(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing 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[ 166246, 3750]*) (*NotebookOutlinePosition[ 166912, 3773]*) (* CellTagsIndexPosition[ 166868, 3769]*) (*WindowFrame->Normal*) Notebook[{ Cell["Written by Ingolf Dahl, ingolf.dahl@telia.com, 2001-11-26.", "Text"], Cell["\<\ Here is a routine to split a triangle, or a list of triangles, into small \ triangles with all sides less than d. The triangles can be 2D or 3D.\ \>", "Text"], Cell[BoxData[ \(\(SplitTriangle[triangle_List, d_] := Module[{A, B, C, a2, b2, c2}, If[Depth[triangle] \[Equal] 4, \[IndentingNewLine]Return[ Flatten[Table[ SplitTriangle[triangle[\([i]\)], d], {i, Length[triangle]}], 1]]]; \[IndentingNewLine]A = triangle[\([2]\)] - triangle[\([1]\)]; \[IndentingNewLine]B = triangle[\([3]\)] - triangle[\([2]\)]; \[IndentingNewLine]C = triangle[\([1]\)] - triangle[\([3]\)]; \[IndentingNewLine]a2 = A . A; b2 = B . B; c2 = C . C; \[IndentingNewLine]If[ d^2 \[GreaterEqual] Max[a2, b2, c2], Return[{triangle}]]; \[IndentingNewLine]If[ And[a2 \[GreaterEqual] b2, a2 \[GreaterEqual] c2], Return[Join[ SplitTriangle[{triangle[\([1]\)], triangle[\([1]\)] + A/2, triangle[\([3]\)]}, d], SplitTriangle[{triangle[\([1]\)] + A/2, triangle[\([2]\)], triangle[\([3]\)]}, d]]]]; \[IndentingNewLine]If[ And[b2 > a2, b2 \[GreaterEqual] c2], Return[Join[ SplitTriangle[{triangle[\([1]\)], triangle[\([2]\)], triangle[\([2]\)] + B/2}, d], SplitTriangle[{triangle[\([1]\)], triangle[\([2]\)] + B/2, triangle[\([3]\)]}, d]]], Return[Join[ SplitTriangle[{triangle[\([3]\)] + C/2, triangle[\([2]\)], triangle[\([3]\)]}, d], SplitTriangle[{triangle[\([1]\)], triangle[\([2]\)], triangle[\([3]\)] + C/2}, d]]]]];\)\)], "Input"], Cell["Examples", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(SplitTriangle[{{0, 0, 0}, {0, 3, 0}, {3, 3, 0}}, 3. ]\)], "Input"], Cell[BoxData[ \({{{3\/2, 3\/2, 0}, {0, 3, 0}, {3, 3, 0}}, {{0, 0, 0}, {0, 3, 0}, {3\/2, 3\/2, 0}}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SplitTriangle[{{{0, 0, 0}, {0, 3, 0}, {3, 3, 0}}, {{0, 0, 0}, {0, 4, 0}, {5, 5, 0}}}, 3. ]\)], "Input"], Cell[BoxData[ \({{{3\/2, 3\/2, 0}, {0, 3, 0}, {3, 3, 0}}, {{0, 0, 0}, {0, 3, 0}, {3\/2, 3\/2, 0}}, {{5\/2, 5\/2, 0}, {0, 4, 0}, {5\/2, 9\/2, 0}}, {{15\/4, 15\/4, 0}, {5\/2, 9\/2, 0}, {5, 5, 0}}, {{5\/2, 5\/2, 0}, {5\/2, 9\/2, 0}, {15\/4, 15\/4, 0}}, {{5\/4, 5\/4, 0}, {0, 2, 0}, {5\/2, 5\/2, 0}}, {{0, 0, 0}, {0, 2, 0}, {5\/4, 5\/4, 0}}, {{0, 2, 0}, {0, 4, 0}, {5\/2, 5\/2, 0}}}\)], "Output"] }, Open ]], Cell["\<\ Two small routines for closing and opening polygons. Closing a polygon is \ needed (?) if one want to draw a polygon as wireframe (with Line command) in \ 2D in Mathematica\ \>", "Text"], Cell[BoxData[ \(ClosePolygon[polygon_List] := If[polygon[\([1]\)] \[NotEqual] polygon[\([Length[polygon]]\)], \[IndentingNewLine]Append[polygon, polygon[\([1]\)]], polygon]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(ClosePolygon[{{0, 0, 0}, {0, 3, 0}, {3, 3, 0}}]\)], "Input"], Cell[BoxData[ \({{0, 0, 0}, {0, 3, 0}, {3, 3, 0}, {0, 0, 0}}\)], "Output"] }, Open ]], Cell[BoxData[ \(OpenPolygon[polygon_List] := If[polygon[\([1]\)] == polygon[\([Length[polygon]]\)], \[IndentingNewLine]Delete[polygon, Length[polygon]], polygon]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(OpenPolygon[{{0, 0, 0}, {0, 3, 0}, {3, 3, 0}, {0, 0, 0}}]\)], "Input"], Cell[BoxData[ \({{0, 0, 0}, {0, 3, 0}, {3, 3, 0}}\)], "Output"] }, Open ]], Cell["\<\ Martin Kraus' polygon triangulation package: I have copied a part of his help \ file and modified \ \>", "Text"], 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