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Graphics MathPictureEnd :[font = subtitle; inactive; preserveAspect; fontSize = 14; fontName = "Times"; startGroup] 1994 Developer Conference in Champaign, Ill. :[font = subsubtitle; inactive; preserveAspect] Roland Jakschewitz :[font = section; inactive; Cclosed; preserveAspect; startGroup] What is it (good for)? :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Functionality :[font = text; inactive; preserveAspect] Using Hershey font descriptions, this Notebook provides scalable Graphics text at user-specifiable angles, which can be seen on screen & in print, independent of hardware and operating system Ð which cannot be done with Mathematica (v2.2) Graphics Text on all (especially non-Display PostScript) platforms. ;[s] 3:0,0;220,1;231,2;307,-1; 3:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = text; inactive; preserveAspect; endGroup] Hershey Fonts are vector fonts of more than a thousand glyphs, which produce quite acceptabel results when used at adequate scaling for printer or screen resolution. Obviously they cannot be used as flexibly as PostScript or TrueType fonts, which use splines for the definition of glyph shapes, and contain additional kerning informationen. :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Origin :[font = text; inactive; preserveAspect; endGroup] The Hershey Fonts were originally created by Dr. A. V. Hershey while working at the U. S. National Bureau of Standards. :[font = subsection; inactive; Cclosed; pageBreak; preserveAspect; startGroup] General Setup :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Raw/compact data :[font = text; inactive; preserveAspect] The format of the Font data in this (the Internet) distribution was originally created by James Hurt Cognition, Inc. 900 Technology Park Drive Billerica, MA 01821 (mit-eddie!ci-dandelion!hurt) ;[s] 3:0,0;37,1;49,2;218,-1; 3:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = text; inactive; preserveAspect] There is one file containing vector descriptions of 1605 (occidental) glyphs Ð these are not in an ASCII sequence. 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.44688 L .68 .518 .659 r F P p .52231 .56883 m .53929 .44749 L .53967 .56716 L .615 .465 .655 r F P p .15 .43206 m .15602 .19503 L .19338 .19347 L .68 .516 .657 r F P p .11679 .43602 m .15602 .19503 L .15 .43206 L .607 .456 .65 r F P p .53967 .56716 m .55822 .44688 L .55877 .56664 L .68 .518 .659 r F P p .15 .43206 m .19338 .19347 L .18801 .43081 L .68 .516 .657 r F P p P p [(Hershey Datei)] .19849 .15985 0 0 Mshowa [(Index-Datei Font 1)] .83332 .501 0 0 Mshowa [(Index-Datei Font 2)] .82867 .34622 0 0 Mshowa [(Index-Datei Font 3)] .82728 .18501 0 0 Mshowa [(usw.)] .56333 .06811 0 0 Mshowa P % End of Graphics MathPictureEnd :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Compiled version (larger but faster to load) :[font = text; inactive; preserveAspect] Thee glyph and font index files in Mathematica format (for shorter loading time) were produced with Mathematica functions defined below in the Functions Defined:Data Conversion subsection. ;[s] 7:0,0;35,1;46,2;100,3;111,4;143,5;176,6;189,-1; 7:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Times,1,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = input; preserveAspect] hglyph.m :[font = input; preserveAspect; endGroup; endGroup; endGroup] hfonts1.m hfonts2.m É :[font = section; inactive; Cclosed; preserveAspect; startGroup] What does it show Ð aside from Graphics text? :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Mathematica«s extensibility ;[s] 2:0,0;11,1;28,-1; 2:1,13,10,Times,3,14,0,0,0;1,12,9,Times,1,14,0,0,0; :[font = text; inactive; preserveAspect; endGroup] Using Mathematica«s programming language it is straightforward and easy Ð and very clear, considering one has to look at only 5-20 lines of function definitions each Ð to extend Mathematica«s Graphics text capability. ;[s] 5:0,0;6,1;17,2;178,3;189,4;218,-1; 5:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] extremely short code compared to C package :[font = text; inactive; preserveAspect] For the 2D functionality, alone, about 20 lines of Mathematica code produce the same functionality as about 20 pages of C code provided with the font descriptions (Hershey font data and accompanying VOGL library source code are available on various servers on the Internet (see archie)). :[font = text; inactive; preserveAspect; endGroup; endGroup] As I will show in the following examples, it takes only another handful of lines of Mathematica input to extend this functionality to 3D text. ;[s] 3:0,0;84,1;95,2;143,-1; 3:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = section; inactive; Cclosed; preserveAspect; startGroup] Setup :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Preliminaries :[font = input; initialization; preserveAspect] *) Off[ General::spell1 ]; (* :[font = input; initialization; preserveAspect; endGroup] *) SetDirectory@"swap:hersh:" (* :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Read Fonts :[font = text; inactive; preserveAspect] This will take about 36 seconds on a 486/33MHz under Windows: :[font = input; initialization; preserveAspect; endGroup] *) <<"hglyph.m"; <<"hfonts0.m"; <<"hfonts1.m"; (* :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Check :[font = input; Cclosed; preserveAspect; startGroup] ?@*Font :[font = print; inactive; preserveAspect; endGroup] $DefaultFont hFont symbolFont timesFont futuraBFont loadFont timesBFont timesIFont futuraFont :[font = input; Cclosed; preserveAspect; startGroup] Length@h == 1605 (* glyphs/letters are defined in hglyph.m *) :[font = output; output; inactive; preserveAspect; endGroup] True ;[o] True :[font = input; Cclosed; preserveAspect; startGroup] ByteCount@h (* this is how much RAM we need for all these fonts *) :[font = output; output; inactive; preserveAspect; endGroup] 2325360 ;[o] 2325360 :[font = input; Cclosed; preserveAspect; startGroup] h[[7]] (* number, width, coordinates *) :[font = output; output; inactive; preserveAspect; endGroup] {7, 11, {{{9, 4}, {7, 5}, {5, 5}, {3, 4}, {2, 2}, {2, -1}, {3, -3}, {5, -4}, {7, -4}, {9, -3}, {9, 0}}, {{6, 0}, {9, 0}}}} ;[o] {7, 11, {{{9, 4}, {7, 5}, {5, 5}, {3, 4}, {2, 2}, {2, -1}, {3, -3}, {5, -4}, {7, -4}, {9, -3}, {9, 0}}, {{6, 0}, {9, 0}}}} :[font = input; Cclosed; preserveAspect; startGroup] Show@Graphics[ { Thickness@.05, Line/@h[[7,3]] }, AspectRatio->Automatic, PlotRange->All, Axes->True ]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 223; pictureHeight = 287; endGroup] %! %%Creator: Mathematica %%AspectRatio: 1.28571 MathPictureStart %% Graphics /Helvetica-Bold findfont 16 scalefont setfont % Scaling calculations -0.248299 0.136054 0.57483 0.136054 [ [(3)] .15986 .57483 0 2 Msboxa [(4)] .29592 .57483 0 2 Msboxa [(5)] .43197 .57483 0 2 Msboxa [(6)] .56803 .57483 0 2 Msboxa [(7)] .70408 .57483 0 2 Msboxa [(8)] .84014 .57483 0 2 Msboxa [(9)] .97619 .57483 0 2 Msboxa [(-4)] .01131 .03061 1 0 Msboxa [(-2)] .01131 .30272 1 0 Msboxa [(2)] .01131 .84694 1 0 Msboxa [(4)] .01131 1.11905 1 0 Msboxa [ -0.00119 -0.001 0 0 ] [ 1.00119 1.28671 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .15986 .57483 m .15986 .58108 L s P [(3)] .15986 .57483 0 2 Mshowa p .002 w .29592 .57483 m .29592 .58108 L s P [(4)] .29592 .57483 0 2 Mshowa p .002 w .43197 .57483 m .43197 .58108 L s P [(5)] .43197 .57483 0 2 Mshowa p .002 w .56803 .57483 m .56803 .58108 L s P [(6)] .56803 .57483 0 2 Mshowa p .002 w .70408 .57483 m .70408 .58108 L s P [(7)] .70408 .57483 0 2 Mshowa p .002 w .84014 .57483 m .84014 .58108 L s P [(8)] .84014 .57483 0 2 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.001 w .02381 .52041 m .02756 .52041 L s P p .001 w .02381 .62925 m .02756 .62925 L s P p .001 w .02381 .68367 m .02756 .68367 L s P p .001 w .02381 .7381 m .02756 .7381 L s P p .001 w .02381 .79252 m .02756 .79252 L s P p .001 w .02381 .90136 m .02756 .90136 L s P p .001 w .02381 .95578 m .02756 .95578 L s P p .001 w .02381 1.0102 m .02756 1.0102 L s P p .001 w .02381 1.06463 m .02756 1.06463 L s P p .001 w .02381 1.17347 m .02756 1.17347 L s P p .001 w .02381 1.22789 m .02756 1.22789 L s P p .001 w .02381 1.28231 m .02756 1.28231 L s P p .002 w .02381 0 m .02381 1.28571 L s P P p p .05 w .97619 1.11905 m .70408 1.2551 L .43197 1.2551 L .15986 1.11905 L .02381 .84694 L .02381 .43878 L .15986 .16667 L .43197 .03061 L .70408 .03061 L .97619 .16667 L .97619 .57483 L s .56803 .57483 m .97619 .57483 L s P P 0 0 m 1 0 L 1 1.28571 L 0 1.28571 L closepath clip newpath % End of Graphics MathPictureEnd :[font = input; Cclosed; preserveAspect; startGroup] Last@h (* character number not equal to index in h! *) :[font = output; output; inactive; preserveAspect; endGroup] {3934, 16, {{{0, 12}, {0, -9}, {1, -9}, {1, 12}, {2, 12}, {2, -9}, {3, -9}, {3, 12}, {4, 12}, {4, -9}, {5, -9}, {5, 12}, {6, 12}, {6, -9}, {7, -9}, {7, 12}, {8, 12}, {8, -9}, {9, -9}, {9, 12}, {10, 12}, {10, -9}, {11, -9}, {11, 12}, {12, 12}, {12, -9}, {13, -9}, {13, 12}, {14, 12}, {14, -9}, {15, -9}, {15, 12}, {16, 12}, {16, -9}}} } ;[o] {3934, 16, {{{0, 12}, {0, -9}, {1, -9}, {1, 12}, {2, 12}, {2, -9}, {3, -9}, {3, 12}, {4, 12}, {4, -9}, {5, -9}, {5, 12}, {6, 12}, {6, -9}, {7, -9}, {7, 12}, {8, 12}, {8, -9}, {9, -9}, {9, 12}, {10, 12}, {10, -9}, {11, -9}, {11, 12}, {12, 12}, {12, -9}, {13, -9}, {13, 12}, {14, 12}, {14, -9}, {15, -9}, {15, 12}, {16, 12}, {16, -9}}} } :[font = input; Cclosed; preserveAspect; startGroup] Show@Graphics[ Line/@h[[ Position[ h, {3813, _,_}, {1} ][[1,1]], 3 ]], AspectRatio->Automatic, PlotRange->All, Axes->True ]; :[font = postscript; PostScript; formatAsPostScript; output; 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L s P p .001 w .40476 .45357 m .40476 .45732 L s P p .001 w .45238 .45357 m .45238 .45732 L s P p .001 w .5 .45357 m .5 .45732 L s P p .001 w .54762 .45357 m .54762 .45732 L s P p .001 w .64286 .45357 m .64286 .45732 L s P p .001 w .69048 .45357 m .69048 .45732 L s P p .001 w .7381 .45357 m .7381 .45732 L s P p .001 w .78571 .45357 m .78571 .45732 L s P p .001 w .07143 .45357 m .07143 .45732 L s P p .001 w .02381 .45357 m .02381 .45732 L s P p .001 w .88095 .45357 m .88095 .45732 L s P p .001 w .92857 .45357 m .92857 .45732 L s P p .001 w .97619 .45357 m .97619 .45732 L s P p .002 w 0 .45357 m 1 .45357 L s P p .002 w .11905 .21548 m .1253 .21548 L s P [(-5)] .10655 .21548 1 0 Mshowa p .002 w .11905 .69167 m .1253 .69167 L s P [(5)] .10655 .69167 1 0 Mshowa p .002 w .11905 .92976 m .1253 .92976 L s P [(10)] .10655 .92976 1 0 Mshowa p .001 w .11905 .2631 m .1228 .2631 L s P p .001 w .11905 .31071 m .1228 .31071 L s P p .001 w .11905 .35833 m .1228 .35833 L s P p .001 w .11905 .40595 m 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.69167 L .97619 .45357 L .92857 .31071 L .88095 .2631 L .78571 .21548 L .69048 .12024 L s .11905 .31071 m .07143 .45357 L .07143 .69167 L .11905 .83452 L s .21429 .21548 m .16667 .31071 L .11905 .45357 L .11905 .73929 L .16667 .88214 L .2619 .97738 L s .88095 .83452 m .92857 .69167 L .92857 .45357 L .88095 .31071 L s .7381 .97738 m .83333 .88214 L .88095 .73929 L .88095 .45357 L .83333 .31071 L .78571 .21548 L s .02381 1.025 m .21429 .92976 L .40476 .88214 L .59524 .88214 L .78571 .92976 L .97619 1.025 L s .02381 .025 m .16667 .07262 L .35714 .12024 L .64286 .12024 L .83333 .07262 L .97619 .025 L s P 0 0 m 1 0 L 1 1.05 L 0 1.05 L closepath clip newpath % End of Graphics MathPictureEnd :[font = input; Cclosed; preserveAspect; startGroup] Show@Graphics[ hText[ "R", {10,11}, .01, 45 Degree, hFont->timesBFont ], AspectRatio->Automatic, PlotRange->All, Axes->True ]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 259; endGroup; endGroup; endGroup] %! %%Creator: Mathematica %%AspectRatio: .92105 MathPictureStart %% Graphics /Helvetica-Bold findfont 16 scalefont setfont % Scaling calculations -35.169513 3.544395 -38.790975 3.544395 [ [(9.95)] .09722 .19737 0 2 Msboxa [(10.05)] .45166 .19737 0 2 Msboxa [(10.1)] .62888 .19737 0 2 Msboxa [(10.15)] .8061 .19737 0 2 Msboxa [(10.2)] .98332 .19737 0 2 Msboxa [(10.95)] .26194 .02015 1 0 Msboxa [(11.05)] .26194 .37459 1 0 Msboxa [(11.1)] .26194 .55181 1 0 Msboxa [(11.15)] .26194 .72903 1 0 Msboxa [(11.2)] .26194 .90625 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .92205 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .09722 .19737 m .09722 .20362 L s P [(9.95)] .09722 .19737 0 2 Mshowa p .002 w .45166 .19737 m .45166 .20362 L s P [(10.05)] .45166 .19737 0 2 Mshowa p .002 w .62888 .19737 m .62888 .20362 L s P [(10.1)] .62888 .19737 0 2 Mshowa p .002 w .8061 .19737 m .8061 .20362 L s P 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inactive; Cclosed; preserveAspect; startGroup] 3D Examples :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Projection onto plane surface :[font = text; inactive; preserveAspect] It is easy to transform the 2D graphics text into a Graphics3D object: :[font = input; preserveAspect] zPlane = First@multiLine /. coord2D -> {x, 240+1.7 y, 30}; :[font = input; preserveAspect] xPlane = First@multiLine /. coord2D -> {0, 280-x, y-20}; :[font = input; preserveAspect] yPlane = First@multiLine /. coord2D -> {20+x, 0, y-20}; :[font = input; Cclosed; preserveAspect; startGroup] Show @ Graphics3D[ { { EdgeForm@Thickness@.001, GrayLevel@.7, Cuboid[{0,0,-150},{310,300,10}] }, xPlane, yPlane, zPlane }, ViewPoint->{-3.590, -3.040, 3.630}, Boxed->False, Lighting->False ]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 100; pictureWidth = 300; pictureHeight = 277; endGroup; endGroup] %! %%Creator: Mathematica %%AspectRatio: .92373 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L .47752 .11715 L p 0 0 0 r F P s P p P p P % End of Graphics MathPictureEnd :[font = subsection; inactive; Cclosed; pageBreak; preserveAspect; startGroup] Projection onto sphere :[font = input; preserveAspect] toSphere[ p:{x_, y_}, r_ ] := With[ { denom= 2r + x^2 + y^2 }, { x/denom, y/denom, -2r/denom } ] ;[s] 9:0,0;38,1;43,2;68,3;73,4;77,5;82,6;88,7;93,8;99,-1; 9:1,10,8,Courier,1,12,0,0,0;1,9,7,Times,1,10,0,0,0;1,10,8,Courier,1,12,0,0,0;1,9,7,Times,1,10,0,0,0;1,10,8,Courier,1,12,0,0,0;1,9,7,Times,1,10,0,0,0;1,10,8,Courier,1,12,0,0,0;1,9,7,Times,1,10,0,0,0;1,10,8,Courier,1,12,0,0,0; :[font = input; preserveAspect] kugelText = First[multiLine] /. coord2D -> toSphere[ {x-100, 60+y}, 20000 ]; :[font = input; Cclosed; preserveAspect; startGroup] Show @ Graphics3D[ kugelText, ViewPoint->{0.000,0.000,-1.580}, Boxed->False ]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 100; pictureWidth = 299; pictureHeight = 202; endGroup] %! 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P p .002 w .73424 .11275 m .72549 .10746 L .7332 .10241 L p 0 .34 .769 r F P s P p .002 w .71217 .10464 m .69847 .11208 L .70526 .10719 L p .361 .802 .646 r F P s P p .002 w .70014 .12035 m .70526 .10719 L .69847 .11208 L p 0 0 0 r F P s P p .002 w .71943 .0995 m .7332 .10241 L .72549 .10746 L p .004 .556 .823 r F P s P p .002 w .72549 .10746 m .71217 .10464 L .71943 .0995 L p .004 .556 .823 r F P s P p .002 w .70526 .10719 m .71943 .0995 L .71217 .10464 L p .361 .802 .646 r F P s P p P p P % End of Graphics MathPictureEnd :[font = section; inactive; Cclosed; preserveAspect; startGroup] 3D Animations :[font = subsection; inactive; preserveAspect; startGroup] Animation of string in whole :[font = input; preserveAspect] SetOptions[ Graphics3D, Boxed->False ]; :[font = input; preserveAspect] SpinShow[ Graphics3D @ { EdgeForm[], threeDstring } ]; :[font = input; preserveAspect; endGroup] SpinShow[ Graphics3D @ { EdgeForm[], threeDcity }, SpinTilt->{12,30} ]; ;[s] 3:0,0;37,1;47,2;75,-1; 3:1,10,8,Courier,1,12,0,0,0;1,9,7,Times,1,10,0,0,0;1,10,8,Courier,1,12,0,0,0; :[font = subsection; inactive; Cclosed; pageBreak; preserveAspect; startGroup] Animation of characters of Hershey strings :[font = input; preserveAspect] SetOptions[ Graphics3D, Boxed->False, ViewPoint->{0.0,-0.079,2.199} ]; :[font = input; preserveAspect] anim2 = make3Dstring[ hText[ "Mathematica", {0,0}, 1, 0, hFont->timesIFont ], (* zPlane: *) 10, (* depth : *) 10, (* yScale: *) 1.7 ]; :[font = input; Cclosed; preserveAspect; startGroup] Show @ Graphics3D @ anim2; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 56; endGroup] %! %%Creator: Mathematica %%AspectRatio: .20186 MathPictureStart %% Graphics3D /Helvetica-Bold findfont 16 scalefont setfont % Scaling calculations 0.02381 0.952381 -0.375935 0.952381 [ [ 0 0 0 0 ] [ 1 .20186 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 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.03433 m .81918 .02746 L .82552 .02749 L p 0 0 0 r F P s P p .002 w .77196 .02749 m .7678 .0345 L .76258 .03433 L p 0 0 0 r F P s P p .002 w .76258 .03433 m .76665 .02746 L .77196 .02749 L p 0 0 0 r F P s P p .002 w .76784 .02749 m .76368 .0345 L .75854 .03433 L p 0 0 0 r F P s P p .002 w .75854 .03433 m .76261 .02746 L .76784 .02749 L p 0 0 0 r F P s P p .002 w .71015 .02749 m .706 .0345 L .70199 .03433 L p 0 0 0 r F P s P p .002 w .70199 .03433 m .70605 .02746 L .71015 .02749 L p 0 0 0 r F P s P p .002 w .70603 .02749 m .70188 .0345 L .69795 .03433 L p 0 0 0 r F P s P p .002 w .69795 .03433 m .70201 .02746 L .70603 .02749 L p 0 0 0 r F P s P p .002 w .65239 .05551 m .6442 .0345 L .64139 .03433 L p 0 0 .352 r F P s P p .002 w .63333 .02746 m .64139 .03433 L .6442 .0345 L p 0 .118 .601 r F P s P p .002 w .62774 .02749 m .61948 .0345 L .61715 .03433 L p 0 0 0 r F P s P p .002 w .61715 .03433 m .62525 .02746 L .62774 .02749 L p 0 0 0 r F P s P p .002 w .6607 .02749 m .65656 .0345 L .65351 .03433 L p 0 0 0 r F P s P p .002 w .65351 .03433 m .65757 .02746 L .6607 .02749 L p 0 0 0 r F P s P p .002 w .65658 .02749 m .65244 .0345 L .64947 .03433 L p 0 0 0 r F P s P p .002 w .64947 .03433 m .65353 .02746 L .65658 .02749 L p 0 0 0 r F P s P p .002 w .56593 .02749 m .5618 .0345 L .5606 .03433 L p 0 0 0 r F P s P p .002 w .5606 .03433 m .56464 .02746 L .56593 .02749 L p 0 0 0 r F P s P p .002 w .57005 .02749 m .56592 .0345 L .56464 .03433 L p 0 0 0 r F P s P p .002 w .56464 .03433 m .56868 .02746 L .57005 .02749 L p 0 0 0 r F P s P p .002 w .44645 .04851 m .4382 .0345 L .4394 .03433 L p .651 .24 0 r F P s P p .002 w .42728 .02746 m .4394 .03433 L .4382 .0345 L p .377 0 0 r F P s P p .002 w .41759 .02749 m .40936 .0345 L .41113 .03433 L p .496 .844 .576 r F P s P p .002 w .41113 .03433 m .4192 .02746 L .41759 .02749 L p .496 .844 .576 r F P s P p .002 w .3599 .02749 m .3558 .0345 L .35861 .03433 L p .693 .856 .444 r F P s P p .002 w .35861 .03433 m .36263 .02746 L .3599 .02749 L p .693 .856 .444 r F P s P p .002 w .36402 .02749 m .35992 .0345 L .36265 .03433 L p .691 .855 .442 r F P s P p .002 w .36265 .03433 m .36667 .02746 L .36402 .02749 L p .691 .855 .442 r F P s P p .002 w .26513 .02749 m .26104 .0345 L .26569 .03433 L p .743 .893 .497 r F P s P p .002 w .26569 .03433 m .26971 .02746 L .26513 .02749 L p .743 .893 .497 r F P s P p .002 w .26925 .02749 m .26516 .0345 L .26973 .03433 L p .741 .891 .495 r F P s P p .002 w .26973 .03433 m .27375 .02746 L .26925 .02749 L p .741 .891 .495 r F P s P p .002 w .2117 .05551 m .20336 .0345 L .20914 .03433 L p .831 .476 0 r F P s P p .002 w .20102 .02746 m .20914 .03433 L .20336 .0345 L p .593 .054 0 r F P s P p .002 w .18684 .02749 m .17864 .0345 L .1849 .03433 L p .595 .916 .673 r F P s P p .002 w .1849 .03433 m .19294 .02746 L .18684 .02749 L p .595 .916 .673 r F P s P p .002 w .21568 .02749 m .2116 .0345 L .21722 .03433 L p .766 .909 .523 r F P s P p .002 w .21722 .03433 m .22122 .02746 L .21568 .02749 L p .766 .909 .523 r F P s P p .002 w .2198 .02749 m .21572 .0345 L .22126 .03433 L p .764 .908 .521 r F P s P p .002 w .22126 .03433 m .22526 .02746 L .2198 .02749 L p .764 .908 .521 r F P s P p .002 w .91612 .0345 m .90793 .02749 L .89998 .02746 L p 0 .217 .708 r F P s P p .002 w .90793 .02749 m .89969 .02749 L .8919 .02746 L p .001 0 0 r F P s P p .002 w .8919 .02746 m .89998 .02746 L .90793 .02749 L p .001 0 0 r F P s P p .002 w .9409 .02749 m .92854 .02749 L .92018 .02746 L p .001 0 0 r F P s P p .002 w .92018 .02746 m .9323 .02746 L .9409 .02749 L p .001 0 0 r F P s P p .002 w .84608 .0345 m .83376 .02749 L .82726 .02746 L p 0 .312 .726 r F P s P p .002 w .83376 .02749 m .82552 .02749 L .81918 .02746 L p .001 0 0 r F P s P p .002 w .81918 .02746 m .82726 .02746 L .83376 .02749 L p .001 0 0 r F P s P p .002 w .78837 .04151 m .7802 .02749 L .77474 .02746 L p 0 0 .521 r F P s P p .002 w .7802 .02749 m .76784 .02749 L .76261 .02746 L p .001 0 0 r F P s P p .002 w .76261 .02746 m .77474 .02746 L .7802 .02749 L p .001 0 0 r F P s P p .002 w .72658 .04151 m .71839 .02749 L .71413 .02746 L p 0 0 .488 r F P s P p .002 w .71839 .02749 m .70603 .02749 L .70201 .02746 L p .001 0 0 r F P s P p .002 w .70201 .02746 m .71413 .02746 L .71839 .02749 L p .001 0 0 r F P s P p .002 w .6442 .0345 m .63598 .02749 L .63333 .02746 L p 0 .118 .601 r F P s P p .002 w .63598 .02749 m .62774 .02749 L .62525 .02746 L p .001 0 0 r F P s P p .002 w .62525 .02746 m .63333 .02746 L .63598 .02749 L p .001 0 0 r F P s P p .002 w .67714 .04151 m .66894 .02749 L .66565 .02746 L p 0 0 .461 r F P s P p .002 w .66894 .02749 m .65658 .02749 L .65353 .02746 L p .001 0 0 r F P s P p .002 w .65353 .02746 m .66565 .02746 L .66894 .02749 L p .001 0 0 r F P s P p .002 w .58651 .04151 m .57829 .02749 L .57676 .02746 L p 0 0 .407 r F P s P p .002 w .57829 .02749 m .56593 .02749 L .56464 .02746 L p .001 0 0 r F P s P p .002 w .56464 .02746 m .57676 .02746 L .57829 .02749 L p .001 0 0 r F P s P p .002 w .4382 .0345 m .42583 .02749 L .42728 .02746 L p .377 0 0 r F P s P p .002 w .42583 .02749 m .41759 .02749 L .4192 .02746 L p .001 0 0 r F P s P p .002 w .4192 .02746 m .42728 .02746 L .42583 .02749 L p .001 0 0 r F P s P p .002 w .38053 .04151 m .37226 .02749 L .37475 .02746 L p .687 .271 0 r F P s P p .002 w .37226 .02749 m .3599 .02749 L .36263 .02746 L p .001 0 0 r F P s P p .002 w .36263 .02746 m .37475 .02746 L .37226 .02749 L p .001 0 0 r F P s P p .002 w .28578 .04151 m .27749 .02749 L .28183 .02746 L p .738 .316 0 r F P s P p .002 w .27749 .02749 m .26513 .02749 L .26971 .02746 L p .001 0 0 r F P s P p .002 w .26971 .02746 m .28183 .02746 L .27749 .02749 L p .001 0 0 r F P s P p .002 w .20336 .0345 m .19508 .02749 L .20102 .02746 L p .593 .054 0 r F P s P p .002 w .19508 .02749 m .18684 .02749 L .19294 .02746 L p .001 0 0 r F P s P p .002 w .19294 .02746 m .20102 .02746 L .19508 .02749 L p .001 0 0 r F P s P p .002 w .23635 .04151 m .22804 .02749 L .23335 .02746 L p .761 .338 0 r F P s P p .002 w .22804 .02749 m .21568 .02749 L .22122 .02746 L p .001 0 0 r F P s P p .002 w .22122 .02746 m .23335 .02746 L .22804 .02749 L p .001 0 0 r F P s P p .002 w .13327 .02749 m .10443 .02749 L .11214 .02746 L p .001 0 0 r F P s P p .002 w .11214 .02746 m .14042 .02746 L .13327 .02749 L p .001 0 0 r F P s P p .002 w .07146 .02749 m .04674 .02749 L .05558 .02746 L p .001 0 0 r F P s P p .002 w .05558 .02746 m .07982 .02746 L .07146 .02749 L p .001 0 0 r F P s P p P p P % End of Graphics MathPictureEnd :[font = input; preserveAspect] Unprotect@Out; Clear@Out; Protect@Out; :[font = input; preserveAspect] rotateEachLetter[ anim2, 15 Degree, 23 ]; :[font = input; preserveAspect; endGroup; endGroup] Scan[ Show, % ]; :[font = section; inactive; Cclosed; preserveAspect; startGroup] Perspectives :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Enhancements of Functions :[font = text; inactive; preserveAspect; endGroup] For further use of Hershey text as Graphics3D object, function hText could be modified/extended to allow strings to be positioned in R3 directly, or to have a certain 3D tilt, É. ;[s] 5:0,0;63,1;68,2;133,3;134,4;179,-1; 5:1,11,8,Times,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Variations of Data Conversion :[font = text; inactive; preserveAspect] Since loading the Hershey database into Mathematica is not as fast as one would wish: there are at least three ways in which reading the data can be speeded up. ;[s] 3:0,0;40,1;51,2;162,-1; 3:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Data Reduction :[font = text; inactive; preserveAspect; endGroup] If it is known in advance that only a small subset of fonts will be needed, a reduced version of database file hersh.oc.mma could be used, thus saving on disk space compared to the following solution. In this case the Hershey data would be converted on the fly (using functions hconvert and loadFont). ;[s] 5:0,0;278,1;286,2;291,3;299,4;302,-1; 5:1,11,8,Times,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Conversion of External Data only Once (this method has been used here) :[font = text; inactive; preserveAspect; endGroup] The overall fastest solution is probably to convert the database once into Mathematica format, and Getting these data when needed. One major drawback is that the converted database file (hglyph.m) is about four times as big as the original (compact) version. ;[s] 5:0,0;75,1;86,2;99,3;102,4;259,-1; 5:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Conversion with external MathLink-connected program ;[s] 3:0,0;25,1;33,2;52,-1; 3:1,10,8,Times,1,12,0,0,0;1,10,8,Times,3,12,0,0,0;1,10,8,Times,1,12,0,0,0; :[font = text; inactive; preserveAspect; endGroup] In this case the compact database version Ð possibly cut down to needed fonts only Ð could be used to be converted on the fly by an external MathLink program. One drawback here is that C code is not as portable across platforms as pure Mathematica code. ;[s] 5:0,0;141,1;149,2;236,3;247,4;254,-1; 5:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Code for reading raw data & saving converted data :[font = text; inactive; preserveAspect] On the fly conversion of compact database: :[font = input; inactive; preserveAspect] h = hconvert /@ ReadList[ "hersh.oc.mma", { Number, Number, Character, String } ]; :[font = input; inactive; preserveAspect] timesFont = loadFont[ "romanc.hmp" ]; timesBFont = loadFont[ "romant.hmp" ]; futuraFont = loadFont[ "romans.hmp" ]; futuraBFont = loadFont[ "romand.hmp" ]; :[font = input; inactive; preserveAspect] timesIFont = loadFont[ "italicc.hmp" ]; symbolFont = loadFont[ "symbol.hmp" ]; :[font = text; inactive; preserveAspect] Saving databse in Mathematica format for later use: ;[s] 3:0,0;18,1;29,2;52,-1; 3:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0; :[font = input; inactive; preserveAspect; endGroup; endGroup; endGroup] Save[ "hglyph.m", h ]; Save[ "hfonts0.m", timesFont, timesBFont, futuraFont, futuraBFont ]; Save[ "hfonts1.m", timesIFont, symbolFont ]; :[font = section; inactive; Cclosed; preserveAspect; startGroup] Functions defined :[font = subsection; inactive; Cclosed; preserveAspect; startGroup] Packages used :[font = input; initialization; preserveAspect] *) Needs@"Geometry`Rotations`"; (* :[font = input; initialization; preserveAspect] *) Needs@"Graphics`Shapes`"; Unprotect@RotateShape; RotateShape[ shape_, rotmat_ ] := shape /. { poly:Polygon[_] :> Map[(rotmat . #)&, poly, {2}], line:Line[_] :> Map[(rotmat . #)&, line, {2}], point:Point[_] :> Map[(rotmat . #)&, point,{1}] } Protect@RotateShape; (* :[font = input; initialization; preserveAspect; endGroup] *) Needs@"Graphics`Animation`"; (* :[font = subsection; inactive; Cclosed; pageBreak; preserveAspect; startGroup] Data Conversion :[font = input; initialization; Cclosed; preserveAspect; startGroup] *) rCode = First @ ToCharacterCode @ "R" (* :[font = output; output; inactive; preserveAspect; endGroup] 82 ;[o] 82 :[font = input; initialization; preserveAspect] *) makeLines[ a_List ] := Block[ { pl, pos = -1 }, (* ----------------------------------------------- *) If[ (pl = Flatten @ Position[ a, {32,_}, {1} ]) == {}, {a}, AppendTo[ pl, Length[a]+1 ]; Take[ a, { pos+2, pos = #-1 } ]& /@ pl ] ] (* :[font = input; initialization; preserveAspect] *) hconvert[ { charNo_, _, _, charVector_ } ] := Block[ (* ---------------------------------------------------- *) { coordVector = Partition[ ToCharacterCode @ charVector, 2], width }, { charNo, width = #[[2]]-#[[1]]&[ First @ coordVector ], width = Round[ .5 width]; makeLines @ Rest @ coordVector /. {x_Integer, y_Integer} :> {width + x-rCode, rCode-y} } ]; (* :[font = input; initialization; preserveAspect; endGroup] *) loadFont[ translationFile_String ] := Module[ { glyphNumbers }, (* ------ *) glyphNumbers = ReadList[ translationFile, {Number, Number} ] /. {a_, 0} -> a /. {a_, b_} :> Range[a,b] // Flatten; Position[ h, {#,_,_}, {1} ]& /@ glyphNumbers // Flatten ] (* :[font = subsection; inactive; Cclosed; pageBreak; preserveAspect; startGroup] Basic Hershey Text Generation :[font = input; initialization; preserveAspect] *) Options[ hText ] = { hFont->futuraFont, hAlign->AlignLeft }; (* :[font = input; initialization; preserveAspect; endGroup] *) hText[ s_String, pos:{x_,y_}, scale_:1, angle_:0, opts___ ] := (* -------------------------------------------------------------- *) Module[ { sCodes, (* indices in h of letters of string s *) font = hFont /. {opts} /. Options[ hText ], mat = N @ RotationMatrix2D @ (-angle), widths, (* horizontal offsets of single letters in string *) align, (* horizontal alignment of string *) sGraph (* vector description of string s *) }, sCodes = font[[ ToCharacterCode@s - 31 ]]; (* only letters >= ' ' *) widths = FoldList[Plus, 0, h[[ sCodes, 2 ]] ]; align = Switch[ hAlign /. {opts} /. Options[ hText ], AlignLeft, 0, AlignCenter, .5 Last[ widths ], AlignRight, Last[ widths ] ]; widths = Drop[ widths, -1 ]; sGraph = MapThread[ (#1 /. {cx_Integer, cy_Integer} -> {cx+#2, cy})&, {h[[sCodes,3]], widths} ]; Map[ Line, (* perform 2D-transformation of string: *) sGraph /. {cx_Integer, cy_Integer} -> {x-align,y} + mat.{scale cx, scale cy}, {2} ] ] (* :[font = subsection; inactive; Cclosed; pageBreak; preserveAspect; startGroup] 3D Functions :[font = input; initialization; preserveAspect] *) coord2D = {x_/;NumberQ@x, y_/;NumberQ@y }; coord3D = {x_/;NumberQ@x, y_/;NumberQ@y, z_/;NumberQ@z }; (* :[font = input; initialization; preserveAspect] *) make3Dstring[ theString_List, zPlane_, zDepth_, yScale_ ] := (* ------------------------------------------------------------ *) Module[ { z1, z2 }, z1 = theString /. coord2D -> {x, yScale y, zPlane}; z2 = z1 /. coord3D -> {x, y, z+zDepth}; Map[ Polygon[Join[ #[[1]], Reverse[ #[[2]] ], {#[[1,1]]} ]]&, (* collect corresponding line sequences: *) Map[ Transpose, Map[ Flatten[#,1]&, (* collect corresponding letters: *) Transpose[ {z1,z2} /. Line[x_]:>Partition[ x, 2, 1 ] ], {-5} ], {-5} ], {-4} ] ] (* :[font = input; initialization; preserveAspect; endGroup; endGroup] *) rotateEachLetter[ threeDhershey_, degreesPerStep_, steps_ ] := (* -------------------------------------------------------------- *) Module[ { centers, rotation }, (* center of each character in string *) centers = Map[ { .5 (Min@#[[1]] + Max@#[[1]]), (* x center *) .5 (Min@#[[2]] + Max@#[[2]]), (* y center *) Min@#[[3]] (* z bottom *) }&, Transpose /@ Map[ Flatten[ #, 1 ]&, Level[ #, {-3} ]& /@ threeDhershey ] ]; (* rotation in xz-plane around y-axis *) rotation = { { Cos[degreesPerStep], 0, -Sin[degreesPerStep] }, { 0, 1, 0 }, { Sin[degreesPerStep], 0, Cos[degreesPerStep] } } // N; (* apply rotation around its center to each character *) NestList[ Function[ obj, MapThread[ TranslateShape[ RotateShape[ TranslateShape[ #1, -#2 ], rotation ], #2 ]&, { obj, centers } ] ], Graphics3D@{EdgeForm[], #}& /@ threeDhershey, steps ] ] (* :[font = section; inactive; Cclosed; preserveAspect; startGroup] Further Reference :[font = text; inactive; preserveAspect; endGroup; endGroup; endGroup] Data conversion functions and basic Hershey text generation function have been extensively covered in a Notebook/article in Carsten Herrmann«s book "Mathematica: Probleme, Lšsungen, Beispiele", ISBN 3-929821-10-9, due to be available in May 1994. ;[s] 3:0,0;149,1;160,2;247,-1; 3:1,11,8,Times,0,12,0,0,0;1,10,8,Times,2,12,0,0,0;1,11,8,Times,0,12,0,0,0; ^*)