8\ y\^2\)\)\/\@2\)\)}, { z \[Rule] 1\/2\ \((\(-1\) + \@\(5 - 8\ y\^2\))\), x \[Rule] \@\(\(-1\) + 2\ y\^2 + \@\(5 - 8\ y\^2\)\)\/\@2}}\)], "Output", CellLabel->"Out[44]="] }, Open ]], Cell[TextData[{ "This produces 4 parametrizations, with parameter ", Cell[BoxData[ \(TraditionalForm\`\(y, \)\)]], " for parts of the curve of intersection. From the solution it is evident \ that the values of ", Cell[BoxData[ \(TraditionalForm\`y\)]], " are restricted to be at least between ", Cell[BoxData[ \(TraditionalForm\`\(\[PlusMinus]\@\(5/8\)\)\)]], ". 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ImageRangeCache->{{{0, 143}, {141.5625, 0}} -> {-0.122621, -0.064314, 0.007418, 0.007418}}] }, Open ]], Cell[TextData[{ "\tUnfortunately, this is not a very general method because it relies \ heavily on our ability to algebraically solve for two of the three \ coordinate variables in terms of the remaining one. This will almost never \ work if one or both of the surfaces are non-algebraic. For example, try it on \ a sphere and the trigonometric surface ", Cell[BoxData[ \(TraditionalForm\`z = \(sin(x\ y).\)\)]], " Even if both surfaces are algebraic as in the first example, we have \ already seen that certain undesirable effects can occur. In particular, that \ first example had four parametrizations with different domains for one \ connected intersection component.\n\tLet me present a technique for deriving \ parametrizations for the curves of intersection that overcome some of these \ limitations. Furthermore, the algorithm gives you control over the type of \ parametrization you wish to obtain. The only restrictions on this technique \ are that it will only give the curves of intersection one connected component \ at a time, the surfaces must be sufficiently smooth or differentiable, and \ you need to know at least one point on the curve to get the algorithm \ started.\n\tThe algorithm involves solving a system of ordinary differential \ equations with an initial condition. The method is a variation of an \ algorithm first presented by [Bajaj, Hoffmann, and Lynch 1988] in which they \ used Taylor polynomials to approximate the curve. By setting the problem up \ as an initial-value problem, all the details on the accuracy and precision of \ the approximations can be left to the differential equations solver, here the \ ", StyleBox["NDSolve", "Input"], " command.\n\tI have implemented this algorithm in a ", StyleBox["Mathematica", FontSlant->"Italic"], " package called ", StyleBox["ParametrizeCurve`", "Input"], ". The syntax of the one command is very similar to that of the ", StyleBox["NDSolve", "Input"], " command since it is based on it. As an example of its use, let\ \[CloseCurlyQuote]s find a parametrization for the intersection of the sphere \ centered at the origin of radius 2 and the trigonometric surface ", Cell[BoxData[ \(TraditionalForm\`z = sin(x\ y)\)]], ". The command requires a rough approximation to one point on the \ intersection, and a quick check shows that the point ", Cell[BoxData[ \(TraditionalForm\`\((\@2, 0, 0)\)\)]], " lies on the curve. After finding a parametrization of the intersection we \ will plot it and determine its length." }], "Text"], Cell[BoxData[ \(Needs["\"]\)], "Input", CellLabel->"In[48]:="], Cell[CellGroupData[{ Cell[BoxData[ \(solution\ = \ \n ParametrizeCurve[{x\^2 + y\^2 + z\^2 == 2, z == Sin[x\ y], x[0] == \@2, y[0] == 0, z[0] == 0}, {x, y, z}, {t, 0, 11}]\)], "Input", CellLabel->"In[49]:="], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 11.0000000000000008`}}, "<>"] \), False, Editable->False]}], ",", RowBox[{"y", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 11.0000000000000008`}}, "<>"] \), False, Editable->False]}], ",", RowBox[{"z", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 11.0000000000000008`}}, "<>"] \), False, Editable->False]}]}], "}"}]], "Output", CellLabel->"Out[49]="] }, Open ]], Cell[BoxData[ \(\(r[t_] := Evaluate[{x[t], y[t], z[t]} /. solution]; \)\)], "Input", CellLabel->"In[50]:="], Cell[BoxData[ 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L .34112 .37509 L .898 .899 .819 r F .30293 .43091 m .37631 .34319 L .36732 .39573 L .364 .096 .367 r F .36459 .39976 m .36732 .39573 L .36682 .39863 L F .30293 .43091 m .36732 .39573 L .36459 .39976 L F .30393 .45754 m .36753 .45538 L .34266 .48537 L .86 .802 .792 r F .30393 .45754 m .34229 .41157 L .36753 .45538 L F .27572 .4532 m .30393 .45754 L .34229 .41157 L .898 .899 .819 r F .31523 .52717 m .34266 .48537 L .30393 .45754 L .884 .79 .752 r F .31523 .52717 m .30393 .45754 L .28505 .48596 L F .28505 .48596 m .27572 .4532 L .30393 .45754 L .923 .87 .768 r F .30462 .50206 m .30293 .43091 L .36459 .39976 L .473 .289 .55 r F .35939 .41099 m .36459 .39976 L .36682 .39863 L F .30462 .50206 m .36459 .39976 L .35939 .41099 L F .33697 .48074 m .32955 .47546 L .34473 .44267 L .91 .818 .744 r F .34266 .48537 m .36753 .45538 L .41492 .48914 L .816 .721 .759 r F .41492 .48914 m .40423 .41978 L .36753 .45538 L .795 .728 .79 r F .34266 .48537 m .41492 .48914 L .37846 .53345 L .816 .721 .759 r F 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L .25618 .67682 L F .258 .65837 m .25618 .67682 L .26292 .66607 L F .26169 .67168 m .2438 .67306 L .24042 .61434 L .973 .671 .376 r F .27656 .7118 m .25158 .68226 L .26231 .67336 L F .25175 .68665 m .25009 .68381 L .25226 .68306 L .871 .454 .016 r F .25009 .68381 m .25051 .68338 L .25226 .68306 L F .2499 .68349 m .25103 .68161 L .25226 .68306 L F .27656 .7118 m .26084 .66939 L .27259 .6537 L .973 .671 .376 r F .24906 .68489 m .24856 .68527 L .2489 .68506 L 0 0 0 r F .25033 .68809 m .24973 .6881 L .24864 .68533 L .871 .454 .016 r F .29876 .76702 m .24864 .68533 L .25009 .68381 L F .25175 .68665 m .25226 .68306 L .27656 .7118 L F .24856 .68527 m .24917 .68575 L .27691 .66742 L 0 0 0 r F .25009 .68381 m .24864 .68533 L .2438 .67306 L .871 .454 .016 r F .24856 .68527 m .24032 .6916 L .24663 .68742 L 0 0 0 r F .2487 .68549 m .24865 .68534 L .24864 .68533 L 0 0 .291 r F .29876 .76702 m .26574 .72872 L .24973 .6881 L .871 .454 .016 r F .29876 .76702 m .24973 .6881 L .25033 .68809 L F .26574 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L F .26942 .61409 m .27392 .60618 L .27332 .60745 L F .24876 .6492 m .23029 .64869 L .27071 .6093 L F .24876 .6492 m .27071 .6093 L .26942 .61409 L F .25983 .64951 m .24876 .6492 L .26942 .61409 L F .25983 .64951 m .26833 .61811 L .26945 .62282 L .09 .14 .621 r F .27358 .60764 m .27332 .60745 L .27513 .60437 L .402 .315 .643 r F .27427 .60583 m .23029 .64869 L .2747 .60451 L .87 .952 .861 r F .29434 .56351 m .25497 .54494 L .30462 .50206 L .402 .315 .643 r F .29223 .57615 m .29068 .57486 L .29434 .56351 L F .29068 .57486 m .25497 .54494 L .29434 .56351 L F .31941 .55418 m .29987 .54635 L .33697 .48074 L .909 .867 .786 r F .29987 .54635 m .30794 .5213 L .33697 .48074 L F .30794 .5213 m .30462 .50206 L .31851 .49532 L .528 .402 .652 r F .33697 .48074 m .34473 .44267 L .38265 .41591 L .91 .818 .744 r F .30462 .50206 m .36682 .39863 L .34694 .43827 L .473 .289 .55 r F .34473 .44267 m .36682 .39863 L .38265 .41591 L .91 .818 .744 r F .30462 .50206 m .36719 .40774 L .31851 .49532 L .473 .289 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r F .32955 .47546 m .31861 .46767 L .34473 .44267 L F .34868 .42326 m .30886 .46073 L .35608 .38692 L F .31861 .46767 m .30886 .46073 L .34868 .42326 L F .39133 .37119 m .35608 .38692 L .40229 .31469 L .889 .781 .735 r F .36682 .39863 m .35608 .38692 L .39133 .37119 L F .43159 .33141 m .43457 .32841 L .43504 .32829 L .53 .238 .415 r F .34937 .32637 m .43212 .28609 L .41574 .28992 L .535 .922 .824 r F .41574 .28992 m .43212 .28609 L .50597 .27017 L 0 0 0 r F .41574 .28992 m .50597 .27017 L .48296 .27559 L F .39709 .30414 m .41574 .28992 L .48296 .27559 L .138 0 0 r F .39709 .30414 m .48296 .27559 L .47144 .28494 L F .43159 .33141 m .40229 .31469 L .44736 .24945 L .859 .746 .737 r F .4209 .3422 m .40229 .31469 L .43159 .33141 L F .43159 .33141 m .43181 .33025 L .43504 .32829 L F .43504 .32829 m .45395 .31675 L .43613 .32801 L .401 0 .153 r F .45719 .31471 m .47144 .28494 L .50504 .29468 L .562 .155 .227 r F .45395 .31675 m .44736 .24945 L .47178 .29281 L .859 .746 .737 r F .43181 .33025 m .44736 .24945 L .45395 .31675 L F .45228 .3887 m .4547 .31575 L .46827 .31007 L .847 .744 .749 r F .43613 .32801 m .45719 .31471 L .45285 .32377 L .401 0 .153 r F .45468 .31629 m .45395 .31675 L .4547 .31575 L .847 .744 .749 r F .46827 .31007 m .4547 .31575 L .47178 .29281 L F .50504 .29468 m .47144 .28494 L .5291 .28126 L .562 .155 .227 r F .45285 .32377 m .45719 .31471 L .50504 .29468 L F .45285 .32377 m .49129 .30234 L .55285 .29207 L F .49129 .30234 m .50094 .29696 L .5098 .29613 L F .49129 .30234 m .5098 .29613 L .55285 .29207 L F .46827 .31007 m .47178 .29281 L .47928 .30637 L .847 .744 .749 r F .5291 .28126 m .47144 .28494 L .48296 .27559 L .389 0 0 r F .50345 .29837 m .51534 .24083 L .53793 .2885 L .813 .71 .752 r F .50345 .29837 m .47178 .29281 L .51534 .24083 L F .47928 .30637 m .47178 .29281 L .50345 .29837 L F .53855 .28831 m .53793 .2885 L .53869 .28765 L .802 .704 .758 r F .53893 .2882 m .54219 .28722 L .54252 .28737 L .562 .155 .227 r F .53896 .28822 m .54252 .28737 L 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Therefore, to \ determine the length of this intersection we only need to determine the \ period of the parametrization. Since the construction of this intersection \ was done numerically, we will determine its period by calculating the minimum \ value of ", Cell[BoxData[ \(TraditionalForm\`\(\(|r(t) - r(0)\)\(|\^2\)\)\)]], " for ", Cell[BoxData[ \(TraditionalForm\`t\)]], " around 11." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(FindMinimum[\((r[t] - r[0])\).\((r[t] - r[0])\), {t, 11}]\)], "Input", CellLabel->"In[53]:="], Cell[BoxData[ \({7.83820724364113186`*^-12, {t \[Rule] 10.5111036996646101`}}\)], "Output", CellLabel->"Out[53]="] }, Open ]], Cell["So, the approximate length of the intersection is 10.5111.", "Text"], Cell[CellGroupData[{ Cell["A tangential note on plotting curves on surfaces.", "Subsection"], Cell[TextData[{ "\tYou may have experienced the problem of plotting curves that lie on \ surfaces that the above picture points out. 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This is due to the fact that ", StyleBox["Mathematica", FontSlant->"Italic"], " plots surfaces as the union of polygonal pieces of planes and curves as \ the union of line segments. Whenever a curve is plotted with more points than \ a surface, as is usually the case, if the curve has nonzero curvature it will \ appear to lie on only one side of each polygon that makes up the surface. One \ way to ameliorate this situation is to slightly move the curve towards the \ viewer by translating the curve along the vector that points from the middle \ of the viewing box to the viewpoint. This can be done by using the options ", StyleBox["BoxRatios", "Input"], ", ", StyleBox["PlotRange", "Input"], " and ", StyleBox["ViewPoint", "Input"], " for the graphics. Here is how to obtain the values of those three options \ for ", StyleBox["hemisphere", "Input"], "." }], "Text"], Cell[BoxData[ \(\({boxratios, plotrange, viewpoint} = Map[FullOptions[hemisphere, #]&, {BoxRatios, PlotRange, ViewPoint}]; \)\)], "Input", CellLabel->"In[55]:="], Cell[TextData[{ StyleBox["ViewPoint", "Input"], " is actually given in a scaled coordinate system, and to use it we will \ need to convert it to the coordinate system of ", StyleBox["PlotRange", "Input"], "." }], "Text"], Cell[BoxData[ \(\(viewPtConverted\ = Apply[Plus, \ plotrange, \ {1}]/2\ + \ \n\ \ \ \((\(-viewpoint\)*Apply[Subtract, \ plotrange, \ {1}])\) Max[boxratios]/boxratios; \)\)], "Input", CellLabel->"In[56]:="], Cell["\<\ Define a parametrization of the lifted curve by bringing every \ point toward the view point by a certain percentage, say 3%.\ \>", "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(rLifted[t_]\), "=", "\n", "\t", RowBox[{\(r[t]\), "+", RowBox[{"0.03", RowBox[{ RowBox[{"(", 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.822 .647 .665 r F .3938 .65165 m .40438 .5962 L .39927 .59688 L F .3919 .58884 m .36982 .59199 L .40412 .59613 L .267 0 0 r F .3753 .60102 m .40104 .57913 L .36066 .56095 L .822 .647 .665 r F .3938 .65165 m .39925 .59703 L .3753 .60102 L F .39925 .59703 m .40104 .57913 L .3753 .60102 L F .40421 .59621 m .3813 .60527 L .41705 .60713 L .31 0 0 r F .40373 .59629 m .3813 .60527 L .40421 .59621 L F .40421 .59621 m .41705 .60713 L .40453 .5962 L F .40438 .5962 m .40453 .5962 L .40438 .5962 L .822 .647 .665 r F .37665 .59989 m .3813 .60527 L .40373 .59629 L .342 0 0 r F .43212 .5971 m .40412 .59613 L .4392 .60227 L .335 0 0 r F .39934 .5962 m .40725 .5962 L .40104 .57913 L .822 .647 .665 r F .41359 .59619 m .40615 .5962 L .43212 .5971 L .335 0 0 r F .40725 .5962 m .42423 .58699 L .40104 .57913 L .793 .634 .684 r F .41897 .59646 m .42423 .58699 L .40725 .5962 L F .41971 .59649 m .41897 .59646 L .41925 .59595 L .755 .584 .664 r F .43039 .59605 m .41925 .59595 L .42423 .58699 L F .35714 .60442 m .35721 .61866 L .3813 .60527 L .291 0 0 r F .31924 .61879 m .32173 .61775 L .34632 .60404 L .343 0 0 r F .32173 .61775 m .33632 .61164 L .34355 .60614 L F .32173 .61775 m .34355 .60614 L .34632 .60404 L F .32024 .68593 m .30027 .63178 L .33233 .62523 L .893 .675 .599 r F .30027 .63178 m .30469 .6289 L .33233 .62523 L F .28599 .62754 m .29072 .63801 L .31176 .6243 L .256 0 0 r F .3135 .62328 m .32239 .61821 L .33233 .62523 L .893 .675 .599 r F .3743 .59827 m .37351 .59612 L .33877 .61062 L .822 .647 .665 r F .34659 .60441 m .33783 .61087 L .33884 .61045 L .291 0 0 r F .34791 .60618 m .33884 .61045 L .34821 .60658 L F .34659 .60441 m .33884 .61045 L .34791 .60618 L F .34355 .60614 m .33632 .61164 L .34659 .60441 L F .33233 .62523 m .33044 .61441 L .33877 .61062 L .868 .707 .68 r F .33044 .61441 m .33632 .61164 L .33877 .61062 L F .33632 .61164 m .33761 .61103 L .34659 .60441 L .291 0 0 r F .33039 .61412 m .31523 .52717 L .33874 .6105 L .868 .707 .68 r F .33632 .61164 m .33874 .6105 L .33877 .61062 L F .33783 .61087 m .33761 .61103 L .33884 .61045 L .291 0 0 r F .33039 .61412 m .33874 .6105 L .33632 .61164 L .868 .707 .68 r F .33877 .61062 m .33874 .6105 L .33884 .61045 L F .37351 .59612 m .33884 .61045 L .33877 .61062 L .822 .647 .665 r F .31205 .60352 m .28599 .62754 L .30873 .62468 L .343 0 0 r F .31205 .60352 m .30873 .62468 L .31178 .62297 L F .31205 .60352 m .31176 .6243 L .31935 .61902 L F .33014 .61269 m .28572 .59231 L .31523 .52717 L .868 .707 .68 r F .33233 .62523 m .32145 .61755 L .33014 .61269 L F .32145 .61755 m .28572 .59231 L .33014 .61269 L F .31178 .62297 m .30873 .62468 L .31176 .6243 L .343 0 0 r F .33884 .61045 m .32127 .6231 L .34821 .60658 L .291 0 0 r F .33761 .61103 m .32127 .6231 L .33884 .61045 L F .33632 .61164 m .32127 .6231 L .33761 .61103 L F .33044 .61441 m .33039 .61412 L .33632 .61164 L .868 .707 .68 r F .33884 .61045 m .31523 .52717 L .36066 .56095 L F .33874 .6105 m .31523 .52717 L .33884 .61045 L F .34632 .60404 m .34355 .60614 L 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r F .24856 .68527 m .24032 .6916 L .24663 .68742 L 0 0 0 r F .2487 .68549 m .24865 .68534 L .24864 .68533 L 0 0 .291 r F .29876 .76702 m .26574 .72872 L .24973 .6881 L .871 .454 .016 r F .29876 .76702 m .24973 .6881 L .25033 .68809 L F .26574 .72872 m .25107 .68924 L .24949 .68674 L 0 0 .291 r F .24973 .6881 m .24949 .68674 L .2487 .68549 L F .26574 .72872 m .24949 .68674 L .24973 .6881 L F .25009 .68381 m .2499 .68349 L .25051 .68338 L .871 .454 .016 r F .26231 .67336 m .25103 .68161 L .26169 .67168 L .973 .671 .376 r F .25158 .68226 m .25103 .68161 L .26231 .67336 L F .25291 .67849 m .24906 .68489 L .26643 .67156 L 0 0 0 r F .25103 .68161 m .2438 .67306 L .26169 .67168 L .973 .671 .376 r F .2499 .68349 m .2438 .67306 L .25103 .68161 L .871 .454 .016 r F .2438 .67306 m .22455 .56687 L .24042 .61434 L .919 .666 .174 r F .2438 .67306 m .22768 .6263 L .22455 .56687 L F .24864 .68533 m .22768 .6263 L .2438 .67306 L 0 0 .291 r F .24865 .68534 m .22768 .6263 L .24864 .68533 L F .25107 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.31941 .55418 L .894 .924 .833 r F .27504 .60456 m .27549 .60361 L .31941 .55418 L F .30353 .60861 m .31941 .55418 L .34689 .5645 L F .28556 .61602 m .29161 .57982 L .31953 .58834 L .402 .315 .643 r F .29161 .57982 m .30462 .50206 L .30799 .52155 L F .29161 .57982 m .30799 .52155 L .31953 .58834 L F .25497 .54494 m .30293 .43091 L .30462 .50206 L .299 .157 .514 r F .29084 .54272 m .30886 .46073 L .32238 .47035 L .916 .854 .766 r F .31485 .49714 m .32238 .47035 L .32716 .47376 L F .29084 .54272 m .32238 .47035 L .31485 .49714 L F .29084 .54272 m .32716 .47376 L .30961 .5175 L F .30794 .5213 m .30883 .51855 L .30961 .5175 L .909 .867 .786 r F .34689 .5645 m .31941 .55418 L .36407 .49992 L .897 .882 .811 r F .31953 .58834 m .30794 .5213 L .36971 .47048 L .528 .402 .652 r F .30794 .5213 m .31957 .49481 L .36971 .47048 L F .29987 .54635 m .29084 .54272 L .30883 .51855 L .909 .867 .786 r F .2783 .59917 m .25497 .54494 L .29223 .57615 L .402 .315 .643 r F .2747 .60451 m .29084 .54272 L .29987 .54635 L .901 .902 .816 r F .2747 .60451 m .29987 .54635 L .27549 .60361 L F .27797 .59839 m .27769 .59845 L .27784 .59809 L .402 .315 .643 r F .28556 .61602 m .27358 .60764 L .27797 .59839 L F .27504 .60456 m .2747 .60451 L .27549 .60361 L .894 .924 .833 r F .27427 .60583 m .2747 .60451 L .27504 .60456 L .87 .952 .861 r F .28556 .61602 m .2783 .59917 L .29223 .57615 L .402 .315 .643 r F .25366 .68122 m .25672 .65814 L .27161 .63188 L .09 .14 .621 r F .25961 .65013 m .25983 .64951 L .26032 .64952 L .826 .959 .898 r F .25672 .65814 m .26945 .62282 L .27161 .63188 L .09 .14 .621 r F .21749 .68616 m .23029 .64869 L .25983 .64951 L .826 .959 .898 r F .21749 .68616 m .25983 .64951 L .25961 .65013 L F .24721 .67604 m .24359 .66383 L .25961 .65013 L .802 .994 .869 r F .25366 .68122 m .25002 .67015 L .25199 .66605 L .09 .14 .621 r F .25366 .68122 m .24857 .6732 L .25002 .67015 L F .2469 .67667 m .21749 .68616 L .24359 .66383 L .802 .994 .869 r F .24767 .67965 m .24522 .68018 L .2469 .67667 L F 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m .43181 .33025 L .43504 .32829 L F .43504 .32829 m .45395 .31675 L .43613 .32801 L .401 0 .153 r F .45719 .31471 m .47144 .28494 L .50504 .29468 L .562 .155 .227 r F .45395 .31675 m .44736 .24945 L .47178 .29281 L .859 .746 .737 r F .43181 .33025 m .44736 .24945 L .45395 .31675 L F .45228 .3887 m .4547 .31575 L .46827 .31007 L .847 .744 .749 r F .43613 .32801 m .45719 .31471 L .45285 .32377 L .401 0 .153 r F .45468 .31629 m .45395 .31675 L .4547 .31575 L .847 .744 .749 r F .46827 .31007 m .4547 .31575 L .47178 .29281 L F .50504 .29468 m .47144 .28494 L .5291 .28126 L .562 .155 .227 r F .45285 .32377 m .45719 .31471 L .50504 .29468 L F .45285 .32377 m .49129 .30234 L .55285 .29207 L F .49129 .30234 m .50094 .29696 L .5098 .29613 L F .49129 .30234 m .5098 .29613 L .55285 .29207 L F .46827 .31007 m .47178 .29281 L .47928 .30637 L .847 .744 .749 r F .5291 .28126 m .47144 .28494 L .48296 .27559 L .389 0 0 r F .50345 .29837 m .51534 .24083 L .53793 .2885 L .813 .71 .752 r F .50345 .29837 m 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m .75026 .54803 L .77926 .57801 L .41 .34 .667 r F .78065 .63438 m .75855 .57103 L .80341 .56551 L .587 .525 .753 r F .75855 .57103 m .78023 .49118 L .80341 .56551 L .624 .541 .741 r F .79675 .66964 m .80213 .5498 L .81793 .5845 L .982 .851 .634 r F .79675 .66964 m .81793 .5845 L .81685 .6114 L F .81695 .60905 m .81701 .60754 L .81739 .60874 L .587 .525 .753 r F .81193 .63561 m .81739 .60874 L .82627 .63617 L F .8019 .69207 m .81193 .63561 L .82627 .63617 L .551 .516 .77 r F .80252 .68742 m .80267 .68771 L .80287 .68663 L .94 .897 .499 r F .77797 .73394 m .80157 .6943 L .80044 .70247 L .502 .516 .804 r F .79653 .70132 m .80134 .69595 L .80252 .68742 L .94 .897 .499 r F .80044 .70247 m .80228 .6931 L .80403 .69744 L .502 .516 .804 r F .80157 .6943 m .80228 .6931 L .80044 .70247 L F .80403 .69744 m .80228 .6931 L .80654 .69368 L .522 .519 .794 r F .80403 .69744 m .80654 .69368 L .84837 .69934 L F .7933 .71397 m .79458 .71154 L .79602 .71021 L 0 0 0 r F .79458 .71154 m .79748 .70722 L 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0.006467, 0.006467}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["The Algorithm", "Subsection"], Cell[TextData[{ "If the two surfaces whose intersection we wish to parametrize are given by \ ", Cell[BoxData[ \(TraditionalForm\`\(F\_1\)(x, y, z) = 0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(\(F\_2\)(x, y, z) = 0, \)\)]], " and we already have a parametrization, ", Cell[BoxData[ \(TraditionalForm\`X(t) = \((x(t), y(t), z(t))\)\)]], ", of the intersection, then ", Cell[BoxData[ \(TraditionalForm\`\(F\_i\)(X(t)) = 0\)]], " for ", Cell[BoxData[ \(TraditionalForm\`i = 1, 2.\)]], " Differentiate these last two equations to get" }], "Text"], Cell[BoxData[ FormBox[ FormBox[ \(\[Del]F\_i \((X \((t)\))\)\[CenterDot]X\^\[Prime] \((t)\) = 0.\), "TextForm"], TraditionalForm]], "NumberedEquation"], Cell[TextData[{ "This says that ", Cell[BoxData[ \(TraditionalForm\`X(t)\)]], " is perpendicular to both the gradients ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2\)]], ". As long as these two gradients are linearly independent for points on \ the intersection, then ", Cell[BoxData[ \(TraditionalForm\`\(X\^\[Prime]\)(t)\)]], " is some multiple of the cross product ", Cell[BoxData[ \(TraditionalForm \`\(\[Del]\(\(F\_1\)(X(t))\)\[Times]\[Del]\(\(F\_2\)(X(t))\), \)\)]] }], "Text"], Cell[BoxData[ FormBox[ RowBox[{\(\(X\^\[Prime]\)(t)\), "=", RowBox[{\(\[Lambda](t)\), FormBox[\(\[Del]\(\(F\_1\)(X(t)) \)\[Times]\(\[Del]\(\(F\_2\)(X(t))\).\)\), "TraditionalForm"]}]}], TraditionalForm]], "NumberedEquation"], Cell[TextData[{ "For this problem we are given the two surfaces, ", Cell[BoxData[ \(TraditionalForm\`\(F\_1\)(x, y, z) = 0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(\(F\_2\)(x, y, z) = 0, \)\)]], " and we wish to find a parametrization for the intersection, ", Cell[BoxData[ \(TraditionalForm\`\(X(t).\)\)]], " Equation (2) is a differential equation in the unknown ", Cell[BoxData[ \(TraditionalForm\`\(X(t).\)\)]], " The appearance of the scalar function ", Cell[BoxData[ \(TraditionalForm\`\[Lambda](t)\)]], " is not incidental to the discussion. For if ", Cell[BoxData[ \(TraditionalForm\`X(t)\)]], " is a parametrization for this intersection, then so is any \ reparametrization of it. Moreover, the derivative of the reparametrization \ will be a scalar multiple of the derivative of the original parametrization. \ That is the source of ", Cell[BoxData[ \(TraditionalForm\`\(\[Lambda](t).\)\)]], " Choose ", Cell[BoxData[ \(TraditionalForm\`\[Lambda](t)\)]], " however you want to obtain the type of parametrization you desire. For \ example, if you want ", Cell[BoxData[ \(TraditionalForm\`X(t)\)]], " to be parametrized by arclength, ", Cell[BoxData[ \(TraditionalForm\`\(|\(X\^\[Prime]\)(t) | \) = 1\)]], ", then choose ", Cell[BoxData[ \(TraditionalForm \`\[Lambda](t) = \(\((\[Del]\(\(F\_1\)(X(t))\)\[Times]\[Del]\(\(F\_2\)(X(t))\))\)\^\(-1 \).\)\)]], " One more thing is needed to solve equation (2), namely an initial \ condition. This corresponds to a choice of a point on the curve and a choice \ of a parameter value to go with it, ", Cell[BoxData[ \(TraditionalForm\`X(t\_0) = \(\((x\_0, y\_0, z\_0)\).\)\)]], "\n\tAs an example consider the intersection of the sphere centered at the \ origin of radius 2 and the trigonometric surface ", Cell[BoxData[ \(TraditionalForm\`z = sin(x\ y)\)]], ". Here, ", Cell[BoxData[ \(TraditionalForm\`\(F\_1\)(x, y, z) = x\^2 + y\^2 + z\^2 - 1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(\(F\_2\)(x, y, z) = sin(x\ y) - z, \)\)]], " so that" }], "Text"], Cell[BoxData[ \(TraditionalForm \`\[Del]F\_1\[Times]\[Del]F\_2 = \((\(-2\) y - 2 x\ z\ \(cos(x\ y)\), 2 x + 2 y\ z\ \(cos(x\ y)\), 2 x\^2\ \(cos(x\ y)\) - 2 \( y\^2\) \(cos(x\ y)\))\)\)], "DisplayFormula"], Cell[TextData[{ "The point ", Cell[BoxData[ \(TraditionalForm\`\((\@2, 0, 0)\)\)]], " lies on the curve of intersection, so use that as the initial point when \ ", Cell[BoxData[ \(TraditionalForm\`t = 0.\)]], " For the sake of simplicity take ", Cell[BoxData[ \(TraditionalForm\`\[Lambda](t) = 1.\)]], " This gives the initial condition problem:" }], "Text"], Cell[BoxData[ \(TraditionalForm \`\((\(x\^\[Prime]\)(t), \(y\^\[Prime]\)(t), \(z\^\[Prime]\)(t))\) = \((\(-2\) y - 2 x\ z\ \(cos(x\ y)\), 2 x + 2 y\ z\ \(cos(x\ y)\), 2 x\^2\ \(cos(x\ y)\) - 2 \( y\^2\) \(cos(x\ y)\))\), \n \((x(0), y(0), z(0))\) = \((\@2, 0, 0)\)\)], "DisplayFormula"], Cell[TextData[{ "To solve it for ", Cell[BoxData[ \(TraditionalForm\`0 \[LessEqual] t \[LessEqual] 11\)]], " use ", StyleBox["NDSolve", "Input"], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(NDSolve[\n \t{\(x'\)[t] == \(-2\) y[t] - 2 x[t]\ z[t]\ Cos[x[t] y[t]], \n\t\t \(y'\)[t] == 2 x[t] + 2 y[t] z[t] Cos[x[t] y[t]], \n\t\t \(z'\)[t] == 2 \( x[t]\^2\) Cos[x[t] y[t]] - 2 \( y[t]\^2\) Cos[x[t] y[t]], \n\t x[0] == \@2, y[0] == 0, z[0] == 0}, \n\t{x, y, z}, {t, 0, 11}]\)], "Input", CellLabel->"In[61]:="], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 11.0000000000000008`}}, "<>"]\), False, Editable->False]}], ",", RowBox[{"y", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 11.0000000000000008`}}, "<>"]\), False, Editable->False]}], ",", RowBox[{"z", "\[Rule]", TagBox[\(InterpolatingFunction[{{0.`, 11.0000000000000008`}}, "<>"]\), False, Editable->False]}]}], "}"}], "}"}]], "Output", CellLabel->"Out[61]="] }, Open ]], Cell[TextData[{ "This is essentially what ", StyleBox["ParametrizeCurve", "Input"], " does", StyleBox[" if", FontSlant->"Italic"], " the two gradients ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1, \[Del]F\_2\)]], " are linearly independent along the curve." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Dealing with singular points", "Subsection"], Cell[TextData[{ "\tThe algorithm has a problem if it runs into a point on the intersection \ where ", Cell[BoxData[ FormBox[ RowBox[{\(\[Del]F\_1\), " ", "and", " ", FormBox[\(\[Del]F\_2\), "TraditionalForm"]}], TraditionalForm]]], " are linearly dependent since equation (1) no longer implies equation (2). \ Such points are called ", StyleBox["singular points", FontSlant->"Italic"], " of the intersection. One\[CloseCurlyQuote]s first attempt to deal with \ such points may be to simply ignore them. Since singular points are rare \ (linearly dependence of two vectors in space is a degenerate case), and we \ are numerically solving an intial value problem, it is highly unlikely that \ we will ever integrate right through a singular point. However, as the next \ example will illustrate, difficulties can still arise. Parametrize the \ intersection of the sphere ", Cell[BoxData[ \(TraditionalForm\`x\^2 + y\^2 + z\^2 = 1\)]], " and the cylinder ", Cell[BoxData[ \(TraditionalForm\`\((2 x - 1)\)\^2 + \((2 y)\)\^2 = 1\)]], ". With ", Cell[BoxData[ \(TraditionalForm\`\(F\_1\)(x, y, z) = x\^2 + y\^2 + z\^2 - 1\)]], " and ", Cell[BoxData[ \(TraditionalForm \`\(F\_2\)(x, y, z) = \((2 x - 1)\)\^2 + \((2 y)\)\^2 - 1\)]], " a quick check shows that the point ", Cell[BoxData[ \(TraditionalForm\`\((1, 0, 0)\)\)]], " is on the intersection and at that point ", Cell[BoxData[ FormBox[ RowBox[{\(\[Del]F\_1\), " ", ",", " ", FormBox[\(\[Del]F\_2\), "TraditionalForm"]}], TraditionalForm]]], " are both multiples of the vector ", Cell[BoxData[ \(TraditionalForm\`\((1, 0, 0)\)\)]], "." }], "Text"], Cell[BoxData[ RowBox[{"Block", "[", RowBox[{\({$DisplayFunction = Identity}\), ",", RowBox[{ \(sphere\ = ContourPlot3D[ x\^2 + y\^2 + z\^2, {x, \(-1\), 1}, {y, \(-1\), 1}, {z, \(-1\), 1}, Contours \[Rule] {1}]\), ";", "\n", "\t", \(cylinder = ContourPlot3D[ \((2 x - 1)\)\^2 + \((2 y)\)\^2, {x, 0, 1}, {y, \(-1\), 1}, { z, \(-1\), 1}, Contours \[Rule] {1}]\), ";", "\n", "\t", StyleBox[ \(solution\ = \ \n\t\t ParametrizeCurve[{x\^2 + y\^2 + z\^2 == 1, \((2 x - 1)\)\^2 + \((2 y)\)\^2 == 1, x[0] == 0, y[0] == 0, z[0] == 1}, {x, y, z}, {t, 0, 8}, CheckSingularPoints \[Rule] False]\), "Text"], StyleBox[";", "Text"], StyleBox["\n", "Text"], StyleBox["\t", "Text"], RowBox[{ StyleBox[\(r[t_]\), "Text"], StyleBox[":=", "Text"], RowBox[{"Evaluate", "[", StyleBox[\({x[t], y[t], z[t]} /. solution\), "Text"], StyleBox["]", "Text"]}]}], StyleBox[";", "Text"], StyleBox["\n", "Text"], StyleBox["\t", "Text"], StyleBox[ \(surfaces = Show[sphere, cylinder, ViewPoint -> {2.6, \ \(-1.7\), \ 1.3}]\), "Text"], StyleBox[";", "Text"], StyleBox["\n", "Text"], StyleBox["\t", "Text"], StyleBox[ \(intersection = ParametricPlot3D[Evaluate[r[t]], {t, 0, 3}, PlotRange \[Rule] {{\(-1\), 1}, {\(-1\), 1}, {\(-1\), 1}}, ViewPoint -> {2.6, \ \(-1.7\), \ 1.3}]\), "Text"], StyleBox[";", "Text"]}]}], StyleBox["\n", "Text"], "]"}]], "Input", CellLabel->"In[62]:="], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[GraphicsArray[{surfaces, intersection}]]; \)\)], "Input", CellLabel->"In[63]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .48001 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.47619 0.0114288 0.47619 [ [ 0 0 0 0 ] [ 1 .48001 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .48001 L 0 .48001 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.0114288 0.477324 0.468582 MathSubStart %% Graphics3D /Courier findfont 10 scalefont setfont % Scaling calculations -0.0917273 1.14136 1.11022e-16 1.14136 [ [ 0 0 0 0 ] [ 1 1.00802 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .05005 .3195 m 0 .92857 L s 0 .92857 m .56593 1.00802 L s .56593 1.00802 m .55793 .46488 L s .55793 .46488 m .05005 .3195 L s .36546 0 m .9413 .2252 L s .9413 .2252 m 1 .87582 L s 1 .87582 m .34819 .74585 L s .34819 .74585 m .36546 0 L s .05005 .3195 m 0 .92857 L s 0 .92857 m .34819 .74585 L s .34819 .74585 m .36546 0 L s .36546 0 m .05005 .3195 L s .55793 .46488 m .9413 .2252 L s .9413 .2252 m 1 .87582 L s 1 .87582 m .56593 1.00802 L s .56593 1.00802 m .55793 .46488 L s 0 0 m 1 0 L 1 1.00802 L 0 1.00802 L closepath clip newpath .5 Mabswid .48124 .56034 m .48901 .53391 L p .56451 .60546 L .671 .55 .709 r F P 0 g s .56451 .60546 m .50504 .61006 L .48124 .56034 L p .671 .55 .709 r F P 0 g s .48124 .56034 m .48901 .53391 L .46142 .53348 L closepath p .713 .594 .722 r F P 0 g s .50504 .61006 m .48124 .56034 L .47013 .61059 L closepath p .7 .562 .696 r F P 0 g s .47013 .61059 m .48124 .56034 L .46142 .53348 L p .737 .599 .704 r F P 0 g s .48901 .53391 m .56826 .52726 L p .56451 .60546 L .671 .55 .709 r F P 0 g s .56826 .52726 m .52051 .46209 L .48901 .53391 L closepath p .673 .585 .748 r F P 0 g s .50056 .44344 m .52051 .46209 L .48901 .53391 L p .71 .628 .764 r F P 0 g s .44466 .4425 m .50056 .44344 L p .48901 .53391 L .71 .628 .764 r F P 0 g s .42144 .49683 m .44466 .4425 L p .48901 .53391 L .71 .628 .764 r F P 0 g s .48901 .53391 m .46142 .53348 L .42144 .49683 L p .71 .628 .764 r F P 0 g s .47013 .61059 m .50504 .61006 L .51728 .67961 L p .697 .526 .652 r F P 0 g s .51728 .67961 m .46445 .68035 L .47013 .61059 L p .697 .526 .652 r F P 0 g s .39354 .60561 m .47013 .61059 L .46445 .68035 L p .738 .562 .655 r F P 0 g s .41041 .52988 m .39354 .60561 L .47013 .61059 L p .737 .599 .704 r F P 0 g s .46142 .53348 m .41041 .52988 L p .47013 .61059 L .737 .599 .704 r F P 0 g s .46142 .53348 m .42144 .49683 L .41041 .52988 L closepath p .733 .628 .741 r F P 0 g s .50504 .61006 m .56451 .60546 L .55726 .67675 L p .665 .505 .657 r F P 0 g s .55726 .67675 m .51728 .67961 L .50504 .61006 L p .665 .505 .657 r F P 0 g s .34348 .51745 m .41041 .52988 L .39354 .60561 L p .78 .643 .71 r F P 0 g s .36004 .46717 m .34348 .51745 L .41041 .52988 L p .771 .67 .751 r F P 0 g s .41041 .52988 m .42144 .49683 L .36004 .46717 L p .771 .67 .751 r F P 0 g s .46445 .68035 m .38716 .67571 L .39354 .60561 L p .738 .562 .655 r F P 0 g s .32628 .5941 m .39354 .60561 L .38716 .67571 L p .786 .606 .656 r F P 0 g s .39354 .60561 m .32628 .5941 L .34348 .51745 L p .78 .643 .71 r F P 0 g s .56451 .60546 m .59785 .60069 L .60771 .67009 L p .629 .473 .651 r F P 0 g s .60771 .67009 m .55726 .67675 L .56451 .60546 L p .629 .473 .651 r F P 0 g s .59785 .60069 m .58032 .55225 L .56451 .60546 L closepath p .638 .515 .697 r F P 0 g s .56826 .52726 m .58032 .55225 L .56451 .60546 L p .671 .55 .709 r F P 0 g s .44466 .4425 m .42144 .49683 L .36004 .46717 L p .755 .681 .78 r F P 0 g s .58032 .55225 m .59383 .52235 L .56826 .52726 L closepath p .626 .529 .725 r F P 0 g s .59383 .52235 m .56826 .52726 L .52051 .46209 L p .633 .573 .769 r F P 0 g s .59785 .60069 m .58032 .55225 L .59383 .52235 L p .591 .489 .707 r F P 0 g s .46445 .68035 m .51728 .67961 L .50568 .74541 L p .691 .482 .599 r F P 0 g s .50568 .74541 m .46991 .74588 L .46445 .68035 L p .691 .482 .599 r F P 0 g s .38716 .67571 m .46445 .68035 L .46991 .74588 L p .734 .515 .594 r F P 0 g s .52051 .46209 m .5339 .4404 L p .59383 .52235 L .633 .573 .769 r F P 0 g s .52051 .46209 m .5339 .4404 L .50056 .44344 L closepath p .673 .626 .794 r F P 0 g s .51728 .67961 m .55726 .67675 L .56663 .74139 L p .655 .448 .591 r F P 0 g s .56663 .74139 m .50568 .74541 L .51728 .67961 L p .655 .448 .591 r F P 0 g s .60771 .67009 m .59785 .60069 L .66618 .58422 L p .576 .435 .652 r F P 0 g s .63909 .51051 m .66618 .58422 L .59785 .60069 L p .591 .489 .707 r F P 0 g s .59383 .52235 m .63909 .51051 L p .59785 .60069 L .591 .489 .707 r F P 0 g s .63909 .51051 m .62166 .47932 L .59383 .52235 L closepath p .602 .532 .748 r F P 0 g s .58541 .42957 m .62166 .47932 L .59383 .52235 L p .633 .573 .769 r F P 0 g s .5339 .4404 m .58541 .42957 L p .59383 .52235 L .633 .573 .769 r F P 0 g s .5339 .4404 m .50056 .44344 L .4603 .41324 L p .671 .655 .825 r F P 0 g s .50056 .44344 m .4603 .41324 L .44466 .4425 L closepath p .706 .653 .795 r F P 0 g s .55726 .67675 m .60771 .67009 L .6008 .73723 L p .617 .421 .594 r F P 0 g s .6008 .73723 m .56663 .74139 L .55726 .67675 L p .617 .421 .594 r F P 0 g s .36004 .46717 m .37539 .4304 L .44466 .4425 L p .755 .681 .78 r F P 0 g s .39853 .38576 m .37539 .4304 L .44466 .4425 L p .743 .701 .812 r F P 0 g s .44466 .4425 m .4603 .41324 L .39853 .38576 L p .743 .701 .812 r F P 0 g s .46991 .74588 m .39143 .74152 L .38716 .67571 L p .734 .515 .594 r F P 0 g s .31923 .66498 m .38716 .67571 L .39143 .74152 L p .787 .555 .585 r F P 0 g s .38716 .67571 m .31923 .66498 L .32628 .5941 L p .786 .606 .656 r F P 0 g s .58541 .42957 m .56126 .40373 L .5339 .4404 L closepath p .637 .605 .801 r F P 0 g s .50035 .3571 m .56126 .40373 L .5339 .4404 L p .671 .655 .825 r F P 0 g s .4603 .41324 m .50035 .3571 L p .5339 .4404 L .671 .655 .825 r F P 0 g s .28493 .49745 m .34348 .51745 L .32628 .5941 L p .829 .694 .715 r F P 0 g s .29605 .46325 m .28493 .49745 L .34348 .51745 L p .814 .718 .76 r F P 0 g s .34348 .51745 m .36004 .46717 L .29605 .46325 L p .814 .718 .76 r F P 0 g s .26728 .57558 m .32628 .5941 L .31923 .66498 L p .842 .657 .653 r F P 0 g s .32628 .5941 m .26728 .57558 L .28493 .49745 L p .829 .694 .715 r F P 0 g s .37539 .4304 m .36004 .46717 L .29605 .46325 L p .806 .744 .794 r F P 0 g s .50035 .3571 m .4603 .41324 L .39853 .38576 L p .712 .715 .851 r F P 0 g s .6008 .73723 m .60771 .67009 L .6769 .6547 L p .555 .367 .581 r F P 0 g s .66618 .58422 m .6769 .6547 L .60771 .67009 L p .576 .435 .652 r F P 0 g s .63909 .51051 m .62166 .47932 L .66555 .43954 L p .542 .505 .765 r F P 0 g s .64092 .40558 m .66555 .43954 L .62166 .47932 L p .569 .551 .795 r F P 0 g s .62166 .47932 m .58541 .42957 L .64092 .40558 L p .569 .551 .795 r F P 0 g s .66618 .58422 m .63909 .51051 L .69231 .48736 L p .521 .45 .717 r F P 0 g s .66555 .43954 m .69231 .48736 L .63909 .51051 L p .542 .505 .765 r F P 0 g s .29605 .46325 m .31909 .40688 L .37539 .4304 L p .806 .744 .794 r F P 0 g s .33443 .37643 m .31909 .40688 L .37539 .4304 L p .786 .757 .827 r F P 0 g s .37539 .4304 m .39853 .38576 L .33443 .37643 L p .786 .757 .827 r F P 0 g s .48133 .78721 m .46991 .74588 L .50568 .74541 L closepath p .681 .429 .535 r F P 0 g s .46991 .74588 m .48133 .78721 L .46053 .80701 L p .725 .455 .519 r F P 0 g s .39143 .74152 m .46991 .74588 L p .46053 .80701 L .725 .455 .519 r F P 0 g s .50568 .74541 m .56663 .74139 L p .57279 .80227 L .637 .376 .508 r F P 0 g s .48133 .78721 m .50568 .74541 L p .57279 .80227 L .637 .376 .508 r F P 0 g s .6041 .36581 m .64092 .40558 L .58541 .42957 L p .582 .592 .828 r F P 0 g s .58541 .42957 m .56126 .40373 L .6041 .36581 L p .582 .592 .828 r F P 0 g s .39143 .74152 m .32246 .73146 L .31923 .66498 L p .787 .555 .585 r F P 0 g s .25957 .64771 m .31923 .66498 L .32246 .73146 L p .848 .604 .569 r F P 0 g s .31923 .66498 m .25957 .64771 L .26728 .57558 L p .842 .657 .653 r F P 0 g s .6041 .36581 m .56126 .40373 L .50035 .3571 L p .614 .651 .863 r F P 0 g s .6769 .6547 m .66618 .58422 L .72031 .56263 L p .492 .376 .649 r F P 0 g s .69231 .48736 m .72031 .56263 L .66618 .58422 L p .521 .45 .717 r F P 0 g s .46053 .80701 m .40694 .80427 L .39143 .74152 L p .725 .455 .519 r F P 0 g s .32246 .73146 m .39143 .74152 L .40694 .80427 L p .779 .488 .495 r F P 0 g s .58456 .78076 m .56663 .74139 L .6008 .73723 L closepath p .599 .36 .525 r F P 0 g s .56663 .74139 m .58456 .78076 L .57279 .80227 L p .637 .376 .508 r F P 0 g s .39853 .38576 m .43794 .32825 L .50035 .3571 L p .712 .715 .851 r F P 0 g s .43794 .32825 m .39853 .38576 L .33443 .37643 L p .76 .787 .875 r F P 0 g s .6008 .73723 m .67091 .72283 L .64735 .78949 L p .525 .284 .491 r F P 0 g s .58456 .78076 m .6008 .73723 L p .64735 .78949 L .525 .284 .491 r F P 0 g s .6769 .6547 m .67091 .72283 L .6008 .73723 L p .555 .367 .581 r F P 0 g s .25128 .47863 m .28493 .49745 L .26728 .57558 L p .881 .75 .712 r F P 0 g s .28493 .49745 m .25128 .47863 L .29605 .46325 L closepath p .859 .77 .763 r F P 0 g s .21576 .5492 m .26728 .57558 L .25957 .64771 L p .901 .715 .64 r F P 0 g s .22792 .49568 m .25128 .47863 L p .26728 .57558 L .881 .75 .712 r F P 0 g s .26728 .57558 m .21576 .5492 L .22792 .49568 L p .881 .75 .712 r F P 0 g s .25128 .47863 m .29605 .46325 L .31909 .40688 L p .861 .813 .801 r F P 0 g s .67091 .72283 m .6769 .6547 L .73184 .63451 L p .451 .279 .555 r F P 0 g s .72031 .56263 m .73184 .63451 L .6769 .6547 L p .492 .376 .649 r F P 0 g s .50035 .3571 m .54223 .31765 L .6041 .36581 L p .614 .651 .863 r F P 0 g s .54223 .31765 m .50035 .3571 L .43794 .32825 L p .655 .727 .902 r F P 0 g s .57279 .80227 m .48952 .80733 L .48133 .78721 L p .637 .376 .508 r F P 0 g s .48952 .80733 m .46053 .80701 L .48133 .78721 L closepath p .688 .401 .482 r F P 0 g s .40694 .80427 m .33654 .79479 L .32246 .73146 L p .779 .488 .495 r F P 0 g s .26188 .71526 m .32246 .73146 L .33654 .79479 L p .842 .528 .459 r F P 0 g s .32246 .73146 m .26188 .71526 L .25957 .64771 L p .848 .604 .569 r F P 0 g s .69231 .48736 m .66555 .43954 L .71266 .42523 L p .45 .461 .779 r F P 0 g s .67475 .37277 m .71266 .42523 L .66555 .43954 L p .461 .509 .822 r F P 0 g s .66555 .43954 m .64092 .40558 L .67475 .37277 L p .461 .509 .822 r F P 0 g s .31909 .40688 m .28992 .38287 L p .25128 .47863 L .861 .813 .801 r F P 0 g s .31909 .40688 m .28992 .38287 L .33443 .37643 L closepath p .83 .818 .837 r F P 0 g s .72031 .56263 m .69231 .48736 L .73102 .458 L p .407 .384 .721 r F P 0 g s .71266 .42523 m .73102 .458 L .69231 .48736 L p .45 .461 .779 r F P 0 g s .20735 .6231 m .25957 .64771 L .26188 .71526 L p .913 .658 .539 r F P 0 g s .25957 .64771 m .20735 .6231 L .21576 .5492 L p .901 .715 .64 r F P 0 g s .64963 .34542 m .67475 .37277 L .64092 .40558 L p .495 .566 .857 r F P 0 g s .64092 .40558 m .6041 .36581 L .64963 .34542 L p .495 .566 .857 r F P 0 g s .64735 .78949 m .59968 .79852 L .58456 .78076 L p .525 .284 .491 r F P 0 g s .59968 .79852 m .57279 .80227 L .58456 .78076 L closepath p .558 .287 .461 r F P 0 g s .52353 .85158 m .48952 .80733 L .57279 .80227 L closepath p .609 .291 .407 r F P 0 g s .48952 .80733 m .52353 .85158 L .50226 .86277 L p .654 .296 .353 r F P 0 g s .46053 .80701 m .48952 .80733 L p .50226 .86277 L .654 .296 .353 r F P 0 g s .41791 .82815 m .46053 .80701 L p .50226 .86277 L .654 .296 .353 r F P 0 g s .41791 .82815 m .40694 .80427 L .46053 .80701 L closepath p .707 .384 .428 r F P 0 g s .73184 .63451 m .72031 .56263 L .76004 .53524 L p .347 .275 .632 r F P 0 g s .73102 .458 m .76004 .53524 L .72031 .56263 L p .407 .384 .721 r F P 0 g s .43794 .32825 m .47895 .28751 L .54223 .31765 L p .655 .727 .902 r F P 0 g s .47895 .28751 m .52508 .29467 L p .52871 .30328 L .768 .556 .612 r F P 0 g s .52508 .29467 m .55446 .29923 L .55464 .3115 L p .768 .556 .612 r F P 0 g s .55464 .3115 m .54223 .31765 L .47895 .28751 L p .538 .723 .959 r F P 0 g s .6041 .36581 m .54223 .31765 L p .58477 .32865 L .514 .633 .905 r F P 0 g s .57941 .29762 m .62765 .29039 L p .60628 .32446 L .632 .447 .614 r F P 0 g s .54223 .31765 m .5509 .31335 L p .59451 .32752 L .514 .633 .905 r F P 0 g s .57764 .32681 m .59451 .32752 L .64963 .34542 L .514 .633 .905 r F .54223 .31765 m .59451 .32752 L .57764 .32681 L F .62765 .29039 m .66625 .27953 L p .64296 .32956 L .567 .396 .609 r F P 0 g s .5509 .31335 m .57129 .31744 L .64963 .34542 L .514 .633 .905 r F .57983 .31915 m .57941 .29762 L p .60628 .32446 L .632 .447 .614 r F P 0 g s .55446 .29923 m .57941 .29762 L .57983 .31915 L p .672 .479 .616 r F P 0 g s .55999 .31312 m .55446 .29923 L .57983 .31915 L .672 .479 .616 r F .5509 .31335 m .55464 .3115 L p .57129 .31744 L .514 .633 .905 r F P 0 g s .63921 .33721 m .64963 .34542 L p .57129 .31744 L .514 .633 .905 r F P 0 g s .55464 .3115 m .57983 .31915 L .57129 .31744 L .514 .633 .905 r F .57983 .31915 m .63921 .33721 L .57129 .31744 L F .60628 .32446 m .60848 .32095 L .62876 .32896 L .632 .447 .614 r F .62765 .29039 m .62876 .32896 L p .60848 .32095 L F P 0 g s .62876 .32896 m .62765 .29039 L p .64296 .32956 L .567 .396 .609 r F P 0 g s .66625 .27953 m .69528 .26487 L p .671 .34075 L .455 .31 .593 r F P 0 g s .68192 .34437 m .66884 .3448 L p .66001 .33953 L .331 .573 .929 r F P 0 g s .68192 .34437 m .66001 .33953 L .66845 .34047 L .331 .573 .929 r F .68192 .34437 m .66845 .34047 L .6759 .3413 L F .66884 .3448 m .64963 .34542 L .62876 .32896 L p F P 0 g s .66625 .27953 m .66845 .34047 L p .64152 .33266 L .567 .396 .609 r F P 0 g s .64152 .33266 m .62876 .32896 L .64296 .32956 L .567 .396 .609 r F .62876 .32896 m .58654 .29567 L p .65511 .3366 L .331 .573 .929 r F P 0 g s .66884 .3448 m .62876 .32896 L .65511 .3366 L .331 .573 .929 r F .62876 .32896 m .63921 .33721 L p .57983 .31915 L .514 .633 .905 r F P 0 g s .64963 .34542 m .62981 .35429 L p .58477 .32865 L .514 .633 .905 r F P 0 g s .62981 .35429 m .6041 .36581 L p .58477 .32865 L .514 .633 .905 r F P 0 g s .6296 .35827 m .62876 .32896 L p .64152 .33266 L .567 .396 .609 r F P 0 g s .67475 .37277 m .64963 .34542 L .68192 .34437 L closepath p .353 .511 .876 r F P 0 g s .66872 .34788 m .6296 .35827 L p .64152 .33266 L .567 .396 .609 r F P 0 g s .66845 .34047 m .66625 .27953 L p .671 .34075 L .455 .31 .593 r F P 0 g s .69528 .26487 m .69817 .33383 L .68126 .3419 L p .455 .31 .593 r F P 0 g s .68192 .34437 m .6759 .3413 L .67945 .3417 L .331 .573 .929 r F .671 .34075 m .67168 .33864 L .68126 .3419 L .455 .31 .593 r F .67168 .33864 m .69528 .26487 L .68126 .3419 L F .69876 .34784 m .68192 .34437 L .68126 .3419 L p .205 .47 .886 r F P 0 g s .63401 .29243 m .67723 .32683 L .68126 .3419 L p .331 .573 .929 r F P 0 g s .68126 .3419 m .68192 .34437 L p .67945 .3417 L .331 .573 .929 r F P 0 g s .67945 .3417 m .63401 .29243 L .68126 .3419 L .331 .573 .929 r F .74652 .43391 m .71266 .42523 L .67475 .37277 L p .268 .419 .828 r F P 0 g s .67475 .37277 m .68192 .34437 L p .74652 .43391 L .268 .419 .828 r F P 0 g s .67126 .41805 m .66872 .34788 L .68126 .3419 L p .455 .31 .593 r F P 0 g s .68126 .3419 m .69817 .33383 L p .6951 .34344 L .455 .31 .593 r F P 0 g s .74652 .43391 m .68552 .34937 L .69876 .34784 L .268 .419 .828 r F .68192 .34437 m .69876 .34784 L p .68552 .34937 L F P 0 g s .69817 .33383 m .71785 .31587 L p .71212 .34631 L .241 .146 .542 r F P 0 g s .69876 .34784 m .75102 .42035 L .74652 .43391 L p .268 .419 .828 r F P 0 g s .74197 .37978 m .75102 .42035 L .70967 .36299 L p 0 .235 .752 r F P 0 g s .70967 .36299 m .69876 .34784 L .71642 .3609 L p 0 .235 .752 r F P 0 g s .71642 .3609 m .74197 .37978 L p .70967 .36299 L 0 .235 .752 r F P 0 g s .71785 .31587 m .7275 .29366 L p .72308 .35883 L 0 0 .379 r F P 0 g s .71997 .36223 m .71986 .35983 L p .72278 .36327 L 0 0 .379 r F P 0 g s .71035 .3557 m .69876 .34784 L .71212 .34631 L .241 .146 .542 r F .71642 .3609 m .69876 .34784 L p .71997 .36223 L 0 .182 .689 r F P 0 g s .70114 .40466 m .69876 .34784 L p .71035 .3557 L .241 .146 .542 r F P 0 g s .72113 .38753 m .70114 .40466 L p .71035 .3557 L .241 .146 .542 r F P 0 g s .71785 .31587 m .71997 .36223 L p .71035 .3557 L .241 .146 .542 r F P 0 g s .74197 .37978 m .71642 .3609 L p .71997 .36223 L 0 .182 .689 r F P 0 g s .71997 .36223 m .72113 .38753 L p .71035 .3557 L .241 .146 .542 r F P 0 g s .72308 .36433 m .71997 .36223 L .72095 .36259 L 0 .182 .689 r F .74197 .37978 m .71997 .36223 L .72308 .36433 L F .71997 .36223 m .69876 .34784 L .72095 .36259 L F .69876 .34784 m .69817 .33383 L p .71212 .34631 L .241 .146 .542 r F P 0 g s .67126 .41805 m .68126 .3419 L .6951 .34344 L .455 .31 .593 r F .69817 .33383 m .70114 .40466 L .67126 .41805 L p F P 0 g s .69876 .34784 m .67723 .32683 L p .72095 .36259 L 0 .182 .689 r F P 0 g s .72278 .36327 m .71986 .35983 L .72308 .35883 L 0 0 .379 r F .71986 .35983 m .71785 .31587 L p .72308 .35883 L F P 0 g s .72278 .36327 m .72417 .34274 L .73097 .36634 L 0 0 .379 r F .7275 .29366 m .73097 .36634 L p .72417 .34274 L F P 0 g s .67723 .32683 m .65416 .29923 L p .7248 .36403 L 0 .182 .689 r F P 0 g s .74197 .37978 m .72095 .36259 L .7248 .36403 L 0 .182 .689 r F .72095 .36259 m .67723 .32683 L .7248 .36403 L F .65416 .29923 m .68603 .32239 L p .73094 .36847 L F P 0 g s .74197 .37978 m .73093 .36965 L .73094 .36847 L 0 .182 .689 r F .73093 .36965 m .65416 .29923 L .73094 .36847 L F .73097 .36634 m .73017 .34065 L p .73105 .36086 L 0 0 .048 r F P 0 g s .73102 .458 m .71266 .42523 L .74652 .43391 L closepath p .304 .386 .782 r F P 0 g s .68603 .32239 m .73097 .36634 L .74197 .37978 L p 0 .182 .689 r F P 0 g s .73455 .44108 m .73097 .36634 L p .73206 .38388 L 0 0 .048 r F P 0 g s .7223 .37034 m .72278 .36327 L .73097 .36634 L 0 0 .379 r F .73097 .36634 m .72113 .38753 L p .7223 .37034 L F P 0 g s .72113 .38753 m .71997 .36223 L p .72278 .36327 L 0 0 .379 r F P 0 g s .72451 .46119 m .72113 .38753 L .73097 .36634 L p 0 0 .379 r F P 0 g s .73097 .36634 m .73455 .44108 L .72451 .46119 L p 0 0 .379 r F P 0 g s .73097 .36634 m .70215 .34238 L p .73206 .38388 L .881 .45 .075 r F P 0 g s .73869 .39309 m .73097 .36634 L .73206 .38388 L .881 .45 .075 r F .75102 .42035 m .74197 .37978 L p .78794 .4847 L 0 0 .541 r F P 0 g s .75373 .39795 m .78209 .45569 L .78794 .4847 L p 0 0 .541 r F P 0 g s .74197 .37978 m .75373 .39795 L p .78794 .4847 L 0 0 .541 r F P 0 g s .77176 .43899 m .73097 .36634 L .73869 .39309 L .881 .45 .075 r F .75373 .39795 m .74197 .37978 L .73097 .36634 L closepath p .668 .213 0 r F P 0 g s .77176 .43899 m .75373 .39795 L .73097 .36634 L p .881 .45 .075 r F P 0 g s .73206 .38388 m .73097 .36634 L .73105 .36086 L 0 0 .048 r F .68126 .3419 m .67723 .32683 L .69876 .34784 L p .205 .47 .886 r F P 0 g s .68126 .3419 m .66872 .34788 L p .671 .34075 L .455 .31 .593 r F P 0 g s .58654 .29567 m .63401 .29243 L p .67945 .3417 L .331 .573 .929 r F P 0 g s .6759 .3413 m .58654 .29567 L .67945 .3417 L .331 .573 .929 r F .6759 .3413 m .66001 .33953 L .58654 .29567 L F .66845 .34047 m .66872 .34788 L p .64152 .33266 L .567 .396 .609 r F P 0 g s .66872 .34788 m .66845 .34047 L p .671 .34075 L .455 .31 .593 r F P 0 g s .58072 .3652 m .55544 .36674 L .55464 .3115 L p .672 .479 .616 r F P 0 g s .55464 .3115 m .55446 .29923 L p .55999 .31312 L .672 .479 .616 r F P 0 g s .58072 .3652 m .55464 .3115 L .55999 .31312 L .672 .479 .616 r F .55464 .3115 m .58654 .29567 L .62876 .32896 L p .514 .633 .905 r F P 0 g s .55464 .3115 m .62876 .32896 L .57983 .31915 L .514 .633 .905 r F .6296 .35827 m .58072 .3652 L p .60628 .32446 L .632 .447 .614 r F P 0 g s .62876 .32896 m .6296 .35827 L p .60628 .32446 L .632 .447 .614 r F P 0 g s .58072 .3652 m .57983 .31915 L p .60628 .32446 L .632 .447 .614 r F P 0 g s .57983 .31915 m .58072 .3652 L p .55999 .31312 L .672 .479 .616 r F P 0 g s .55464 .3115 m .55544 .36674 L p .52508 .29467 L .768 .556 .612 r F P 0 g s .58654 .29567 m .55464 .3115 L p .47895 .28751 L .538 .723 .959 r F P 0 g s .55544 .36674 m .47895 .28751 L .52871 .30328 L .768 .556 .612 r F .33443 .37643 m .37328 .31765 L .43794 .32825 L p .76 .787 .875 r F P 0 g s .28992 .38287 m .33443 .37643 L .37328 .31765 L p .809 .865 .89 r F P 0 g s .40694 .80427 m .41791 .82815 L .35198 .83115 L p .758 .404 .384 r F P 0 g s .35198 .83115 m .33654 .79479 L .40694 .80427 L p .758 .404 .384 r F P 0 g s .64735 .78949 m .67091 .72283 L .72655 .70393 L p .396 .157 .429 r F P 0 g s .73184 .63451 m .72655 .70393 L .67091 .72283 L p .451 .279 .555 r F P 0 g s .47895 .28751 m .43794 .32825 L .37328 .31765 L p .702 .82 .938 r F P 0 g s .22792 .49568 m .236 .46741 L .25128 .47863 L closepath p .896 .797 .742 r F P 0 g s .26701 .39006 m .236 .46741 L .25128 .47863 L p .861 .813 .801 r F P 0 g s .28992 .38287 m .26701 .39006 L p .25128 .47863 L .861 .813 .801 r F P 0 g s .57279 .80227 m .59968 .79852 L p .59388 .85358 L .506 .16 .314 r F P 0 g s .52353 .85158 m .57279 .80227 L p .59388 .85358 L .506 .16 .314 r F P 0 g s .63058 .81552 m .59968 .79852 L .64735 .78949 L closepath p .486 .185 .381 r F P 0 g s .59968 .79852 m .63058 .81552 L .59388 .85358 L p .506 .16 .314 r F P 0 g s .72655 .70393 m .73184 .63451 L .77232 .60889 L p .264 .125 .496 r F P 0 g s .76004 .53524 m .77232 .60889 L .73184 .63451 L p .347 .275 .632 r F P 0 g s .33654 .79479 m .27479 .77951 L .26188 .71526 L p .842 .528 .459 r F P 0 g s .20886 .69216 m .26188 .71526 L .27479 .77951 L p .905 .571 .403 r F P 0 g s .26188 .71526 m .20886 .69216 L .20735 .6231 L p .913 .658 .539 r F P 0 g s .19831 .5353 m .22792 .49568 L .236 .46741 L p .954 .87 .716 r F P 0 g s .21576 .5492 m .19831 .5353 L .22792 .49568 L closepath p .931 .806 .699 r F P 0 g s .236 .46741 m .20932 .43027 L p .19831 .5353 L .954 .87 .716 r F P 0 g s .236 .46741 m .20932 .43027 L .26701 .39006 L closepath p .911 .881 .792 r F P 0 g s .19831 .5353 m .21576 .5492 L .20735 .6231 L p .956 .771 .612 r F P 0 g s .50226 .86277 m .44196 .86214 L .41791 .82815 L p .654 .296 .353 r F P 0 g s .44196 .86214 m .41791 .82815 L .35198 .83115 L p .712 .303 .27 r F P 0 g s .33654 .79479 m .35198 .83115 L .28443 .80391 L p .815 .429 .322 r F P 0 g s .28443 .80391 m .27479 .77951 L .33654 .79479 L p .815 .429 .322 r F P 0 g s .26701 .39006 m .27977 .36646 L .28992 .38287 L closepath p .851 .876 .858 r F P 0 g s .30551 .32624 m .27977 .36646 L .28992 .38287 L p .809 .865 .89 r F P 0 g s .37328 .31765 m .30551 .32624 L p .28992 .38287 L .809 .865 .89 r F P 0 g s .37328 .31765 m .41349 .27588 L .47895 .28751 L p .702 .82 .938 r F P 0 g s .41349 .27588 m .37328 .31765 L .30551 .32624 L p .743 .917 .951 r F P 0 g s .76004 .53524 m .73102 .458 L .74652 .43391 L p .215 .268 .702 r F P 0 g s .63058 .81552 m .64735 .78949 L .70358 .7718 L p .325 .013 .272 r F P 0 g s .72655 .70393 m .70358 .7718 L .64735 .78949 L p .396 .157 .429 r F P 0 g s .18056 .60351 m .20735 .6231 L .20886 .69216 L p .967 .708 .488 r F P 0 g s .20735 .6231 m .18056 .60351 L .19831 .5353 L p .956 .771 .612 r F P 0 g s .20932 .43027 m .26701 .39006 L .27977 .36646 L p .896 .958 .83 r F P 0 g s .70358 .7718 m .72655 .70393 L .76752 .67992 L p .155 0 .305 r F P 0 g s .77232 .60889 m .76752 .67992 L .72655 .70393 L p .264 .125 .496 r F P 0 g s .55544 .36674 m .47895 .35552 L .47895 .28751 L p .768 .556 .612 r F P 0 g s .47895 .28751 m .41349 .27588 L p .43747 .27333 L .555 .829 .997 r F P 0 g s .43381 .27208 m .43218 .26907 L .47895 .28751 L .903 .671 .576 r F .42542 .25658 m .44668 .26886 L p .43218 .26907 L F P 0 g s .44668 .26886 m .47895 .28751 L p .43218 .26907 L .903 .671 .576 r F P 0 g s .41349 .27588 m .34497 .2837 L p .394 .26962 L .537 .906 .958 r F P 0 g s .43008 .27412 m .42529 .26917 L .43747 .27333 L .555 .829 .997 r F .41349 .27588 m .42529 .26917 L p .43008 .27412 L F P 0 g s .41757 .2437 m .42542 .25658 L .42529 .26917 L p .996 .767 .43 r F P 0 g s .41757 .2437 m .41018 .21654 L p .41288 .25651 L .931 .736 .254 r F P 0 g s .41438 .25636 m .41757 .2437 L .41288 .25651 L .931 .736 .254 r F .4173 .26595 m .41757 .2437 L p .41319 .26107 L F P 0 g s .41924 .26292 m .41757 .2437 L .42529 .26917 L .996 .767 .43 r F .42009 .26924 m .4173 .26595 L .42529 .26917 L .537 .906 .958 r F .394 .26962 m .4173 .26595 L .42009 .26924 L F .42529 .26917 m .41349 .27588 L p .394 .26962 L F P 0 g s .4247 .32589 m .41674 .31355 L .4173 .26595 L p .996 .767 .43 r F P 0 g s .4173 .26595 m .41757 .2437 L p .41958 .26686 L .996 .767 .43 r F P 0 g s .4247 .32589 m .4173 .26595 L .41958 .26686 L .996 .767 .43 r F .34497 .2837 m .38608 .25939 L .39791 .25812 L p .537 .906 .958 r F P 0 g s .41319 .26107 m .41438 .25636 L .41288 .25651 L .931 .736 .254 r F .42529 .26917 m .42542 .25658 L p .43381 .27208 L .903 .671 .576 r F P 0 g s .41293 .26418 m .40774 .26209 L .40964 .25685 L .537 .906 .958 r F .39791 .25812 m .40964 .25685 L p .40774 .26209 L F P 0 g s .41018 .21654 m .40964 .25685 L p .41319 .26107 L .931 .736 .254 r F P 0 g s .41018 .21654 m .41423 .19228 L p .41104 .25298 L 0 0 .131 r F P 0 g s .41293 .26418 m .40964 .25685 L .41525 .26351 L .537 .906 .958 r F .34497 .2837 m .39791 .25812 L .41293 .26418 L F .394 .26962 m .41293 .26418 L .4173 .26595 L F .30551 .32624 m .34497 .2837 L .41349 .27588 L p .743 .917 .951 r F P 0 g s .40964 .25685 m .40923 .28751 L p .41319 .26107 L .931 .736 .254 r F P 0 g s .40964 .25685 m .45563 .25191 L p .41525 .26351 L .537 .906 .958 r F P 0 g s .45353 .25209 m .41264 .25651 L .45563 .25191 L .077 .637 .704 r F .41084 .25672 m .40964 .25685 L .41104 .25298 L 0 0 .131 r F .40964 .25685 m .41018 .21654 L p .41104 .25298 L F P 0 g s .41264 .25651 m .4115 .25664 L .45563 .25191 L .077 .637 .704 r F .41958 .26686 m .41924 .26292 L .42529 .26917 L .996 .767 .43 r F .45563 .25191 m .42529 .26917 L p .41293 .26418 L .537 .906 .958 r F P 0 g s .40923 .28751 m .41674 .31355 L p .41319 .26107 L .931 .736 .254 r F P 0 g s .40964 .25685 m .45563 .25191 L p .4115 .25664 L .077 .637 .704 r F P 0 g s .41331 .26423 m .40923 .28751 L p .41084 .25672 L 0 0 .131 r F P 0 g s .41423 .19228 m .41341 .25643 L p .41084 .25672 L 0 0 .131 r F P 0 g s .41674 .31355 m .4173 .26595 L p .41319 .26107 L .931 .736 .254 r F P 0 g s .41341 .25643 m .41423 .19228 L p .41477 .25628 L .07 0 .452 r F P 0 g s .41471 .25628 m .38608 .25939 L p .40818 .257 L .077 .637 .704 r F P 0 g s .45353 .25209 m .42024 .25568 L p .40818 .257 L .077 .637 .704 r F P 0 g s .41423 .19228 m .43032 .17131 L p .41477 .25628 L .07 0 .452 r F P 0 g s .43032 .17131 m .42962 .2441 L .42024 .25568 L p .07 0 .452 r F P 0 g s .42024 .25568 m .41331 .26423 L p .4152 .25392 L .07 0 .452 r F P 0 g s .4152 .25392 m .43032 .17131 L .42024 .25568 L .07 0 .452 r F .42024 .25568 m .41471 .25628 L p .40818 .257 L .077 .637 .704 r F P 0 g s .41331 .26423 m .41341 .25643 L p .41477 .25628 L .07 0 .452 r F P 0 g s .42024 .25568 m .45353 .25209 L .42948 .25891 L p .243 0 0 r F P 0 g s .42529 .26917 m .4247 .32589 L p .41958 .26686 L .996 .767 .43 r F P 0 g s .41674 .31355 m .4247 .32589 L .42396 .39708 L p .996 .767 .43 r F P 0 g s .41588 .38531 m .41674 .31355 L .40923 .28751 L p .931 .736 .254 r F P 0 g s .42396 .39708 m .41588 .38531 L .41674 .31355 L p .996 .767 .43 r F P 0 g s .40923 .28751 m .40824 .36047 L .41588 .38531 L p .931 .736 .254 r F P 0 g s .41237 .33825 m .41331 .26423 L .42962 .2441 L p .07 0 .452 r F P 0 g s .47895 .35552 m .4247 .32589 L .42529 .26917 L p .903 .671 .576 r F P 0 g s .47895 .35552 m .42529 .26917 L .43381 .27208 L .903 .671 .576 r F .42529 .26917 m .45563 .25191 L p .43747 .27333 L .555 .829 .997 r F P 0 g s .42891 .31902 m .41237 .33825 L p .42744 .25601 L .07 0 .452 r F P 0 g s .42962 .2441 m .42948 .25891 L p .42744 .25601 L .07 0 .452 r F P 0 g s .42948 .25891 m .42891 .31902 L p .42744 .25601 L .07 0 .452 r F P 0 g s .45563 .25191 m .52215 .26433 L p .43747 .27333 L .555 .829 .997 r F P 0 g s .52215 .26433 m .47895 .28751 L p .43747 .27333 L .555 .829 .997 r F P 0 g s .47895 .28751 m .47895 .35552 L p .43381 .27208 L .903 .671 .576 r F P 0 g s .47895 .28751 m .52215 .26433 L .58654 .29567 L p .538 .723 .959 r F P 0 g s .42948 .25891 m .45353 .25209 L p .50077 .29082 L .552 .076 .078 r F P 0 g s .45829 .30312 m .4584 .27638 L p .46926 .28009 L .538 .36 .587 r F P 0 g s .50077 .29082 m .4584 .27638 L .42948 .25891 L .552 .076 .078 r F .50077 .29082 m .45829 .30312 L p .46926 .28009 L .538 .36 .587 r F P 0 g s .56823 .25999 m .52215 .26433 L .45563 .25191 L p .201 .695 .92 r F P 0 g s .45563 .25191 m .50039 .24705 L .56823 .25999 L p .201 .695 .92 r F P 0 g s .45563 .25191 m .50039 .24705 L .45353 .25209 L p .077 .637 .704 r F P 0 g s .52215 .26433 m .56823 .25999 L .63401 .29243 L p .287 .648 .968 r F P 0 g s .65416 .29923 m .63401 .29243 L .56823 .25999 L p 0 .401 .777 r F P 0 g s .56823 .25999 m .59767 .26969 L .65416 .29923 L p 0 .401 .777 r F P 0 g s .59767 .26969 m .56823 .25999 L .50039 .24705 L p .282 0 0 r F P 0 g s .50039 .24705 m .51922 .2534 L .59767 .26969 L p .282 0 0 r F P 0 g s .51922 .2534 m .45353 .25209 L .50039 .24705 L closepath p .353 0 0 r F P 0 g s .45353 .25209 m .51922 .2534 L p .50077 .29082 L .552 .076 .078 r F P 0 g s .50044 .2146 m .50077 .29082 L p .46926 .28009 L .538 .36 .587 r F P 0 g s .4586 .22746 m .45829 .30312 L .42891 .31902 L p .389 .242 .557 r F P 0 g s .48169 .29045 m .46643 .29016 L .44456 .27167 L p .552 .076 .078 r F P 0 g s .42891 .31902 m .42948 .25891 L p .4453 .26847 L .389 .242 .557 r F P 0 g s .44456 .27167 m .42948 .25891 L p .4584 .27638 L .552 .076 .078 r F P 0 g s .48169 .29045 m .44456 .27167 L .4584 .27638 L .552 .076 .078 r F .50077 .29082 m .48169 .29045 L p .4584 .27638 L F P 0 g s .4586 .22746 m .50044 .2146 L p .46926 .28009 L .538 .36 .587 r F P 0 g s .4584 .27638 m .4586 .22746 L p .46926 .28009 L .538 .36 .587 r F P 0 g s .42962 .2441 m .4586 .22746 L p .4453 .26847 L .389 .242 .557 r F P 0 g s .42948 .25891 m .42962 .2441 L p .4453 .26847 L .389 .242 .557 r F P 0 g s .42948 .25891 m .46643 .29016 L .45247 .29162 L p .508 .097 .196 r F P 0 g s .40923 .28751 m .40964 .25685 L p .41084 .25672 L 0 0 .131 r F P 0 g s .40824 .36047 m .40923 .28751 L .41331 .26423 L p 0 0 .131 r F P 0 g s .41331 .26423 m .41237 .33825 L .40824 .36047 L p 0 0 .131 r F P 0 g s .45247 .29162 m .36941 .3003 L .42948 .25891 L p .508 .097 .196 r F P 0 g s .42948 .25891 m .41471 .25628 L .42024 .25568 L p .243 0 0 r F P 0 g s .41341 .25643 m .41331 .26423 L p .41084 .25672 L 0 0 .131 r F P 0 g s .405 .25734 m .40964 .25685 L .4115 .25664 L .077 .637 .704 r F .41264 .25651 m .405 .25734 L .4115 .25664 L F .38608 .25939 m .40964 .25685 L p .405 .25734 L F P 0 g s .17718 .50907 m .19831 .5353 L .18056 .60351 L p .99 .827 .586 r F P 0 g s .19395 .45013 m .17718 .50907 L .19831 .5353 L p .954 .87 .716 r F P 0 g s .20932 .43027 m .19395 .45013 L p .19831 .5353 L .954 .87 .716 r F P 0 g s .77232 .60889 m .76004 .53524 L .78468 .50113 L p .089 .093 .567 r F P 0 g s .76454 .44791 m .78468 .50113 L .76004 .53524 L p .215 .268 .702 r F P 0 g s .74652 .43391 m .76454 .44791 L p .76004 .53524 L .215 .268 .702 r F P 0 g s .59388 .85358 m .53822 .86075 L .52353 .85158 L p .506 .16 .314 r F P 0 g s .53822 .86075 m .50226 .86277 L .52353 .85158 L closepath p .536 .122 .204 r F P 0 g s .55544 .36674 m .58072 .3652 L .58206 .43456 L p .672 .479 .616 r F P 0 g s .58206 .43456 m .55645 .43602 L .55544 .36674 L p .672 .479 .616 r F P 0 g s .47895 .35552 m .55544 .36674 L .55645 .43602 L p .768 .556 .612 r F P 0 g s .27977 .36646 m .27722 .33774 L p .20932 .43027 L .896 .958 .83 r F P 0 g s .27977 .36646 m .27722 .33774 L .30551 .32624 L closepath p .849 .938 .882 r F P 0 g s .58206 .43456 m .58072 .3652 L .6296 .35827 L p .632 .447 .614 r F P 0 g s .70358 .7718 m .67856 .81173 L .63058 .81552 L p .325 .013 .272 r F P 0 g s .59388 .85358 m .63058 .81552 L .67856 .81173 L p .287 0 .13 r F P 0 g s .35198 .83115 m .36716 .85413 L .44196 .86214 L p .712 .303 .27 r F P 0 g s .36716 .85413 m .35198 .83115 L .28443 .80391 L p .772 .306 .139 r F P 0 g s .28443 .80391 m .27479 .77951 L .23915 .76511 L closepath p .866 .451 .234 r F P 0 g s .21676 .7355 m .20886 .69216 L p .27479 .77951 L .905 .571 .403 r F P 0 g s .27479 .77951 m .23915 .76511 L .21676 .7355 L p .905 .571 .403 r F P 0 g s .45867 .87692 m .50226 .86277 L .53822 .86075 L p .429 0 0 r F P 0 g s .45867 .87692 m .44196 .86214 L .50226 .86277 L closepath p .601 .175 .204 r F P 0 g s .63159 .42796 m .6296 .35827 L .66872 .34788 L p .567 .396 .609 r F P 0 g s .6296 .35827 m .63159 .42796 L .58206 .43456 L p .632 .447 .614 r F P 0 g s .44196 .86214 m .45867 .87692 L .39106 .87656 L p .635 .147 .075 r F P 0 g s .39106 .87656 m .36716 .85413 L .44196 .86214 L p .635 .147 .075 r F P 0 g s .76752 .67992 m .77232 .60889 L .79767 .57696 L p 0 0 .351 r F P 0 g s .78468 .50113 m .79767 .57696 L .77232 .60889 L p .089 .093 .567 r F P 0 g s .63401 .29243 m .58654 .29567 L .52215 .26433 L p .287 .648 .968 r F P 0 g s .55645 .43602 m .47895 .42533 L .47895 .35552 L p .768 .556 .612 r F P 0 g s .4247 .32589 m .47895 .35552 L .47895 .42533 L p .903 .671 .576 r F P 0 g s .21676 .7355 m .20886 .69216 L .19084 .67997 L closepath p .949 .605 .321 r F P 0 g s .20886 .69216 m .19084 .67997 L .18056 .60351 L p .967 .708 .488 r F P 0 g s .56851 .87088 m .53822 .86075 L .59388 .85358 L closepath p .436 .018 .146 r F P 0 g s .53822 .86075 m .56851 .87088 L p .45867 .87692 L .429 0 0 r F P 0 g s .55645 .43602 m .58206 .43456 L .58344 .50577 L p .672 .479 .616 r F P 0 g s .58344 .50577 m .55748 .50715 L .55645 .43602 L p .672 .479 .616 r F P 0 g s .47895 .42533 m .55645 .43602 L .55748 .50715 L p .768 .556 .612 r F P 0 g s .27722 .33774 m .30551 .32624 L .34497 .2837 L p .753 .984 .907 r F P 0 g s .58344 .50577 m .58206 .43456 L .63159 .42796 L p .632 .447 .614 r F P 0 g s .69817 .33383 m .69528 .26487 L .71466 .24612 L p .241 .146 .542 r F P 0 g s .16605 .58709 m .18056 .60351 L .19084 .67997 L p .988 .718 .371 r F P 0 g s .18056 .60351 m .16605 .58709 L .17718 .50907 L p .99 .827 .586 r F P 0 g s .76454 .44791 m .74652 .43391 L .75102 .42035 L closepath p .132 .262 .732 r F P 0 g s .66872 .34788 m .67126 .41805 L .63159 .42796 L p .567 .396 .609 r F P 0 g s .67856 .81173 m .70358 .7718 L .74473 .7493 L p .028 0 .069 r F P 0 g s .76752 .67992 m .74473 .7493 L .70358 .7718 L p .155 0 .305 r F P 0 g s .19395 .45013 m .20716 .41662 L .20932 .43027 L closepath p .948 .956 .716 r F P 0 g s .23306 .36768 m .20716 .41662 L .20932 .43027 L p .896 .958 .83 r F P 0 g s .27722 .33774 m .23306 .36768 L p .20932 .43027 L .896 .958 .83 r F P 0 g s .28443 .80391 m .30608 .83851 L .36716 .85413 L p .772 .306 .139 r F P 0 g s .30608 .83851 m .28443 .80391 L .23915 .76511 L p .791 .292 0 r F P 0 g s .36716 .85413 m .39106 .87656 L .32136 .85347 L p .652 .106 0 r F P 0 g s .32136 .85347 m .30608 .83851 L .36716 .85413 L p .652 .106 0 r F P 0 g s .63364 .49952 m .63159 .42796 L .67126 .41805 L p .567 .396 .609 r F P 0 g s .63159 .42796 m .63364 .49952 L .58344 .50577 L p .632 .447 .614 r F P 0 g s .56851 .87088 m .59388 .85358 L .65411 .83765 L p .162 0 0 r F P 0 g s .67856 .81173 m .65411 .83765 L .59388 .85358 L p .287 0 .13 r F P 0 g s .56851 .87088 m .50253 .89301 L .45867 .87692 L p .429 0 0 r F P 0 g s .50253 .89301 m .45867 .87692 L .39106 .87656 L p .391 0 0 r F P 0 g s .55748 .50715 m .47895 .49703 L .47895 .42533 L p .768 .556 .612 r F P 0 g s .42396 .39708 m .47895 .42533 L .47895 .49703 L p .903 .671 .576 r F P 0 g s .47895 .42533 m .42396 .39708 L .4247 .32589 L p .903 .671 .576 r F P 0 g s .17077 .49289 m .17718 .50907 L .16605 .58709 L p .987 .848 .475 r F P 0 g s .17718 .50907 m .17077 .49289 L .19395 .45013 L closepath p .978 .916 .652 r F P 0 g s .19084 .67997 m .16893 .65695 L p .22291 .75652 L .898 .513 .068 r F P 0 g s .22291 .75652 m .21676 .7355 L .19084 .67997 L p .898 .513 .068 r F P 0 g s .19084 .67997 m .16893 .65695 L .16605 .58709 L p .988 .718 .371 r F P 0 g s .23306 .36768 m .27722 .33774 L .30187 .30078 L p .752 .992 .805 r F P 0 g s .34497 .2837 m .30187 .30078 L .27722 .33774 L p .753 .984 .907 r F P 0 g s .79311 .64998 m .76752 .67992 L .74473 .7493 L p 0 0 .057 r F P 0 g s .79767 .57696 m .79311 .64998 L .76752 .67992 L p 0 0 .351 r F P 0 g s .23915 .76511 m .22291 .75652 L p .30608 .83851 L .791 .292 0 r F P 0 g s .23915 .76511 m .21676 .7355 L .22291 .75652 L closepath p .91 .517 .247 r F P 0 g s .17077 .49289 m .19395 .45013 L .20716 .41662 L p .878 .929 .544 r F P 0 g s .55748 .50715 m .58344 .50577 L .58485 .57891 L p .672 .479 .616 r F P 0 g s .58485 .57891 m .55854 .58021 L .55748 .50715 L p .672 .479 .616 r F P 0 g s .47895 .49703 m .55748 .50715 L .55854 .58021 L p .768 .556 .612 r F P 0 g s .78794 .4847 m .76454 .44791 L .75102 .42035 L p 0 0 .541 r F P 0 g s .58485 .57891 m .58344 .50577 L .63364 .49952 L p .632 .447 .614 r F P 0 g s .71466 .24612 m .71785 .31587 L .69817 .33383 L p .241 .146 .542 r F P 0 g s .78468 .50113 m .76454 .44791 L .78794 .4847 L closepath p 0 .07 .614 r F P 0 g s .67387 .49013 m .67126 .41805 L .70114 .40466 L p .455 .31 .593 r F P 0 g s .67126 .41805 m .67387 .49013 L .63364 .49952 L p .567 .396 .609 r F P 0 g s .71785 .31587 m .71466 .24612 L .72411 .22295 L p 0 0 .379 r F P 0 g s .20716 .41662 m .21102 .39061 L p .17077 .49289 L .878 .929 .544 r F P 0 g s .20716 .41662 m .21102 .39061 L .23306 .36768 L closepath p .889 .988 .74 r F P 0 g s .65411 .83765 m .61594 .8641 L .56851 .87088 L p .162 0 0 r F P 0 g s .61594 .8641 m .56851 .87088 L .50253 .89301 L p .018 0 0 r F P 0 g s .74473 .7493 m .72807 .77634 L .67856 .81173 L p .028 0 .069 r F P 0 g s .65411 .83765 m .67856 .81173 L .72807 .77634 L p 0 0 0 r F P 0 g s .78794 .4847 m .78468 .50113 L .79767 .57696 L p 0 0 .389 r F P 0 g s .15601 .56432 m .16605 .58709 L .16893 .65695 L p .928 .694 .208 r F P 0 g s .16605 .58709 m .15601 .56432 L .17077 .49289 L p .987 .848 .475 r F P 0 g s .63575 .57302 m .63364 .49952 L .67387 .49013 L p .567 .396 .609 r F P 0 g s .63364 .49952 m .63575 .57302 L .58485 .57891 L p .632 .447 .614 r F P 0 g s .67723 .32683 m .63401 .29243 L .65416 .29923 L closepath p .016 .417 .86 r F P 0 g s .55854 .58021 m .47895 .57068 L .47895 .49703 L p .768 .556 .612 r F P 0 g s .4232 .47025 m .47895 .49703 L .47895 .57068 L p .903 .671 .576 r F P 0 g s .47895 .49703 m .4232 .47025 L .42396 .39708 L p .903 .671 .576 r F P 0 g s .22291 .75652 m .25049 .80229 L p .30608 .83851 L .791 .292 0 r F P 0 g s .25049 .80229 m .22291 .75652 L .19426 .72798 L closepath p .714 .247 0 r F P 0 g s .1807 .69889 m .19426 .72798 L .22291 .75652 L p .898 .513 .068 r F P 0 g s .16893 .65695 m .1807 .69889 L p .22291 .75652 L .898 .513 .068 r F P 0 g s .30187 .30078 m .34497 .2837 L .38608 .25939 L p .453 .879 .787 r F P 0 g s .55854 .58021 m .58485 .57891 L .5863 .65405 L p .672 .479 .616 r F P 0 g s .5863 .65405 m .55963 .65527 L .55854 .58021 L p .672 .479 .616 r F P 0 g s .47895 .57068 m .55854 .58021 L .55963 .65527 L p .768 .556 .612 r F P 0 g s .15601 .56432 m .17077 .49289 L .17538 .45575 L p .762 .73 .203 r F P 0 g s .21102 .39061 m .17538 .45575 L .17077 .49289 L p .878 .929 .544 r F P 0 g s .5863 .65405 m .58485 .57891 L .63575 .57302 L p .632 .447 .614 r F P 0 g s .70418 .47743 m .70114 .40466 L .72113 .38753 L p .241 .146 .542 r F P 0 g s .70114 .40466 m .70418 .47743 L .67387 .49013 L p .455 .31 .593 r F P 0 g s .39106 .87656 m .43351 .89296 L .50253 .89301 L p .391 0 0 r F P 0 g s .43351 .89296 m .39106 .87656 L .32136 .85347 L p .282 0 0 r F P 0 g s .67654 .56418 m .67387 .49013 L .70418 .47743 L p .455 .31 .593 r F P 0 g s .67387 .49013 m .67654 .56418 L .63575 .57302 L p .567 .396 .609 r F P 0 g s .72411 .22295 m .7275 .29366 L .71785 .31587 L p 0 0 .379 r F P 0 g s .32136 .85347 m .30608 .83851 L .27418 .8225 L closepath p .613 .054 0 r F P 0 g s .25049 .80229 m .27418 .8225 L .30608 .83851 L p .791 .292 0 r F P 0 g s .80296 .55369 m .79767 .57696 L .79311 .64998 L p 0 0 .069 r F P 0 g s .79767 .57696 m .80296 .55369 L .78794 .4847 L p 0 0 .389 r F P 0 g s .30187 .30078 m .27201 .32077 L .23306 .36768 L p .752 .992 .805 r F P 0 g s .21102 .39061 m .23306 .36768 L .27201 .32077 L p .621 .89 .57 r F P 0 g s .61594 .8641 m .65411 .83765 L .6912 .81576 L p 0 0 0 r F P 0 g s .72807 .77634 m .6912 .81576 L .65411 .83765 L p 0 0 0 r F P 0 g s .72807 .77634 m .76141 .73078 L .74473 .7493 L closepath p 0 0 0 r F P 0 g s .77785 .69711 m .79311 .64998 L p .74473 .7493 L 0 0 .057 r F P 0 g s .74473 .7493 m .76141 .73078 L .77785 .69711 L p 0 0 .057 r F P 0 g s .63791 .64855 m .63575 .57302 L .67654 .56418 L p .567 .396 .609 r F P 0 g s .63575 .57302 m .63791 .64855 L .5863 .65405 L p .632 .447 .614 r F P 0 g s .7275 .29366 m .72411 .22295 L .72318 .1949 L p 0 0 .048 r F P 0 g s .78209 .45569 m .78794 .4847 L .80296 .55369 L p 0 0 .161 r F P 0 g s .41588 .38531 m .42396 .39708 L .4232 .47025 L p .996 .767 .43 r F P 0 g s .55963 .65527 m .47895 .64637 L .47895 .57068 L p .768 .556 .612 r F P 0 g s .42242 .54546 m .47895 .57068 L .47895 .64637 L p .903 .671 .576 r F P 0 g s .47895 .57068 m .42242 .54546 L .4232 .47025 L p .903 .671 .576 r F P 0 g s .1807 .69889 m .16893 .65695 L .16221 .64273 L closepath p .775 .451 0 r F P 0 g s .16893 .65695 m .16221 .64273 L .15601 .56432 L p .928 .694 .208 r F P 0 g s .55963 .65527 m .5863 .65405 L .5878 .73128 L p .672 .479 .616 r F P 0 g s .5878 .73128 m .56075 .73241 L .55963 .65527 L p .672 .479 .616 r F P 0 g s .47895 .64637 m .55963 .65527 L .56075 .73241 L p .768 .556 .612 r F P 0 g s .27201 .32077 m .23857 .35545 L .21102 .39061 L p .621 .89 .57 r F P 0 g s .17538 .45575 m .21102 .39061 L .23857 .35545 L p 0 0 0 r F P 0 g s .5878 .73128 m .5863 .65405 L .63791 .64855 L p .632 .447 .614 r F P 0 g s .70732 .55223 m .70418 .47743 L .72451 .46119 L p .241 .146 .542 r F P 0 g s .72113 .38753 m .72451 .46119 L .70418 .47743 L p .241 .146 .542 r F P 0 g s .70418 .47743 m .70732 .55223 L .67654 .56418 L p .455 .31 .593 r F P 0 g s .38608 .25939 m .35712 .27077 L .30187 .30078 L p .453 .879 .787 r F P 0 g s .27201 .32077 m .30187 .30078 L .35712 .27077 L p 0 0 0 r F P 0 g s .50253 .89301 m .54913 .88673 L .61594 .8641 L p .018 0 0 r F P 0 g s .54913 .88673 m .50253 .89301 L .43351 .89296 L p .174 .706 .837 r F P 0 g s .6912 .81576 m .72807 .77634 L .76141 .73078 L p .729 .943 .627 r F P 0 g s .17538 .45575 m .16015 .52916 L .15601 .56432 L p .762 .73 .203 r F P 0 g s .16221 .64273 m .15601 .56432 L .16015 .52916 L p 0 0 .205 r F P 0 g s .65416 .29923 m .68603 .32239 L .61828 .28486 L p .498 0 0 r F P 0 g s .61828 .28486 m .59767 .26969 L .65416 .29923 L p .498 0 0 r F P 0 g s .6793 .6403 m .67654 .56418 L .70732 .55223 L p .455 .31 .593 r F P 0 g s .67654 .56418 m .6793 .6403 L .63791 .64855 L p .567 .396 .609 r F P 0 g s .32136 .85347 m .36211 .86934 L .43351 .89296 L p .282 0 0 r F P 0 g s .28908 .82128 m .36211 .86934 L .32136 .85347 L p 0 .361 .792 r F P 0 g s .26294 .81154 m .28908 .82128 L p .32136 .85347 L 0 .361 .792 r F P 0 g s .32136 .85347 m .27418 .8225 L .26294 .81154 L p 0 .361 .792 r F P 0 g s .415 .45909 m .41588 .38531 L .40824 .36047 L p .931 .736 .254 r F P 0 g s .4232 .47025 m .415 .45909 L .41588 .38531 L p .996 .767 .43 r F P 0 g s .79311 .64998 m .79659 .63553 L .80296 .55369 L p 0 0 .069 r F P 0 g s .77785 .69711 m .79659 .63553 L .79311 .64998 L closepath p .73 .765 .262 r F P 0 g s .6912 .81576 m .66551 .83361 L .61594 .8641 L p 0 0 0 r F P 0 g s .47895 .80421 m .56191 .81172 L .56287 .87814 L p .768 .556 .612 r F P 0 g s .61594 .8641 m .54913 .88673 L p .59564 .86551 L .537 .925 .864 r F P 0 g s .58933 .81069 m .64243 .80606 L p .61309 .85522 L .632 .447 .614 r F P 0 g s .54913 .88673 m .55873 .88073 L p .60628 .85975 L .537 .925 .864 r F P 0 g s .58788 .86905 m .60628 .85975 L .66551 .83361 L .537 .925 .864 r F .54913 .88673 m .60628 .85975 L .58788 .86905 L F .66551 .83361 m .69943 .79673 L .6912 .81576 L closepath p .726 .983 .779 r F P 0 g s .69943 .79673 m .66551 .83361 L .65452 .83728 L p .789 .968 .916 r F P 0 g s .68536 .80785 m .69943 .79673 L .65452 .83728 L .789 .968 .916 r F .76141 .73078 m .76636 .72034 L p .6912 .81576 L .729 .943 .627 r F P 0 g s .71657 .77318 m .69943 .79673 L .6912 .81576 L p .729 .943 .627 r F P 0 g s .76636 .72034 m .71657 .77318 L p .6912 .81576 L .729 .943 .627 r F P 0 g s .68804 .88194 m .68536 .80785 L p .71726 .78965 L .455 .31 .593 r F P 0 g s .68536 .80785 m .68504 .79909 L .69875 .79507 L p .455 .31 .593 r F P 0 g s .64243 .80606 m .68504 .79909 L p .67871 .8131 L .567 .396 .609 r F P 0 g s .66705 .82231 m .64243 .80606 L .67871 .8131 L .567 .396 .609 r F .65452 .83728 m .64343 .84098 L p .68536 .80785 L .789 .968 .916 r F P 0 g s .64343 .84098 m .64243 .80606 L p .67283 .82612 L .567 .396 .609 r F P 0 g s .5904 .86587 m .58933 .81069 L p .61309 .85522 L .632 .447 .614 r F P 0 g s .55873 .88073 m .58107 .87025 L .66551 .83361 L .537 .925 .864 r F .64343 .84098 m .65452 .83728 L p .5904 .86587 L F P 0 g s .65452 .83728 m .66551 .83361 L p .56287 .87814 L .537 .925 .864 r F P 0 g s .66551 .83361 m .64395 .84687 L p .59564 .86551 L .537 .925 .864 r F P 0 g s .64395 .84687 m .61594 .8641 L p .59564 .86551 L .537 .925 .864 r F P 0 g s .64478 .88821 m .59091 .89238 L p .61309 .85522 L .632 .447 .614 r F P 0 g s .64243 .80606 m .64343 .84098 L p .61309 .85522 L .632 .447 .614 r F P 0 g s .64343 .84098 m .64478 .88821 L p .61309 .85522 L .632 .447 .614 r F P 0 g s .56191 .81172 m .58933 .81069 L .5904 .86587 L p .672 .479 .616 r F P 0 g s .58262 .86934 m .56191 .81172 L .5904 .86587 L .672 .479 .616 r F .55873 .88073 m .56287 .87814 L p .58107 .87025 L .537 .925 .864 r F P 0 g s .59091 .89238 m .56309 .8933 L .56287 .87814 L p .672 .479 .616 r F P 0 g s .56287 .87814 m .56191 .81172 L p .58403 .87324 L .672 .479 .616 r F P 0 g s .59091 .89238 m .56287 .87814 L .58403 .87324 L .672 .479 .616 r F .56287 .87814 m .54913 .88673 L .52606 .88667 L p .612 .893 .989 r F P 0 g s .52606 .88667 m .47895 .88655 L p .56287 .87814 L .612 .893 .989 r F P 0 g s .55254 .88213 m .47895 .80421 L .56287 .87814 L .768 .556 .612 r F .43351 .89296 m .47895 .88655 L .54913 .88673 L p .174 .706 .837 r F P 0 g s .56309 .8933 m .47895 .88655 L .47895 .80421 L p .768 .556 .612 r F P 0 g s .59815 .85609 m .56287 .87814 L p .47895 .88655 L .612 .893 .989 r F P 0 g s .56287 .87814 m .59815 .85609 L .64343 .84098 L p .537 .925 .864 r F P 0 g s .56287 .87814 m .64343 .84098 L .5904 .86587 L .537 .925 .864 r F .68504 .79909 m .68804 .88194 L .64478 .88821 L p .567 .396 .609 r F P 0 g s .64343 .84098 m .59815 .85609 L p .69943 .79673 L .789 .968 .916 r F P 0 g s .68504 .79909 m .68213 .71857 L .71385 .70824 L p .455 .31 .593 r F P 0 g s .68213 .71857 m .68504 .79909 L .64243 .80606 L p .567 .396 .609 r F P 0 g s .71385 .70824 m .71657 .77318 L p .68504 .79909 L .455 .31 .593 r F P 0 g s .71657 .77318 m .69943 .79673 L .69875 .79507 L p .85 .983 .86 r F P 0 g s .71657 .77318 m .71677 .77787 L p .70795 .78377 L .455 .31 .593 r F P 0 g s .68504 .79909 m .71657 .77318 L .70795 .78377 L .455 .31 .593 r F .69875 .79507 m .68504 .79909 L p .71677 .77787 L F P 0 g s .69875 .79507 m .69461 .78494 L .71657 .77318 L p .85 .983 .86 r F P 0 g s .69461 .78494 m .69875 .79507 L p .59815 .85609 L .789 .968 .916 r F P 0 g s .69875 .79507 m .69943 .79673 L p .69316 .80041 L .789 .968 .916 r F P 0 g s .59815 .85609 m .69875 .79507 L .69316 .80041 L .789 .968 .916 r F .71677 .77787 m .71726 .78965 L .69875 .79507 L p .455 .31 .593 r F P 0 g s .69875 .79507 m .71726 .78965 L p .68536 .80785 L .455 .31 .593 r F P 0 g s .67283 .82612 m .66705 .82231 L .67871 .8131 L .567 .396 .609 r F .64478 .88821 m .64343 .84098 L p .67283 .82612 L F P 0 g s .59091 .89238 m .5904 .86587 L p .61309 .85522 L .632 .447 .614 r F P 0 g s .5904 .86587 m .59091 .89238 L p .58262 .86934 L .672 .479 .616 r F P 0 g s .56287 .87814 m .56309 .8933 L p .55254 .88213 L .768 .556 .612 r F P 0 g s .64014 .7262 m .63791 .64855 L .6793 .6403 L p .567 .396 .609 r F P 0 g s .63791 .64855 m .64014 .7262 L .5878 .73128 L p .632 .447 .614 r F P 0 g s .73097 .36634 m .7275 .29366 L .72663 .26675 L p 0 0 .048 r F P 0 g s .72318 .1949 m .72663 .26675 L .7275 .29366 L p 0 0 .048 r F P 0 g s .415 .45909 m .4232 .47025 L .42242 .54546 L p .996 .767 .43 r F P 0 g s .56075 .73241 m .47895 .72418 L .47895 .64637 L p .768 .556 .612 r F P 0 g s .42162 .62282 m .47895 .64637 L .47895 .72418 L p .903 .671 .576 r F P 0 g s .47895 .64637 m .42162 .62282 L .42242 .54546 L p .903 .671 .576 r F P 0 g s .27418 .8225 m .25049 .80229 L .26294 .81154 L closepath p 0 .133 .615 r F P 0 g s .56075 .73241 m .5878 .73128 L .58933 .81069 L p .672 .479 .616 r F P 0 g s .58933 .81069 m .56191 .81172 L .56075 .73241 L p .672 .479 .616 r F P 0 g s .47895 .72418 m .56075 .73241 L .56191 .81172 L p .768 .556 .612 r F P 0 g s .80296 .55369 m .7993 .53544 L .78209 .45569 L p 0 0 .161 r F P 0 g s .7993 .53544 m .80296 .55369 L .79659 .63553 L p .902 .765 .272 r F P 0 g s .16221 .64273 m .16663 .61005 L p .19178 .71747 L 0 0 .513 r F P 0 g s .19178 .71747 m .1807 .69889 L .16221 .64273 L p 0 0 .513 r F P 0 g s .16015 .52916 m .16663 .61005 L .16221 .64273 L p 0 0 .205 r F P 0 g s .35712 .27077 m .31201 .3011 L .27201 .32077 L p 0 0 0 r F P 0 g s .23857 .35545 m .27201 .32077 L .31201 .3011 L p 0 0 0 r F P 0 g s .41471 .25628 m .35712 .27077 L .38608 .25939 L closepath p .028 0 0 r F P 0 g s .58933 .81069 m .5878 .73128 L .64014 .7262 L p .632 .447 .614 r F P 0 g s .71811 .18074 m .72318 .1949 L .72663 .26675 L p .937 .707 .23 r F P 0 g s .71054 .62914 m .70732 .55223 L .72798 .53693 L p .241 .146 .542 r F P 0 g s .72451 .46119 m .72798 .53693 L .70732 .55223 L p .241 .146 .542 r F P 0 g s .70732 .55223 m .71054 .62914 L .6793 .6403 L p .455 .31 .593 r F P 0 g s .76141 .73078 m .76636 .72034 L .77785 .69711 L closepath p .646 .782 .322 r F P 0 g s .26294 .81154 m .25049 .80229 L .19426 .72798 L p 0 .163 .701 r F P 0 g s .68213 .71857 m .6793 .6403 L .71054 .62914 L p .455 .31 .593 r F P 0 g s .6793 .6403 m .68213 .71857 L .64014 .7262 L p .567 .396 .609 r F P 0 g s .72798 .53693 m .72451 .46119 L .73455 .44108 L p 0 0 .379 r F P 0 g s .19426 .72798 m .1807 .69889 L .19178 .71747 L closepath p 0 0 .449 r F P 0 g s .41409 .53495 m .415 .45909 L .40724 .43551 L p .931 .736 .254 r F P 0 g s .40824 .36047 m .40724 .43551 L .415 .45909 L p .931 .736 .254 r F P 0 g s .42242 .54546 m .41409 .53495 L .415 .45909 L p .996 .767 .43 r F P 0 g s .19426 .72798 m .19178 .71747 L p .26294 .81154 L 0 .163 .701 r F P 0 g s .78209 .45569 m .75373 .39795 L .77176 .43899 L closepath p .743 .354 0 r F P 0 g s .76636 .72034 m .77785 .69711 L .79659 .63553 L p .952 .924 .57 r F P 0 g s .64243 .80606 m .64014 .7262 L .68213 .71857 L p .567 .396 .609 r F P 0 g s .64014 .7262 m .64243 .80606 L .58933 .81069 L p .632 .447 .614 r F P 0 g s .72663 .26675 m .73017 .34065 L .73097 .36634 L p 0 0 .048 r F P 0 g s .73097 .36634 m .68603 .32239 L .70215 .34238 L closepath p .666 .152 0 r F P 0 g s .47895 .88655 m .43351 .89296 L .36211 .86934 L p .297 .7 .975 r F P 0 g s .16015 .52916 m .17538 .45575 L .20242 .42186 L p 0 0 .223 r F P 0 g s .23857 .35545 m .20242 .42186 L .17538 .45575 L p 0 0 0 r F P 0 g s .77176 .43899 m .78209 .45569 L .7993 .53544 L p .934 .631 .168 r F P 0 g s .79659 .63553 m .79082 .60999 L p .76636 .72034 L .952 .924 .57 r F P 0 g s .79659 .63553 m .79082 .60999 L .7993 .53544 L p .902 .765 .272 r F P 0 g s .41409 .53495 m .42242 .54546 L .42162 .62282 L p .996 .767 .43 r F P 0 g s .56191 .81172 m .47895 .80421 L .47895 .72418 L p .768 .556 .612 r F P 0 g s .42079 .7024 m .47895 .72418 L .47895 .80421 L p .903 .671 .576 r F P 0 g s .47895 .72418 m .42079 .7024 L .42162 .62282 L p .903 .671 .576 r F P 0 g s .72663 .26675 m .72152 .25316 L .71811 .18074 L p .937 .707 .23 r F P 0 g s .66634 .14417 m .71811 .18074 L .72152 .25316 L p .934 .68 .53 r F P 0 g s .35712 .27077 m .41471 .25628 L p .36941 .3003 L .276 0 0 r F P 0 g s .31201 .3011 m .35712 .27077 L p .36941 .3003 L .276 0 0 r F P 0 g s .40724 .43551 m .40824 .36047 L .41237 .33825 L p 0 0 .131 r F P 0 g s .59767 .26969 m .61828 .28486 L .54876 .27624 L p .577 .023 0 r F P 0 g s .54876 .27624 m .51922 .2534 L .59767 .26969 L p .577 .023 0 r F P 0 g s .28908 .82128 m .26294 .81154 L .25971 .79228 L closepath p 0 .341 .82 r F P 0 g s .21594 .73437 m .25971 .79228 L .26294 .81154 L p 0 .163 .701 r F P 0 g s .19178 .71747 m .21594 .73437 L p .26294 .81154 L 0 .163 .701 r F P 0 g s .70215 .34238 m .68603 .32239 L .61828 .28486 L p .745 .227 0 r F P 0 g s .73522 .69501 m .74592 .67861 L p .7423 .69596 L 0 0 .379 r F P 0 g s .75737 .68902 m .74592 .67861 L p .73737 .71959 L .904 .905 .813 r F P 0 g s .73346 .73835 m .75737 .68902 L p .73941 .71647 L .904 .905 .813 r F P 0 g s .73737 .71959 m .73653 .72363 L .73941 .71647 L .904 .905 .813 r F .73653 .72363 m .73346 .73835 L .73941 .71647 L F .73522 .69501 m .73653 .72363 L p .72379 .75527 L .241 .146 .542 r F P 0 g s .71657 .77318 m .73346 .73835 L p .72793 .74498 L .904 .905 .813 r F P 0 g s .71385 .70824 m .73522 .69501 L p .72379 .75527 L .241 .146 .542 r F P 0 g s .71657 .77318 m .71385 .70824 L p .72379 .75527 L .241 .146 .542 r F P 0 g s .69461 .78494 m .71657 .77318 L p .72793 .74498 L .904 .905 .813 r F P 0 g s .72716 .76194 m .71657 .77318 L .73346 .73835 L p .924 .975 .733 r F P 0 g s .71726 .78965 m .71657 .77318 L p .72379 .75527 L .241 .146 .542 r F P 0 g s .75737 .68902 m .76636 .72034 L .72716 .76194 L p .924 .975 .733 r F P 0 g s .73346 .73835 m .75737 .68902 L p .72716 .76194 L .924 .975 .733 r F P 0 g s .739 .77756 m .71726 .78965 L p .72379 .75527 L .241 .146 .542 r F P 0 g s .73653 .72363 m .73522 .69501 L p .7423 .69596 L 0 0 .379 r F P 0 g s .69461 .78494 m .73346 .73835 L .73737 .71959 L .904 .905 .813 r F .73653 .72363 m .739 .77756 L p .72379 .75527 L .241 .146 .542 r F P 0 g s .73665 .72637 m .73653 .72363 L p .74468 .69627 L 0 0 .379 r F P 0 g s .73653 .72363 m .7423 .69596 L .74468 .69627 L 0 0 .379 r F .69461 .78494 m .73737 .71959 L .74592 .67861 L .904 .905 .813 r F .74468 .69627 m .7423 .69596 L .74592 .67861 L 0 0 .379 r F .739 .77756 m .73665 .72637 L p .74468 .69627 L F P 0 g s .76716 .65679 m .75737 .68902 L .76636 .72034 L p .952 .924 .57 r F P 0 g s .79082 .60999 m .76716 .65679 L p .76636 .72034 L .952 .924 .57 r F P 0 g s .72152 .25316 m .72663 .26675 L .73017 .34065 L p .937 .707 .23 r F P 0 g s .71385 .70824 m .71054 .62914 L .73155 .61484 L p .241 .146 .542 r F P 0 g s .72798 .53693 m .73155 .61484 L .71054 .62914 L p .241 .146 .542 r F P 0 g s .71054 .62914 m .71385 .70824 L .68213 .71857 L p .455 .31 .593 r F P 0 g s .20242 .42186 m .23857 .35545 L .28957 .32461 L p .122 0 .175 r F P 0 g s .31201 .3011 m .28957 .32461 L .23857 .35545 L p 0 0 0 r F P 0 g s .73155 .61484 m .72798 .53693 L .73823 .51798 L p 0 0 .379 r F P 0 g s .73455 .44108 m .73823 .51798 L .72798 .53693 L p 0 0 .379 r F P 0 g s .21594 .73437 m .19178 .71747 L .19548 .69739 L closepath p 0 .158 .693 r F P 0 g s .16663 .61005 m .19548 .69739 L .19178 .71747 L p 0 0 .513 r F P 0 g s .78393 .51181 m .7993 .53544 L .79082 .60999 L p .997 .799 .444 r F P 0 g s .7993 .53544 m .78393 .51181 L .77176 .43899 L p .934 .631 .168 r F P 0 g s .42962 .2441 m .43032 .17131 L .45889 .15397 L p .389 .242 .557 r F P 0 g s .41316 .61299 m .41409 .53495 L .4062 .51273 L p .931 .736 .254 r F P 0 g s .42162 .62282 m .41316 .61299 L .41409 .53495 L p .996 .767 .43 r F P 0 g s .40724 .43551 m .4062 .51273 L .41409 .53495 L p .931 .736 .254 r F P 0 g s .73823 .51798 m .73455 .44108 L .73382 .4167 L p 0 0 .048 r F P 0 g s .77176 .43899 m .78393 .51181 L p .73388 .41456 L .963 .649 .375 r F P 0 g s .73382 .4167 m .73455 .44108 L p .73206 .38388 L 0 0 .048 r F P 0 g s .73357 .40833 m .77176 .43899 L p .73703 .39079 L .881 .45 .075 r F P 0 g s .73703 .39079 m .73206 .38388 L .7329 .39748 L .881 .45 .075 r F .73703 .39079 m .7329 .39748 L .73357 .40833 L F .73206 .38388 m .73051 .34843 L .73285 .39677 L 0 0 .048 r F .73206 .38388 m .73285 .39677 L .73382 .4167 L F .73107 .35946 m .73382 .4167 L p .73051 .34843 L F P 0 g s .7329 .39748 m .73382 .4167 L p .73206 .39884 L .937 .707 .23 r F P 0 g s .73206 .38388 m .70215 .34238 L .73036 .40159 L .881 .45 .075 r F .73382 .4167 m .72864 .40437 L p .73206 .39884 L .937 .707 .23 r F P 0 g s .7329 .39748 m .73036 .40159 L .73357 .40833 L .881 .45 .075 r F .73206 .38388 m .73036 .40159 L .7329 .39748 L F .70215 .34238 m .72864 .40437 L .73357 .40833 L p F P 0 g s .72864 .40437 m .72503 .32767 L p .73206 .39884 L .937 .707 .23 r F P 0 g s .73017 .34065 m .73107 .35946 L p .73051 .34843 L 0 0 .048 r F P 0 g s .72503 .32767 m .73017 .34065 L .7329 .39748 L p .937 .707 .23 r F P 0 g s .73206 .39884 m .72503 .32767 L .7329 .39748 L .937 .707 .23 r F .72864 .40437 m .73357 .40833 L p .73388 .41456 L .963 .649 .375 r F P 0 g s .73357 .40833 m .77176 .43899 L p .73388 .41456 L .963 .649 .375 r F P 0 g s .41316 .61299 m .42162 .62282 L .42079 .7024 L p .996 .767 .43 r F P 0 g s .41471 .25628 m .42948 .25891 L .36941 .3003 L p .276 0 0 r F P 0 g s .41994 .78431 m .47895 .80421 L .47895 .88655 L p .903 .671 .576 r F P 0 g s .47895 .80421 m .41994 .78431 L .42079 .7024 L p .903 .671 .576 r F P 0 g s .42454 .86104 m .42759 .85767 L .43276 .86057 L .592 .776 .968 r F .41698 .86147 m .41923 .85297 L .42454 .86104 L F .40608 .86208 m .41526 .85572 L p .41698 .86147 L F P 0 g s .41526 .85572 m .41923 .85297 L p .41698 .86147 L .592 .776 .968 r F P 0 g s .40608 .86208 m .3313 .81239 L p .40835 .82324 L .551 .669 .916 r F P 0 g s .40854 .82414 m .41122 .77599 L .40709 .81733 L .931 .736 .254 r F .41526 .85572 m .40608 .86208 L p .40807 .82799 L .551 .669 .916 r F P 0 g s .40835 .82324 m .41053 .83351 L .40807 .82799 L .551 .669 .916 r F .41053 .83351 m .41526 .85572 L .40807 .82799 L F .41053 .83351 m .41122 .77599 L p .41739 .84885 L .996 .767 .43 r F P 0 g s .41046 .83963 m .41053 .83351 L p .40811 .83177 L .931 .736 .254 r F P 0 g s .41053 .83351 m .41122 .77599 L p .40854 .82414 L .931 .736 .254 r F P 0 g s .41053 .83351 m .40854 .82414 L .40811 .83177 L .931 .736 .254 r F .41923 .85297 m .41994 .78431 L p .47895 .88655 L .903 .671 .576 r F P 0 g s .41122 .77599 m .41994 .78431 L .41923 .85297 L p .996 .767 .43 r F P 0 g s .41923 .85297 m .41526 .85572 L p .41053 .83351 L .551 .669 .916 r F P 0 g s .41838 .85167 m .4183 .85089 L .41923 .85297 L .996 .767 .43 r F .4183 .85089 m .41122 .77599 L .41923 .85297 L F .41826 .85911 m .41122 .77599 L .41916 .85992 L F .45302 .82954 m .41923 .85297 L p .40835 .82324 L .551 .669 .916 r F P 0 g s .40835 .82324 m .41923 .85297 L .41053 .83351 L .551 .669 .916 r F .36211 .86934 m .40608 .86208 L .43065 .87033 L p .297 .7 .975 r F P 0 g s .52709 .85524 m .47895 .88655 L .43065 .87033 L p .592 .776 .968 r F P 0 g s .43065 .87033 m .40608 .86208 L p .42454 .86104 L .592 .776 .968 r F P 0 g s .42454 .86104 m .52709 .85524 L .43065 .87033 L .592 .776 .968 r F .41752 .85036 m .41053 .83351 L .41739 .84885 L .996 .767 .43 r F .41907 .86864 m .41293 .84339 L .41752 .85036 L F .41293 .84339 m .41053 .83351 L .41752 .85036 L F .41907 .86864 m .4102 .86116 L .41053 .83351 L p F P 0 g s .41122 .77599 m .4029 .7584 L p .40709 .81733 L .931 .736 .254 r F P 0 g s .3313 .81239 m .37675 .77799 L .4024 .79532 L p .551 .669 .916 r F P 0 g s .4029 .7584 m .4024 .79532 L p .40709 .81733 L .931 .736 .254 r F P 0 g s .4024 .79532 m .45302 .82954 L p .40835 .82324 L .551 .669 .916 r F P 0 g s .40403 .67407 m .4029 .7584 L .41122 .77599 L p .931 .736 .254 r F P 0 g s .4122 .6933 m .42079 .7024 L .41994 .78431 L p .996 .767 .43 r F P 0 g s .41122 .77599 m .4122 .6933 L .40403 .67407 L p .931 .736 .254 r F P 0 g s .41994 .78431 m .41122 .77599 L .4122 .6933 L p .996 .767 .43 r F P 0 g s .45115 .73436 m .50256 .76995 L p .40448 .77622 L .65 .679 .865 r F P 0 g s .40504 .771 m .4029 .7584 L .40636 .7589 L 0 0 .131 r F .40616 .76074 m .45115 .73436 L .40448 .77622 L .65 .679 .865 r F .4024 .79532 m .4029 .7584 L p .40504 .771 L 0 0 .131 r F P 0 g s .40448 .77622 m .50256 .76995 L .4024 .79532 L .65 .679 .865 r F .4024 .79532 m .40504 .771 L .40555 .77398 L 0 0 .131 r F .50256 .76995 m .45302 .82954 L .4024 .79532 L p .65 .679 .865 r F P 0 g s .4024 .79532 m .37675 .77799 L p .40448 .77622 L .65 .679 .865 r F P 0 g s .37675 .77799 m .40616 .76074 L .40448 .77622 L .65 .679 .865 r F .4029 .7584 m .40723 .74262 L p .40636 .7589 L 0 0 .131 r F P 0 g s .40513 .59221 m .40403 .67407 L .4122 .6933 L p .931 .736 .254 r F P 0 g s .4029 .7584 m .40403 .67407 L .40832 .65682 L p 0 0 .131 r F P 0 g s .40832 .65682 m .40723 .74262 L .4029 .7584 L p 0 0 .131 r F P 0 g s .4122 .6933 m .41316 .61299 L .40513 .59221 L p .931 .736 .254 r F P 0 g s .42079 .7024 m .4122 .6933 L .41316 .61299 L p .996 .767 .43 r F P 0 g s .40723 .74262 m .40832 .65682 L .42581 .64187 L p .07 0 .452 r F P 0 g s .40616 .76074 m .40711 .75196 L .45115 .73436 L .65 .679 .865 r F .41476 .7368 m .45115 .73436 L p .40711 .75196 L F P 0 g s .39848 .82185 m .4024 .79532 L .40835 .82324 L .551 .669 .916 r F .40173 .84532 m .4102 .86116 L p .40709 .81733 L .931 .736 .254 r F P 0 g s .4024 .79532 m .40173 .84532 L p .40709 .81733 L .931 .736 .254 r F P 0 g s .40811 .83177 m .40854 .82414 L .40709 .81733 L .931 .736 .254 r F .41476 .7368 m .45115 .73436 L .42514 .71129 L p .657 .641 .823 r F P 0 g s .457 .62948 m .45734 .54411 L .50179 .53377 L p .538 .36 .587 r F P 0 g s .45734 .54411 m .457 .62948 L .42581 .64187 L p .389 .242 .557 r F P 0 g s .42581 .64187 m .457 .62948 L p .43663 .69272 L .389 .242 .557 r F P 0 g s .52298 .73525 m .42514 .71129 L .45688 .65999 L .71 .644 .782 r F .45688 .65999 m .457 .62948 L .50215 .61989 L p .538 .36 .587 r F P 0 g s .47694 .64222 m .45688 .65999 L .47291 .63408 L .71 .644 .782 r F .52298 .73525 m .45688 .65999 L .47694 .64222 L F .50179 .53377 m .50215 .61989 L .457 .62948 L p .538 .36 .587 r F P 0 g s .46563 .61937 m .50215 .61989 L p .52298 .73525 L .71 .644 .782 r F P 0 g s .45665 .71757 m .45688 .65999 L p .50215 .61989 L .538 .36 .587 r F P 0 g s .52298 .73525 m .45115 .73436 L .42514 .71129 L p .71 .644 .782 r F P 0 g s .42497 .72892 m .42514 .71129 L p .43663 .69272 L .389 .242 .557 r F P 0 g s .42514 .71129 m .42581 .64187 L p .43663 .69272 L .389 .242 .557 r F P 0 g s .457 .62948 m .45665 .71757 L .42497 .72892 L p .389 .242 .557 r F P 0 g s .42514 .71129 m .46563 .61937 L p .47291 .63408 L .71 .644 .782 r F P 0 g s .42514 .71129 m .46563 .61937 L .45079 .62051 L p .661 .586 .761 r F P 0 g s .42581 .64187 m .42514 .71129 L p .40723 .74262 L .07 0 .452 r F P 0 g s .4062 .51273 m .40513 .59221 L .41316 .61299 L p .931 .736 .254 r F P 0 g s .40403 .67407 m .40513 .59221 L .40938 .5736 L p 0 0 .131 r F P 0 g s .40938 .5736 m .40832 .65682 L .40403 .67407 L p 0 0 .131 r F P 0 g s .40832 .65682 m .40938 .5736 L .42662 .55747 L p .07 0 .452 r F P 0 g s .42662 .55747 m .42581 .64187 L .40832 .65682 L p .07 0 .452 r F P 0 g s .42581 .64187 m .42662 .55747 L .45734 .54411 L p .389 .242 .557 r F P 0 g s .45079 .62051 m .36252 .62729 L .42514 .71129 L p .661 .586 .761 r F P 0 g s .42514 .71129 m .4251 .71632 L p .42275 .71977 L .07 0 .452 r F P 0 g s .40723 .74262 m .42514 .71129 L .42275 .71977 L .07 0 .452 r F .4251 .71632 m .42497 .72892 L .41476 .7368 L p F P 0 g s .41476 .7368 m .40723 .74262 L p .4251 .71632 L .07 0 .452 r F P 0 g s .40711 .75196 m .40723 .74262 L .41476 .7368 L p .07 0 .452 r F P 0 g s .40723 .74262 m .40711 .75196 L p .40636 .7589 L 0 0 .131 r F P 0 g s .37675 .77799 m .40872 .73721 L p .40711 .75196 L .65 .679 .865 r F P 0 g s .40122 .76364 m .40711 .75196 L .40616 .76074 L .65 .679 .865 r F .37675 .77799 m .40711 .75196 L .40122 .76364 L F .42514 .71129 m .40872 .73721 L .41476 .7368 L p .657 .641 .823 r F P 0 g s .40611 .8311 m .40707 .75571 L p .42497 .72892 L .07 0 .452 r F P 0 g s .40707 .75571 m .40711 .75196 L p .41023 .74795 L .07 0 .452 r F P 0 g s .40707 .75571 m .41023 .74795 L .42497 .72892 L .07 0 .452 r F .41476 .7368 m .42497 .72892 L p .40711 .75196 L F P 0 g s .40872 .73721 m .41476 .7368 L p .40711 .75196 L .65 .679 .865 r F P 0 g s .40611 .8311 m .40173 .84532 L p .40636 .7589 L 0 0 .131 r F P 0 g s .40711 .75196 m .40611 .8311 L p .40636 .7589 L 0 0 .131 r F P 0 g s .40555 .77398 m .40504 .771 L .40636 .7589 L 0 0 .131 r F .40173 .84532 m .4024 .79532 L p .40555 .77398 L F P 0 g s .3313 .81239 m .4024 .79532 L .39848 .82185 L .551 .669 .916 r F .4102 .86116 m .41046 .83963 L p .40811 .83177 L .931 .736 .254 r F P 0 g s .41923 .85297 m .45302 .82954 L p .42454 .86104 L .592 .776 .968 r F P 0 g s .43065 .87033 m .47895 .88655 L p .44265 .8812 L .297 .7 .975 r F P 0 g s .36211 .86934 m .43065 .87033 L .44265 .8812 L .297 .7 .975 r F .47895 .88655 m .41907 .86864 L .41923 .85297 L p .903 .671 .576 r F P 0 g s .45302 .82954 m .52709 .85524 L p .43276 .86057 L .592 .776 .968 r F P 0 g s .42759 .85767 m .45302 .82954 L .43276 .86057 L .592 .776 .968 r F .41923 .85297 m .41916 .85992 L p .41838 .85167 L .996 .767 .43 r F P 0 g s .41916 .85992 m .41907 .86864 L p .41826 .85911 L .996 .767 .43 r F P 0 g s .40608 .86208 m .36211 .86934 L .28908 .82128 L p .333 .608 .949 r F P 0 g s .16663 .61005 m .16015 .52916 L .18718 .49703 L p .063 .037 .513 r F P 0 g s .20242 .42186 m .18718 .49703 L .16015 .52916 L p 0 0 .223 r F P 0 g s .51922 .2534 m .54876 .27624 L .50077 .29082 L p .552 .076 .078 r F P 0 g s .73017 .34065 m .72503 .32767 L .72152 .25316 L p .937 .707 .23 r F P 0 g s .66908 .21805 m .72152 .25316 L .72503 .32767 L p .934 .68 .53 r F P 0 g s .72152 .25316 m .66908 .21805 L .66634 .14417 L p .934 .68 .53 r F P 0 g s .4062 .51273 m .40724 .43551 L .4114 .41442 L p 0 0 .131 r F P 0 g s .41237 .33825 m .4114 .41442 L .40724 .43551 L p 0 0 .131 r F P 0 g s .64158 .31475 m .70215 .34238 L .72864 .40437 L p .861 .456 .265 r F P 0 g s .61828 .28486 m .64158 .31475 L .70215 .34238 L p .745 .227 0 r F P 0 g s .73155 .61484 m .73522 .69501 L .71385 .70824 L p .241 .146 .542 r F P 0 g s .64158 .31475 m .61828 .28486 L .54876 .27624 L p .721 .251 .132 r F P 0 g s .73522 .69501 m .73155 .61484 L .74202 .59712 L p 0 0 .379 r F P 0 g s .73823 .51798 m .74202 .59712 L .73155 .61484 L p 0 0 .379 r F P 0 g s .4114 .41442 m .41237 .33825 L .42891 .31902 L p .07 0 .452 r F P 0 g s .4586 .22746 m .45889 .15397 L .50013 .14058 L p .538 .36 .587 r F P 0 g s .45889 .15397 m .4586 .22746 L .42962 .2441 L p .389 .242 .557 r F P 0 g s .36941 .3003 m .33956 .30762 L .31201 .3011 L p .276 0 0 r F P 0 g s .33956 .30762 m .28957 .32461 L .31201 .3011 L closepath p .274 0 .108 r F P 0 g s .74202 .59712 m .73823 .51798 L .73757 .49499 L p 0 0 .048 r F P 0 g s .73382 .4167 m .73757 .49499 L .73823 .51798 L p 0 0 .048 r F P 0 g s .19548 .69739 m .16663 .61005 L .1942 .58017 L p .195 .239 .681 r F P 0 g s .18718 .49703 m .1942 .58017 L .16663 .61005 L p .063 .037 .513 r F P 0 g s .76716 .65679 m .78033 .59528 L .79082 .60999 L closepath p .989 .881 .621 r F P 0 g s .79082 .60999 m .78033 .59528 L .78393 .51181 L p .997 .799 .444 r F P 0 g s .28908 .82128 m .3313 .81239 L .40608 .86208 L p .333 .608 .949 r F P 0 g s .28598 .76738 m .3313 .81239 L .28908 .82128 L p .332 .521 .891 r F P 0 g s .28908 .82128 m .25971 .79228 L .28598 .76738 L p .332 .521 .891 r F P 0 g s .47895 .88655 m .52709 .85524 L .59815 .85609 L p .612 .893 .989 r F P 0 g s .58241 .1293 m .66634 .14417 L .66908 .21805 L p .777 .551 .593 r F P 0 g s .18718 .49703 m .20242 .42186 L .25364 .39209 L p .279 .092 .438 r F P 0 g s .28957 .32461 m .25364 .39209 L .20242 .42186 L p .122 0 .175 r F P 0 g s .67191 .29412 m .72503 .32767 L .72864 .40437 L p .934 .68 .53 r F P 0 g s .72503 .32767 m .67191 .29412 L .66908 .21805 L p .934 .68 .53 r F P 0 g s .25589 .72745 m .28598 .76738 L .25971 .79228 L p .28 .434 .837 r F P 0 g s .25971 .79228 m .21594 .73437 L .25589 .72745 L p .28 .434 .837 r F P 0 g s .50044 .2146 m .50013 .14058 L .55404 .13137 L p .617 .423 .597 r F P 0 g s .50013 .14058 m .50044 .2146 L .4586 .22746 L p .538 .36 .587 r F P 0 g s .40513 .59221 m .4062 .51273 L .41041 .49284 L p 0 0 .131 r F P 0 g s .4114 .41442 m .41041 .49284 L .4062 .51273 L p 0 0 .131 r F P 0 g s .74037 .47889 m .78393 .51181 L .78033 .59528 L p .966 .756 .57 r F P 0 g s .72864 .40437 m .73382 .4167 L .73757 .49499 L p .937 .707 .23 r F P 0 g s .78393 .51181 m .74037 .47889 L .72864 .40437 L p .963 .649 .375 r F P 0 g s .25364 .39209 m .28957 .32461 L .33956 .30762 L p .4 .107 .349 r F P 0 g s .21594 .73437 m .19548 .69739 L .22417 .67018 L p .273 .368 .778 r F P 0 g s .1942 .58017 m .22417 .67018 L .19548 .69739 L p .195 .239 .681 r F P 0 g s .22417 .67018 m .25589 .72745 L .21594 .73437 L p .273 .368 .778 r F P 0 g s .72077 .87345 m .71726 .78965 L .739 .77756 L p .241 .146 .542 r F P 0 g s .71726 .78965 m .72077 .87345 L .68804 .88194 L p .455 .31 .593 r F P 0 g s .59815 .85609 m .64915 .79944 L .69461 .78494 L p .789 .968 .916 r F P 0 g s .64915 .79944 m .59815 .85609 L .52709 .85524 L p .757 .867 .929 r F P 0 g s .74202 .59712 m .74592 .67861 L .73522 .69501 L p 0 0 .379 r F P 0 g s .41041 .49284 m .4114 .41442 L .42817 .39616 L p .07 0 .452 r F P 0 g s .42891 .31902 m .42817 .39616 L .4114 .41442 L p .07 0 .452 r F P 0 g s .42817 .39616 m .42891 .31902 L .45829 .30312 L p .389 .242 .557 r F P 0 g s .55404 .13137 m .58241 .1293 L .58394 .20376 L p .665 .461 .599 r F P 0 g s .58394 .20376 m .55515 .20575 L .55404 .13137 L p .665 .461 .599 r F P 0 g s .55404 .13137 m .55515 .20575 L .50044 .2146 L p .617 .423 .597 r F P 0 g s .66908 .21805 m .58394 .20376 L .58241 .1293 L p .777 .551 .593 r F P 0 g s .74592 .67861 m .74202 .59712 L .74144 .57561 L p 0 0 .048 r F P 0 g s .73757 .49499 m .74144 .57561 L .74202 .59712 L p 0 0 .048 r F P 0 g s .64915 .79944 m .6699 .76632 L .69461 .78494 L closepath p .858 .914 .869 r F P 0 g s .70105 .70113 m .6699 .76632 L .69461 .78494 L p .904 .905 .813 r F P 0 g s .74592 .67861 m .70105 .70113 L p .69461 .78494 L .904 .905 .813 r F P 0 g s .72864 .40437 m .66701 .37746 L .64158 .31475 L p .861 .456 .265 r F P 0 g s .56352 .29634 m .64158 .31475 L .66701 .37746 L p .789 .425 .368 r F P 0 g s .54876 .27624 m .56352 .29634 L .64158 .31475 L p .721 .251 .132 r F P 0 g s .56352 .29634 m .50077 .29082 L .54876 .27624 L closepath p .668 .249 .242 r F P 0 g s .73236 .48336 m .73757 .49499 L .74144 .57561 L p .937 .707 .23 r F P 0 g s .74144 .57561 m .74242 .59615 L p .74592 .67861 L 0 0 .048 r F P 0 g s .78033 .59528 m .74124 .56822 L p .74242 .59615 L .941 .813 .69 r F P 0 g s .74592 .67861 m .7546 .65758 L .74242 .59615 L .941 .813 .69 r F .7546 .65758 m .78033 .59528 L .74242 .59615 L F .73619 .56473 m .74144 .57561 L .74242 .59615 L p .937 .707 .23 r F P 0 g s .74242 .59615 m .74542 .65869 L .74592 .67861 L p 0 0 .048 r F P 0 g s .74144 .57561 m .73619 .56473 L .73236 .48336 L p .937 .707 .23 r F P 0 g s .74124 .56822 m .73619 .56473 L p .74592 .67861 L .941 .813 .69 r F P 0 g s .74242 .59615 m .74542 .65869 L p .73619 .56473 L .937 .707 .23 r F P 0 g s .74592 .67861 m .76716 .65679 L .78033 .59528 L p .941 .813 .69 r F P 0 g s .78033 .59528 m .73619 .56473 L .74037 .47889 L p .966 .756 .57 r F P 0 g s .75737 .68902 m .74592 .67861 L .76716 .65679 L closepath p .956 .88 .719 r F P 0 g s .58394 .20376 m .66908 .21805 L .67191 .29412 L p .777 .551 .593 r F P 0 g s .73757 .49499 m .73236 .48336 L .72864 .40437 L p .937 .707 .23 r F P 0 g s .72864 .40437 m .73236 .48336 L p .70378 .42829 L .934 .68 .53 r F P 0 g s .72864 .40437 m .74037 .47889 L p .70378 .42829 L .893 .598 .48 r F P 0 g s .66701 .37746 m .72864 .40437 L p .70378 .42829 L .893 .598 .48 r F P 0 g s .67482 .37249 m .72864 .40437 L p .70378 .42829 L .934 .68 .53 r F P 0 g s .72864 .40437 m .67482 .37249 L .67191 .29412 L p .934 .68 .53 r F P 0 g s .50077 .29082 m .50044 .2146 L .55515 .20575 L p .617 .423 .597 r F P 0 g s .41041 .49284 m .40938 .5736 L .40513 .59221 L p 0 0 .131 r F P 0 g s .1942 .58017 m .18718 .49703 L .2389 .46879 L p .373 .267 .603 r F P 0 g s .25364 .39209 m .2389 .46879 L .18718 .49703 L p .279 .092 .438 r F P 0 g s .35362 .32137 m .33956 .30762 L .36941 .3003 L closepath p .444 .106 .296 r F P 0 g s .33956 .30762 m .35362 .32137 L p .25364 .39209 L .4 .107 .349 r F P 0 g s .739 .77756 m .74289 .86257 L .72077 .87345 L p .241 .146 .542 r F P 0 g s .74289 .86257 m .739 .77756 L .74994 .76256 L p 0 0 .379 r F P 0 g s .74592 .67861 m .74994 .76256 L .739 .77756 L p 0 0 .379 r F P 0 g s .40938 .5736 m .41041 .49284 L .4274 .4756 L p .07 0 .452 r F P 0 g s .42817 .39616 m .4274 .4756 L .41041 .49284 L p .07 0 .452 r F P 0 g s .45799 .38104 m .45829 .30312 L .50077 .29082 L p .538 .36 .587 r F P 0 g s .45829 .30312 m .45799 .38104 L .42817 .39616 L p .389 .242 .557 r F P 0 g s .4274 .4756 m .42817 .39616 L .45799 .38104 L p .389 .242 .557 r F P 0 g s .55515 .20575 m .58394 .20376 L .58551 .28046 L p .665 .461 .599 r F P 0 g s .58551 .28046 m .5563 .28237 L .55515 .20575 L p .665 .461 .599 r F P 0 g s .55515 .20575 m .5563 .28237 L .50077 .29082 L p .617 .423 .597 r F P 0 g s .36941 .3003 m .46643 .29016 L p .44554 .35228 L .588 .273 .402 r F P 0 g s .35362 .32137 m .36941 .3003 L p .44554 .35228 L .588 .273 .402 r F P 0 g s .67191 .29412 m .58551 .28046 L .58394 .20376 L p .777 .551 .593 r F P 0 g s .74994 .76256 m .74592 .67861 L .74542 .65869 L p 0 0 .048 r F P 0 g s .70105 .70113 m .71568 .66003 L .74592 .67861 L closepath p .909 .845 .768 r F P 0 g s .73619 .56473 m .71568 .66003 L .74592 .67861 L p .941 .813 .69 r F P 0 g s .52709 .85524 m .57752 .79732 L .64915 .79944 L p .757 .867 .929 r F P 0 g s .57752 .79732 m .52709 .85524 L .45302 .82954 L p .702 .764 .9 r F P 0 g s .2389 .46879 m .25364 .39209 L .33015 .36729 L p .475 .265 .513 r F P 0 g s .35362 .32137 m .33015 .36729 L .25364 .39209 L p .4 .107 .349 r F P 0 g s .66701 .37746 m .58714 .3595 L .56352 .29634 L p .789 .425 .368 r F P 0 g s .50077 .29082 m .56352 .29634 L .58714 .3595 L p .719 .39 .422 r F P 0 g s .6699 .76632 m .64915 .79944 L .57752 .79732 L p .806 .825 .866 r F P 0 g s .58551 .28046 m .67191 .29412 L .67482 .37249 L p .777 .551 .593 r F P 0 g s .3459 .74706 m .37675 .77799 L .3313 .81239 L p .511 .587 .867 r F P 0 g s .3313 .81239 m .28598 .76738 L .3459 .74706 L p .511 .587 .867 r F P 0 g s .22417 .67018 m .1942 .58017 L .24675 .55388 L p .426 .384 .708 r F P 0 g s .2389 .46879 m .24675 .55388 L .1942 .58017 L p .373 .267 .603 r F P 0 g s .67782 .45326 m .73236 .48336 L .73619 .56473 L p .934 .68 .53 r F P 0 g s .67782 .45326 m .66701 .37746 L p .70378 .42829 L .893 .598 .48 r F P 0 g s .73236 .48336 m .67782 .45326 L p .70378 .42829 L .934 .68 .53 r F P 0 g s .74037 .47889 m .67782 .45326 L p .70378 .42829 L .893 .598 .48 r F P 0 g s .67782 .45326 m .67482 .37249 L p .70378 .42829 L .934 .68 .53 r F P 0 g s .58714 .3595 m .55748 .36132 L .55718 .34135 L p .665 .461 .599 r F P 0 g s .58714 .3595 m .55718 .34135 L .50077 .29082 L .719 .39 .422 r F .55718 .34135 m .5563 .28237 L p .58714 .3595 L .665 .461 .599 r F P 0 g s .58714 .3595 m .56735 .35046 L .55718 .34135 L .719 .39 .422 r F .5011 .36935 m .50077 .29082 L p .53275 .31947 L .617 .423 .597 r F P 0 g s .50077 .29082 m .5011 .36935 L .45799 .38104 L p .538 .36 .587 r F P 0 g s .55748 .36132 m .5011 .36935 L p .53275 .31947 L .617 .423 .597 r F P 0 g s .5563 .28237 m .55718 .34135 L p .53275 .31947 L .617 .423 .597 r F P 0 g s .55718 .34135 m .55748 .36132 L p .53275 .31947 L .617 .423 .597 r F P 0 g s .49027 .35141 m .47607 .30877 L p .56735 .35046 L .719 .39 .422 r F P 0 g s .58714 .3595 m .57644 .35861 L p .56735 .35046 L .719 .39 .422 r F P 0 g s .57644 .35861 m .49027 .35141 L p .56735 .35046 L .719 .39 .422 r F P 0 g s .47607 .30877 m .50077 .29082 L p .56735 .35046 L .719 .39 .422 r F P 0 g s .50077 .29082 m .5563 .28237 L p .53275 .31947 L .617 .423 .597 r F P 0 g s .47607 .30877 m .46643 .29016 L .50077 .29082 L closepath p .657 .299 .353 r F P 0 g s .46643 .29016 m .47607 .30877 L .44554 .35228 L p .588 .273 .402 r F P 0 g s .44554 .35228 m .37062 .35974 L .35362 .32137 L p .588 .273 .402 r F P 0 g s .37062 .35974 m .33015 .36729 L .35362 .32137 L closepath p .534 .248 .427 r F P 0 g s .29967 .68545 m .3459 .74706 L .28598 .76738 L p .499 .531 .821 r F P 0 g s .28598 .76738 m .25589 .72745 L .29967 .68545 L p .499 .531 .821 r F P 0 g s .67782 .45326 m .74037 .47889 L .73619 .56473 L p .888 .682 .619 r F P 0 g s .25589 .72745 m .22417 .67018 L .27792 .64622 L p .458 .464 .777 r F P 0 g s .24675 .55388 m .27792 .64622 L .22417 .67018 L p .426 .384 .708 r F P 0 g s .57752 .79732 m .60861 .74632 L .6699 .76632 L p .806 .825 .866 r F P 0 g s .62949 .70172 m .60861 .74632 L .6699 .76632 L p .837 .805 .82 r F P 0 g s .6699 .76632 m .70105 .70113 L .62949 .70172 L p .837 .805 .82 r F P 0 g s .74994 .76256 m .75408 .84907 L .74289 .86257 L p 0 0 .379 r F P 0 g s .4274 .4756 m .42662 .55747 L .40938 .5736 L p .07 0 .452 r F P 0 g s .45767 .46134 m .45799 .38104 L .5011 .36935 L p .538 .36 .587 r F P 0 g s .45799 .38104 m .45767 .46134 L .4274 .4756 L p .389 .242 .557 r F P 0 g s .27792 .64622 m .29967 .68545 L .25589 .72745 L p .458 .464 .777 r F P 0 g s .42662 .55747 m .4274 .4756 L .45767 .46134 L p .389 .242 .557 r F P 0 g s .5563 .28237 m .58551 .28046 L .58714 .3595 L p .665 .461 .599 r F P 0 g s .58714 .3595 m .66701 .37746 L .67782 .45326 L p .811 .539 .527 r F P 0 g s .67482 .37249 m .58714 .3595 L .58551 .28046 L p .777 .551 .593 r F P 0 g s .75408 .84907 m .74994 .76256 L .74952 .74432 L p 0 0 .048 r F P 0 g s .74542 .65869 m .74952 .74432 L .74994 .76256 L p 0 0 .048 r F P 0 g s .49027 .35141 m .44554 .35228 L .47607 .30877 L closepath p .659 .358 .451 r F P 0 g s .58714 .3595 m .67482 .37249 L .67782 .45326 L p .777 .551 .593 r F P 0 g s .45302 .82954 m .50256 .76995 L .57752 .79732 L p .702 .764 .9 r F P 0 g s .24675 .55388 m .2389 .46879 L .31648 .44524 L p .519 .375 .625 r F P 0 g s .33015 .36729 m .31648 .44524 L .2389 .46879 L p .475 .265 .513 r F P 0 g s .71568 .66003 m .70105 .70113 L .62949 .70172 L p .848 .768 .773 r F P 0 g s .74542 .65869 m .74014 .6486 L .73619 .56473 L p .937 .707 .23 r F P 0 g s .67284 .54094 m .73619 .56473 L .71568 .66003 L p .87 .734 .71 r F P 0 g s .73619 .56473 m .67284 .54094 L .67782 .45326 L p .888 .682 .619 r F P 0 g s .68091 .53655 m .73619 .56473 L .74014 .6486 L p .934 .68 .53 r F P 0 g s .73619 .56473 m .68091 .53655 L .67782 .45326 L p .934 .68 .53 r F P 0 g s .50144 .4503 m .5011 .36935 L .55748 .36132 L p .617 .423 .597 r F P 0 g s .5011 .36935 m .50144 .4503 L .45767 .46134 L p .538 .36 .587 r F P 0 g s .62949 .70172 m .65168 .63854 L .71568 .66003 L p .848 .768 .773 r F P 0 g s .71568 .66003 m .65168 .63854 L .67284 .54094 L p .87 .734 .71 r F P 0 g s .33015 .36729 m .37062 .35974 L .37837 .43444 L p .575 .355 .544 r F P 0 g s .37837 .43444 m .31648 .44524 L .33015 .36729 L p .575 .355 .544 r F P 0 g s .74014 .6486 m .74542 .65869 L .74952 .74432 L p .937 .707 .23 r F P 0 g s .60861 .74632 m .57752 .79732 L .50256 .76995 L p .751 .745 .846 r F P 0 g s .45734 .54411 m .45767 .46134 L .50144 .4503 L p .538 .36 .587 r F P 0 g s .45767 .46134 m .45734 .54411 L .42662 .55747 L p .389 .242 .557 r F P 0 g s .55748 .36132 m .58714 .3595 L .58882 .44099 L p .665 .461 .599 r F P 0 g s .58882 .44099 m .55869 .44271 L .55748 .36132 L p .665 .461 .599 r F P 0 g s .55748 .36132 m .55869 .44271 L .50144 .4503 L p .617 .423 .597 r F P 0 g s .37062 .35974 m .44554 .35228 L .42934 .42969 L p .63 .394 .542 r F P 0 g s .42934 .42969 m .37837 .43444 L .37062 .35974 L p .63 .394 .542 r F P 0 g s .67782 .45326 m .58882 .44099 L .58714 .3595 L p .777 .551 .593 r F P 0 g s .67782 .45326 m .59652 .43616 L .58714 .3595 L p .811 .539 .527 r F P 0 g s .49027 .35141 m .58714 .3595 L .59652 .43616 L p .74 .488 .548 r F P 0 g s .74952 .74432 m .75376 .83264 L .75408 .84907 L p 0 0 .048 r F P 0 g s .24675 .55388 m .3255 .53195 L p .33085 .63299 L .544 .453 .703 r F P 0 g s .33085 .63299 m .27792 .64622 L .24675 .55388 L p .544 .453 .703 r F P 0 g s .31648 .44524 m .3255 .53195 L .24675 .55388 L p .519 .375 .625 r F P 0 g s .37675 .77799 m .40872 .73721 L .3459 .74706 L closepath p .604 .611 .832 r F P 0 g s .67782 .45326 m .67284 .54094 L p .63477 .48867 L .811 .613 .635 r F P 0 g s .58882 .44099 m .67782 .45326 L p .63477 .48867 L .777 .551 .593 r F P 0 g s .59652 .43616 m .67782 .45326 L p .63477 .48867 L .811 .613 .635 r F P 0 g s .67782 .45326 m .68091 .53655 L p .63477 .48867 L .777 .551 .593 r F P 0 g s .74952 .74432 m .74421 .73509 L .74014 .6486 L p .937 .707 .23 r F P 0 g s .68411 .62246 m .74014 .6486 L .74421 .73509 L p .934 .68 .53 r F P 0 g s .74014 .6486 m .68411 .62246 L .68091 .53655 L p .934 .68 .53 r F P 0 g s .40872 .73721 m .3459 .74706 L .29967 .68545 L p .603 .569 .788 r F P 0 g s .44554 .35228 m .49027 .35141 L .49776 .42844 L p .682 .444 .556 r F P 0 g s .49776 .42844 m .42934 .42969 L .44554 .35228 L p .682 .444 .556 r F P 0 g s .50179 .53377 m .50144 .4503 L .55869 .44271 L p .617 .423 .597 r F P 0 g s .50144 .4503 m .50179 .53377 L .45734 .54411 L p .538 .36 .587 r F P 0 g s .59652 .43616 m .49776 .42844 L .49027 .35141 L p .74 .488 .548 r F P 0 g s .50256 .76995 m .52298 .73525 L .60861 .74632 L p .751 .745 .846 r F P 0 g s .55403 .66708 m .52298 .73525 L .60861 .74632 L p .769 .716 .803 r F P 0 g s .60861 .74632 m .62949 .70172 L .55403 .66708 L p .769 .716 .803 r F P 0 g s .29967 .68545 m .33085 .63299 L .27792 .64622 L closepath p .558 .511 .759 r F P 0 g s .29967 .68545 m .33085 .63299 L p .40872 .73721 L .603 .569 .788 r F P 0 g s .74421 .73509 m .74952 .74432 L .75376 .83264 L p .937 .707 .23 r F P 0 g s .31648 .44524 m .37837 .43444 L .36721 .52526 L p .599 .433 .629 r F P 0 g s .36721 .52526 m .3255 .53195 L .31648 .44524 L p .599 .433 .629 r F P 0 g s .50256 .76995 m .52298 .73525 L .45115 .73436 L closepath p .702 .678 .823 r F P 0 g s .65168 .63854 m .62949 .70172 L .55403 .66708 L p .791 .701 .764 r F P 0 g s .55869 .44271 m .58882 .44099 L .59055 .52505 L p .665 .461 .599 r F P 0 g s .59055 .52505 m .55994 .52665 L .55869 .44271 L p .665 .461 .599 r F P 0 g s .55869 .44271 m .55994 .52665 L .50179 .53377 L p .617 .423 .597 r F P 0 g s .59055 .52505 m .67284 .54094 L .65168 .63854 L p .803 .664 .71 r F P 0 g s .59055 .52505 m .58882 .44099 L p .63477 .48867 L .777 .551 .593 r F P 0 g s .67284 .54094 m .59055 .52505 L p .63477 .48867 L .811 .613 .635 r F P 0 g s .68091 .53655 m .59055 .52505 L p .63477 .48867 L .777 .551 .593 r F P 0 g s .59055 .52505 m .59652 .43616 L p .63477 .48867 L .811 .613 .635 r F P 0 g s .55403 .66708 m .56886 .62419 L .65168 .63854 L p .791 .701 .764 r F P 0 g s .65168 .63854 m .56886 .62419 L .59055 .52505 L p .803 .664 .71 r F P 0 g s .36252 .62729 m .42514 .71129 L .40872 .73721 L p .603 .569 .788 r F P 0 g s .33085 .63299 m .36252 .62729 L p .40872 .73721 L .603 .569 .788 r F P 0 g s .59055 .52505 m .68091 .53655 L .68411 .62246 L p .777 .551 .593 r F P 0 g s .49776 .42844 m .59652 .43616 L .59055 .52505 L p .747 .556 .637 r F P 0 g s .50215 .61989 m .55403 .66708 L .52298 .73525 L p .71 .644 .782 r F P 0 g s .75376 .83264 m .74841 .82431 L .74421 .73509 L p .937 .707 .23 r F P 0 g s .6874 .71114 m .74421 .73509 L .74841 .82431 L p .934 .68 .53 r F P 0 g s .74421 .73509 m .6874 .71114 L .68411 .62246 L p .934 .68 .53 r F P 0 g s .37837 .43444 m .42934 .42969 L .44448 .51866 L p .65 .479 .639 r F P 0 g s .44448 .51866 m .36721 .52526 L .37837 .43444 L p .65 .479 .639 r F P 0 g s .50215 .61989 m .50179 .53377 L .55994 .52665 L p .617 .423 .597 r F P 0 g s .36252 .62729 m .34706 .59465 L .33085 .63299 L closepath p .595 .51 .729 r F P 0 g s .3255 .53195 m .34706 .59465 L .33085 .63299 L p .544 .453 .703 r F P 0 g s .34706 .59465 m .36721 .52526 L .3255 .53195 L closepath p .612 .492 .692 r F P 0 g s .42934 .42969 m .49776 .42844 L .49062 .51788 L p .693 .508 .633 r F P 0 g s .49062 .51788 m .44448 .51866 L .42934 .42969 L p .693 .508 .633 r F P 0 g s .59055 .52505 m .49062 .51788 L .49776 .42844 L p .747 .556 .637 r F P 0 g s .42497 .72892 m .42411 .81875 L .40611 .8311 L p .07 0 .452 r F P 0 g s .34706 .59465 m .36721 .52526 L p .46563 .61937 L .659 .54 .709 r F P 0 g s .46563 .61937 m .36252 .62729 L .34706 .59465 L p .659 .54 .709 r F P 0 g s .42411 .81875 m .42497 .72892 L .45665 .71757 L p .389 .242 .557 r F P 0 g s .55994 .52665 m .56026 .54805 L p .50215 .61989 L .617 .423 .597 r F P 0 g s .59055 .52505 m .56886 .62419 L p .53542 .57876 L .746 .606 .702 r F P 0 g s .53542 .57876 m .56026 .54805 L .59055 .52505 L .746 .606 .702 r F .47592 .58439 m .49062 .51788 L p .56886 .62419 L F P 0 g s .56886 .62419 m .50215 .61989 L .47592 .58439 L p .746 .606 .702 r F P 0 g s .56026 .54805 m .56124 .61328 L .50215 .61989 L p .617 .423 .597 r F P 0 g s .53542 .57876 m .52984 .57117 L .56026 .54805 L .746 .606 .702 r F .55994 .52665 m .59055 .52505 L p .56633 .54344 L .665 .461 .599 r F P 0 g s .59233 .61179 m .56124 .61328 L .55994 .52665 L p .665 .461 .599 r F P 0 g s .49062 .51788 m .59055 .52505 L p .52984 .57117 L .746 .606 .702 r F P 0 g s .59055 .52505 m .59233 .61179 L p .56633 .54344 L .665 .461 .599 r F P 0 g s .55403 .66708 m .56886 .62419 L .50215 .61989 L closepath p .741 .644 .752 r F P 0 g s .36721 .52526 m .44448 .51866 L p .46563 .61937 L .659 .54 .709 r F P 0 g s .68411 .62246 m .59233 .61179 L .59055 .52505 L p .777 .551 .593 r F P 0 g s .59233 .61179 m .68411 .62246 L .6874 .71114 L p .777 .551 .593 r F P 0 g s .74841 .82431 m .6908 .80271 L .6874 .71114 L p .934 .68 .53 r F P 0 g s .47592 .58439 m .49062 .51788 L .44448 .51866 L closepath p .697 .557 .692 r F P 0 g s .44448 .51866 m .47592 .58439 L .46563 .61937 L p .659 .54 .709 r F P 0 g s .50252 .70878 m .50215 .61989 L .56124 .61328 L p .617 .423 .597 r F P 0 g s .50215 .61989 m .50252 .70878 L .45665 .71757 L p .538 .36 .587 r F P 0 g s .50215 .61989 m .47592 .58439 L .46563 .61937 L closepath p .715 .6 .726 r F P 0 g s .45629 .80851 m .45665 .71757 L .50252 .70878 L p .538 .36 .587 r F P 0 g s .45665 .71757 m .45629 .80851 L .42411 .81875 L p .389 .242 .557 r F P 0 g s .56124 .61328 m .59233 .61179 L .59417 .70136 L p .665 .461 .599 r F P 0 g s .59417 .70136 m .56257 .70272 L .56124 .61328 L p .665 .461 .599 r F P 0 g s .56124 .61328 m .56257 .70272 L .50252 .70878 L p .617 .423 .597 r F P 0 g s .6874 .71114 m .59417 .70136 L .59233 .61179 L p .777 .551 .593 r F P 0 g s .59417 .70136 m .6874 .71114 L .6908 .80271 L p .777 .551 .593 r F P 0 g s .50291 .80058 m .50252 .70878 L .56257 .70272 L p .617 .423 .597 r F P 0 g s .50252 .70878 m .50291 .80058 L .45629 .80851 L p .538 .36 .587 r F P 0 g s .56257 .70272 m .59417 .70136 L .59608 .79388 L p .665 .461 .599 r F P 0 g s .59608 .79388 m .56395 .79511 L .56257 .70272 L p .665 .461 .599 r F P 0 g s .56257 .70272 m .56395 .79511 L .50291 .80058 L p .617 .423 .597 r F P 0 g s .6908 .80271 m .59608 .79388 L .59417 .70136 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However, using ", Cell[BoxData[ \(TraditionalForm\`0 \[LessEqual] t \[LessEqual] 3\)]], " we obtain a non-smooth curve. The curve takes a sharp turn at the \ singular point instead of passing through to the lower part of the \ \[OpenCurlyDoubleQuote]figure-eight.\[CloseCurlyDoubleQuote] For a larger \ range of ", StyleBox["t", FontSlant->"Italic"], "-values, we do obtain more of the intersection, but its behavior around \ the singular point is not what is desired. This, in fact, is generally what \ happens around most singular points when you integrate system (2). For a \ discussion why, see [Wilkinson, 1998] where the plane case is fully \ investigated. The plane case can be viewed as the basis for the \ three-dimensional case as is shown in that same reference.\n\tTo proceed it \ is useful to make an affine change of the generators ", Cell[BoxData[ \(TraditionalForm\`F\_1, \ F\_2\)]], " so that one of the gradients, say ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2\)]], ", is the zero vector at the singular point. (In the above example with the \ cylinder and sphere we could make the change ", Cell[BoxData[ \(TraditionalForm\`\(F\&~\_2 = F\_2 - 2 F\_1, \)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`F\&~\_1 = F\_1\)]], ") Now differentiate equation (1) with ", Cell[BoxData[ \(TraditionalForm\`i = 2\)]], " to get" }], "Text"], Cell[BoxData[ \(TraditionalForm \`\((\(X\^\[Prime]\)(t))\)\^T \[CenterDot]\[Del]\^2\(\( F\_2\)(X(t)) \)\[CenterDot]\(\(X\^\[Prime]\)(t)\) + \[Del]\(\(F\_2\)(X(t))\)\[CenterDot]\(\(X\^\[Prime]\[Prime]\)(t)\) = 0.\)], "NumberedEquation"], Cell[TextData[{ "Here, ", Cell[BoxData[ \(TraditionalForm\`\[Del]\^2 F\_2\)]], " is the second derivative Hessian matrix for ", Cell[BoxData[ \(TraditionalForm\`F\_2\)]], "." }], "Text"], Cell[BoxData[ FormBox[ RowBox[{\(\[Del]\^2 F\_2\), "=", RowBox[{"(", GridBox[{ {\(\[PartialD]\_\(x, x\)F\_2\), \(\[PartialD]\_\(x, y\)F\_2\), \(\[PartialD]\_\(x, z\)F\_2\)}, {\(\[PartialD]\_\(y, x\)F\_2\), \(\[PartialD]\_\(y, y\)F\_2\), \(\[PartialD]\_\(y, z\)F\_2\)}, {\(\[PartialD]\_\(z, x\)F\_2\), \(\[PartialD]\_\(z, y\)F\_2\), \(\[PartialD]\_\(z, z\)F\_2\)} }], ")"}]}], TraditionalForm]], "DisplayFormula"], Cell[TextData[{ "Since at a singular point ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2 \((X(t))\) = 0\)]], ", equation (3) is ", Cell[BoxData[ \(TraditionalForm \`\((\(X\^\[Prime]\)(t))\)\^T \[CenterDot]\[Del]\^2\(\( F\_2\)(X(t)) \)\[CenterDot]\(\(X\^\[Prime]\)(t)\) = 0.\)]], " This along with equation (1) for ", Cell[BoxData[ \(TraditionalForm\`i = 1\)]], " implies that ", Cell[BoxData[ \(TraditionalForm\`\(X\^\[Prime]\)(t)\)]], " is mutually perpendicular to ", Cell[BoxData[ \(TraditionalForm\`\[Del]\(\(F\_1\)(X(t))\)\)]], " and ", Cell[BoxData[ \(TraditionalForm \`\((\(X\^\[Prime]\)(t))\)\^T\[CenterDot]\[Del]\^2 F\_2 \((X(t))\)\)]], " at the singular point. Impose the first of two nondegeneracy assumptions \ on the singular points." }], "Text"], Cell[TextData[{ StyleBox["Nondegeneracy Assumption 1.", FontWeight->"Bold"], " If ", Cell[BoxData[ \(TraditionalForm\`\((x\_0, y\_0, z\_0)\)\)]], " is a singular point of the intersection, then the linear span of ", Cell[BoxData[ \(TraditionalForm \`{\[Del]\(\(F\_1\)(x\_0, y\_0, z\_0)\), \[Del]\(\(F\_2\)(x\_0, y\_0, z\_0)\)}\)]], " is one-dimensional. (If the point is singular then this span is at most \ one-dimensional.)" }], "Text"], Cell[TextData[{ "With this assumption and by making ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2 \((X(t))\) = 0\)]], " at the singular point, ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1 \((X(t))\) \[NotEqual] 0\)]], " at the singular point. To determine ", Cell[BoxData[ \(TraditionalForm\`X(t)\)]], ", solve" }], "Text"], Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1\[CenterDot]u = 0, \n u\^T\[CenterDot]\[Del]\^2\( F\_2\[CenterDot]u\) = 0\)], "DisplayFormula", CellLabel->"In[3]:="], Cell[TextData[{ "for ", Cell[BoxData[ \(TraditionalForm\`u\)]], " in the following way. From the first of those two equations ", Cell[BoxData[ \(TraditionalForm\`u\)]], " lies in the orthogonal space to ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1\)]], "; name this space ", Cell[BoxData[ \(TraditionalForm\`\[Del]\(F\_1\^ \[UpTee] \)\)]], ". Restrict the second of these two equations to the two-dimensional vector \ space ", Cell[BoxData[ \(TraditionalForm\`\[Del]\(F\_1\^ \[UpTee] \)\)]], ". Since this subspace is two-dimensional, there exists a transformation \ that rotates every vector 90\[Degree] in the counterclockwise direction with \ respect to the normal ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1\)]], ". Call this transformation ", Cell[BoxData[ \(TraditionalForm\`J\)]], ". Now the equation ", Cell[BoxData[ \(TraditionalForm \`u\^T\[CenterDot]\[Del]\^2\( F\_2\[CenterDot]u\) = 0\)]], " implies that ", Cell[BoxData[ \(TraditionalForm\`u\)]], " is orthogonal to ", Cell[BoxData[ \(TraditionalForm\`\[Del]\^2 F\_2\[CenterDot]u\)]], " since their dot product is zero. Using the transformation ", Cell[BoxData[ \(TraditionalForm\`J\)]], " this means that" }], "Text"], Cell[BoxData[ \(TraditionalForm\`J \[Del]\^2 F\_2\[CenterDot]u = \[Rho]\ u\)], "NumberedEquation"], Cell[TextData[{ "for some scalar ", Cell[BoxData[ \(TraditionalForm\`\[Rho]\)]], ". But then ", Cell[BoxData[ \(TraditionalForm\`u\)]], " is an eigenvector of ", Cell[BoxData[ \(TraditionalForm \`J(\[Del]\^2 F\_2\( \[VerticalSeparator] \_\(\[Del]\(F\_1\^ \[UpTee] \)\)\))\)]], ". Since this is a transformation on a two-dimensional space, there are \ three cases to consider:" }], "Text"], Cell[TextData[{ StyleBox["i. ", FontSlant->"Italic"], "There are two real and distinct eigenvalues and thus two linearly \ independent one-dimensional real eigenspaces. This is the case with the \ intersection of the above sphere and cylinder. Can you see the two \ eigenspaces at the singular point? They are parallel to the two tangent lines \ at the singular point." }], "Text"], Cell[TextData[{ StyleBox["ii.", FontSlant->"Italic"], " There are two complex eigenvalues and thus no real eigenspaces. This \ would be the case if the intersection of two surfaces was an isolated point. \ For example, the intersection of the sphere ", Cell[BoxData[ \(TraditionalForm\`\((x - 1)\)\^2 + y\^2 + z\^2 = 1\)]], " and the cylinder ", Cell[BoxData[ \(TraditionalForm\`x\^2 + y\^2 = 4\)]], " is only the point ", Cell[BoxData[ \(TraditionalForm\`\(\((2, 0, 0)\).\)\)]] }], "Text"], Cell[TextData[{ StyleBox["iii. ", FontSlant->"Italic"], "There is only one real eigenvalue. This degenerate case is more \ complicated and I will not handle it here. One can check that if ", Cell[BoxData[ \(TraditionalForm\`A\)]], " is a ", Cell[BoxData[ \(TraditionalForm\`2\[Times]2\)]], " matrix and ", Cell[BoxData[ \(TraditionalForm\`J\)]], " is a rotation matrix, then ", Cell[BoxData[ \(TraditionalForm\`J\ A\)]], " has at most one real eigenvalue if and only if ", Cell[BoxData[ \(TraditionalForm\`A\)]], " is a singular matrix." }], "Text"], Cell[TextData[{ StyleBox["Nondegeneracy Assumption 2.", FontWeight->"Bold"], " If ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2 \((X(t))\) = 0\)]], " then ", Cell[BoxData[ \(TraditionalForm \`\(\[Del]\^2 F\_2\( \[VerticalSeparator] \_\(\[Del]\(F\_1\^ \[UpTee] \)\)\)\)\)]], " is nonsingular." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Implementing the algorithm around singular points", "Subsection"], Cell[TextData[{ "\tIn the implementation of the package ", StyleBox["ParametrizeCurve`", "Input"], " the singular points are not found in advance. To do so would be difficult \ even in the case where the surfaces were algebraic. Instead the package \ monitors the value of ", Cell[BoxData[ \(TraditionalForm \`\(\(|\[Del]\(\(F\_1\)(X(t))\)\[Times]\[Del]\(\(F\_2\)(X(t))\)\) | \)\)]], " as it integrates the initial condition problem that arises from (2). If \ its value becomes sufficiently close to 0, then it assumes the curve has a \ singular point nearby. If a singular point is near, and assuming the two \ nondegeracy assumptions, there are either nonreal eigenvectors or two \ distinct eigenvectors for equation (4). If they are not real and the package \ is exactly at the singular point it knows it will never move from it since it \ is an isolated point. If they are not real and it is close to it but not at \ the singular point, it can ignore the singular point since it knows it will \ never get to the isolated singular point. However, if the eigenvectors are \ real then there are four directions it can head, two opposing directions for \ each of the two distinct eigendirections. It chooses the direction that most \ closely points in the direction it has been integrating. This gives a smooth \ parametrization through the singular point.\n\tFinding these eigenvectors is \ accomplished by the use of the Singular Value Decomposition Theorem which \ states that any matrix ", Cell[BoxData[ \(TraditionalForm\`A\)]], " can be decomposed in the following way:" }], "Text"], Cell[BoxData[ \(TraditionalForm\`A = U\^T\ D\ V\)], "DisplayFormula"], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`U\)]], " and ", Cell[BoxData[ \(TraditionalForm\`V\)]], " are orthogonal matrices and ", Cell[BoxData[ \(TraditionalForm\`D\)]], " is a diagonal matrix with entries made of the nonnegative eigenvalues of \ ", Cell[BoxData[ \(TraditionalForm\`A\ A\^T\)]], " arranged in decreasing order. ", StyleBox["Mathematica", FontSlant->"Italic"], " has the built-in function ", StyleBox["SingularValues", "Input"], " that computes this decomposition. Decompose the matrix whose first row is \ ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1 \((X(t))\)\)]], " and second row is ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2 \((X(t))\)\)]], ", call that matrix ", Cell[BoxData[ \(TraditionalForm\`A\)]], ". At a singular point ", Cell[BoxData[ \(TraditionalForm\`A\)]], " is a singular matrix since its rows are linearly dependent. There are two \ things this decomposition accomplishes for this problems. First, we needed an \ affine change of generators so that ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2 = 0.\)]], " Since matrix ", Cell[BoxData[ \(TraditionalForm\`U\)]], " is orthogonal, ", Cell[BoxData[ \(TraditionalForm\`U\^T = U\^\(-1\)\)]], ". Therefore, ", Cell[BoxData[ \(TraditionalForm\`U\ A = D\ \(V.\)\)]], " At a singular point, the last row of ", Cell[BoxData[ \(TraditionalForm\`D\)]], " is a zero row. This makes the last row of the product ", Cell[BoxData[ \(TraditionalForm\`D\ V\)]], " a zero row, and thus also the last row of ", Cell[BoxData[ \(TraditionalForm\`U\ \(A.\)\)]], " But the rows of ", Cell[BoxData[ \(TraditionalForm\`A\)]], " are ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2.\)]], " Take the rows of the product ", Cell[BoxData[ \(TraditionalForm\`U\ A\)]], " as ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\&~\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\&~\_2\)]], ". (I will drop the tildes from now on. Assume ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_2 = 0\)]], ".) The other thing to do is solve equation (4) on the two dimensional \ space ", Cell[BoxData[ \(TraditionalForm\`\[Del]\(F\_1\^ \[UpTee] \)\)]], " where ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1\)]], " is now the first row of ", Cell[BoxData[ \(TraditionalForm\`U\ \(A.\)\)]], "The equation ", Cell[BoxData[ \(TraditionalForm\`U\ A = D\ V\)]], " shows that the columns of orthogonal matrix ", Cell[BoxData[ \(TraditionalForm\`V\)]], " form an orthonormal basis for ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^3\)]], " with the first column pointing in the same direction as ", Cell[BoxData[ \(TraditionalForm\`\[Del]F\_1.\)]], " Hence, the last two columns of matrix ", Cell[BoxData[ \(TraditionalForm\`V\)]], ", call those columns ", Cell[BoxData[ \(TraditionalForm\`v\_2, \ v\_3\)]], ", form an orthonormal basis for ", Cell[BoxData[ \(TraditionalForm\`\(\[Del]\(F\_1\^ \[UpTee] \).\)\)]], " The desired rotation matrix ", Cell[BoxData[ \(TraditionalForm\`J\)]], " is" }], "Text"], Cell[BoxData[ FormBox[ RowBox[{"J", "=", RowBox[{ RowBox[{"(", GridBox[{ {\(v\_2\), \(v\_3\)} }], ")"}], RowBox[{"(", GridBox[{ {"0", \(-1\)}, {"1", "0"} }], ")"}], RowBox[{"(", GridBox[{ {\(v\_2\^T\)}, {\(v\_3\^T\)} }], ")"}]}]}], TraditionalForm]], "DisplayFormula"], Cell[TextData[{ "and the projected vector ", Cell[BoxData[ \(TraditionalForm \`\(\[Del]\^2 F\_2\( \[VerticalSeparator] \_\(\[Del]\(F\_1\^ \[UpTee] \)\)\)\)\)]], " is found with the standard projection transformation" }], "Text"], Cell[BoxData[ \(TraditionalForm \`\(proj\_\(\[Del]\(F\_1\^ \[UpTee] \)\)\)(x) = x\ - \ \(x \[CenterDot]\[Del]F\_1\)\/\(\[Del]F\_1\[CenterDot]\[Del]F\_1. \)\)], "DisplayFormula"], Cell[TextData[{ "\tBelow is the last example of the intersection of the cylinder with the \ sphere where this time the package checks for singular points using the above \ algorithm. 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StyleBox["ParametrizeCurve", "Input"], " to increase the flexibility of its use. Also, any option that ", StyleBox["NDSolve", "Input"], " takes can be given to ", StyleBox["ParametrizeCurve", "Input"], " and it will pass it on to ", StyleBox["NDSolve", "Input"], ". What follows are the options to ", StyleBox["ParametrizeCurve", "Input"], " listed in alphabetical order with their default values:", StyleBox["\n\nAdjustInitialPoint", "Input"], " takes boolean values. If set to ", StyleBox["True", "Input"], " any time the given initial point is not on the curve, the nearest point \ on the curve to the given point is taken as the initial point. This initial \ point is found by a variation of the steepest descent method. The default \ value is ", StyleBox["True", "Input"], ".", StyleBox["\n\nCheckSingularPoints", "Input"], " takes boolean values.If set to ", StyleBox["False", "Input"], " the package doesn't bother to check for singular points. The package runs \ much faster in this mode than when it does check for singular points since ", StyleBox["NDSolve", "Input"], " with its default settings spends a great deal of time on its adaptive \ scheme for choosing the stepsize whenever it nears a singular point where the \ package alters the system of differential equations. The default value is ", StyleBox["True", "Input"], ".\n\n", StyleBox["InitialDirection", "Input"], " expresses the general direction, as a vector, in which you wish the \ parametrization to initially head. There is one of two directions a \ parametrization can head, backwards or forwards. The package projects the \ given vector onto the tangent line to determine the desired direction. The \ default value is ", StyleBox["Automatic", "Input"], ".\n\n", StyleBox["MinNorm", "Input"], " expresses the value such that if the norm of the cross product of the \ gradients of the generators is less than that value, the package will \ automatically assume it needs to switch to the singular point algorithm. The \ default value is ", StyleBox["0.\n\nMaxNorm", "Input"], " expresses the value such that if the norm of the cross product of the \ gradients of the generators is greater than that value, the package will \ automatically assume it need not switch to the singular point algorithm. The \ default value is ", StyleBox["Infinity", "Input"], ".\n\n", StyleBox["ParametrizationSpeed", "Input"], " expresses the desired speed for the parametrization. If set to ", StyleBox["UnitSpeed", "Input"], " then the resulting parametrization is a unit speed parametrization. If \ set to a number, the resulting parametrization has constant speed that \ number. It can also be set to a function, either a pure function or an \ expression in terms of the parameter. If set to ", StyleBox["GradientSpeed", "Input"], " the parametrization's speed is the same as the norm of the cross product \ of the gradients of the generators. The default value is ", StyleBox["UnitSpeed", "Input"], ".\n\n", StyleBox["VectorNorm", "Input"], " expresses the type of vector norm used to measure lengths. It can be ", StyleBox["Norm[", "Input"], StyleBox["p", "Input", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["]", "Input"], " which is the standard vector ", StyleBox["p", FontSlant->"Italic"], "-norm with ", StyleBox["p", FontSlant->"Italic"], " any whole number or \[Infinity], or it can be a pure function. The \ default value is ", StyleBox["Norm[2]", "Input"], ".\n" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["In summary", "Subsection"], Cell[TextData[{ "The package ", StyleBox["ParametrizeCurve`", "Input"], " implements an algorithm that allows one to numerically find \ parametrizations for the intersection of two surfaces. Moreover, it can \ parametrize through nondegenerate singular points on the intersection. \ Furthermore, the algorithm extends with little modifications to parametrize \ the curve that is the intersection of ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], " hypersurfaces in ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^n\)]], ", and the package will do so. In particular, it will parametrize a curve \ in the plane that is given implicitly, ", Cell[BoxData[ \(TraditionalForm\`\(F(x, y) = 0, \)\)]], " as a level curve." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["References", "Section"], Cell[TextData[{ "\nBajaj, C. L., Hoffmann, C. M., Hopcroft, J.E.H., Lynch, R. E. 1988.\n\t\ Tracing surface intersections. ", StyleBox["Computer Aided Geometric Design", FontSlant->"Italic"], " 5 (4) 285\[Dash]307.\n\t\nWilkinson, Steven. 1998.\n\tNumerically \ parametrizing curves. ", StyleBox["College Mathematics Journal ", FontSlant->"Italic"], " 29 (2) 104\[Dash]119" }], "Reference"] }, Open ]], Cell[CellGroupData[{ Cell["About the Author", "Section"], Cell["\<\ Steven Wilkinson is an associate professor in the Department of \ Math and CS at Northern Kentucky University. He received his Ph.D. in \ mathematics from Rice University in 1984. Steven Wilkinson Department of Mathematics and Computer Science Northern Kentucky University Highland Heights, Kentucky 41099-1700 wilkinson@nku.edu\ \>", "Text"] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"NeXT 3.0", ScreenRectangle->{{0, 1053}, {0, 832}}, ShowPageBreaks->True, WindowSize->{526, 494}, WindowMargins->{{Automatic, 74}, {Automatic, 29}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, PageHeaders->{{Cell[ TextData[ "Intersections of Surfaces"], "Header"], Inherited, Cell[ TextData[ "Steven Wilkinson (wilkinson@nku.edu)"], "Header"]}, { Cell[ TextData[ "Intersections of Surfaces"], "Header"], Inherited, Cell[ TextData[ "Steven Wilkinson (wilkinson@nku.edu)"], "Header"]}}, PageFooters->{{Inherited, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], Cell[ TextData[ "Last modified 3/3/1999"], "Header"]}, {Inherited, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], Cell[ TextData[ "Last modified 3/3/1999"], "Header"]}}, PrintingOptions->{"FirstPageHeader"->False, "FacingPages"->True, "GraphicsPrintingFormat"->"Automatic"}, ShowCellLabel->False, PrivateFontOptions->{"FontType"->"Outline"}, Magnification->1, StyleDefinitions -> "ArticleClassic.nb" ] (*********************************************************************** Cached data follows. 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