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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[ 64488, 2231]*) (*NotebookOutlinePosition[ 65323, 2257]*) (* CellTagsIndexPosition[ 65279, 2253]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Creating Transparencies\n", StyleBox["by Harry Calkins and Theresa Fulton", FontSize->12] }], "Title", FontFamily->"Times New Roman", FontSlant->"Italic", FontColor->RGBColor[0.992355, 1, 0.770001], Background->RGBColor[0.117708, 0.06392, 0.709987]], Cell[BoxData[ \(rcoord := {Random[Real, {\(-1\), 1}], Random[Real, {\(-1\), 1}], Random[Real, {\(-1\), 1}]}\)], "Input"], Cell[BoxData[ \(\(pts = 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This is important when you use the function that shades the inner \ region of the overlapping circles.\ \>", "Text", FontFamily->"Palatino", FontSize->14, FontColor->RGBColor[0.992355, 1, 0.770001], Background->RGBColor[0.117708, 0.06392, 0.709987]], Cell[BoxData[{ \(\(newpts = List[MapThread[List[#] &, {pts}, 1]];\)\), "\n", \(\(mypts = MapThread[Append[#, 0.2] &, newpts, 1];\)\)}], "Input"], Cell["\<\ We are now pulling out the first coordinates of the two circles \ that will overlap.\ \>", "Text", FontFamily->"Palatino", FontSize->14, FontColor->RGBColor[0.992355, 1, 0.770001], Background->RGBColor[0.117708, 0.06392, 0.709987]], Cell[CellGroupData[{ Cell[BoxData[ \(mypts[\([1, All]\)]\)], "Input"], Cell[BoxData[ \({{0.4255984510117369`, 0.6031640806028986`}, 0.2`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(mypts[\([2, All]\)]\)], "Input"], Cell[BoxData[ \({{0.5651964025574551`, 0.6984474079578151`}, 0.2`}\)], "Output"] }, Open ]], Cell["\<\ Next, we will be using the function provided by my colleague. His \ function uses the Graphics package, so it is necessary to load this before \ defining the function.\ \>", "Text", FontFamily->"Palatino", FontSize->14, FontColor->RGBColor[0.992355, 1, 0.770001], Background->RGBColor[0.117708, 0.06392, 0.709987]], Cell[BoxData[ \(<< Graphics`\)], "Input"], Cell["Here is the IntersectionPlot function and description.", "Text", FontFamily->"Palatino", FontSize->14, FontColor->RGBColor[0.992355, 1, 0.770001], Background->RGBColor[0.117708, 0.06392, 0.709987]], Cell["\<\ This function is designed to allow the area common to two circles \ or ellipses to be shaded. The form of the input is: IntersectionPlot[{center1,radius1},{center2,rad2},plotrange1,plotrange2,opts] where the radius can be given as a single number or an ordered pair of \ numbers. In the second case the first number is the horizontal semi-axis and \ the second the vertical semi-axis. The opts may be any standard options for \ Plot or InequalityPlot except DisplayFunction.\ \>", "Text", FontFamily->"Palatino", FontColor->RGBColor[0.992355, 1, 0.770001], Background->RGBColor[0.117708, 0.06392, 0.709987]], Cell[BoxData[ \(IntersectionPlot[{cent1_, rad1_}, {cent2_, rad2_}, plotrange1_, plotrange2_, opts___?OptionQ] := Module[{rng, func1, func2, plot1}, \[IndentingNewLine]rng1\ = plotrange1 /. plotrange1[\([1]\)] \[Rule] \ xx; \[IndentingNewLine]rng2\ = plotrange2 /. plotrange2[\([1]\)] \[Rule] \ yy; \[IndentingNewLine]func1\ = If[NumberQ[ rad1], \((xx - cent1[\([1]\)])\)^2\ + \ \((yy - cent1[\([2]\)])\)^2\ \[Equal] rad1^2, \((\((xx - cent1[\([1]\)])\)/ rad1[\([1]\)])\)^2\ + \ \((\((yy - cent1[\([2]\)])\)/ rad1[\([2]\)])\)^2\ \[Equal] 1]; \[IndentingNewLine]func2\ = If[NumberQ[ rad2], \((xx - cent2[\([1]\)])\)^2\ + \ \((yy - cent2[\([2]\)])\)^2\ \[Equal] rad2^2, \((\((xx - cent2[\([1]\)])\)/ rad2[\([1]\)])\)^2\ + \ \((\((yy - cent2[\([2]\)])\)/ rad2[\([2]\)])\)^2\ \[Equal] 1]; \[IndentingNewLine]plot1\ = ImplicitPlot[{func1, func2}, rng1, DisplayFunction\ \[Rule] \ Identity, opts]; \[IndentingNewLine]ineq1\ = If[NumberQ[ rad1], \((xx - cent1[\([1]\)])\)^2\ + \ \((yy - cent1[\([2]\)])\)^2\ <= rad1^2, \((\((xx - cent1[\([1]\)])\)/ rad1[\([1]\)])\)^2\ + \ \((\((yy - cent1[\([2]\)])\)/ rad1[\([2]\)])\)^2\ <= 1]; \[IndentingNewLine]ineq2\ = If[NumberQ[ rad2], \((xx - cent2[\([1]\)])\)^2\ + \ \((yy - cent2[\([2]\)])\)^2\ <= rad2^2, \((\((xx - cent2[\([1]\)])\)/ rad2[\([1]\)])\)^2\ + \ \((\((yy - cent2[\([2]\)])\)/ rad2[\([2]\)])\)^2\ <= 1]; \[IndentingNewLine]plot2\ = InequalityPlot[And[ineq1, ineq2], rng1, rng2, DisplayFunction\ \[Rule] \ Identity, opts]; \[IndentingNewLine]plt\ = Show[{plot1, plot2}, DisplayFunction\ \[Rule] \ $DisplayFunction]\[IndentingNewLine]]\ \)], "Input"], Cell["\<\ Now let's use this function with our coordinates to get the \ overlapping segment.\ \>", "Text", FontFamily->"Palatino", FontSize->14, 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