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| Notebook[{ |
| Cell["\<\ |
| PolytopeSkeleton.m |
| Visualizing Convex Polytope Skeletons (with cddmathlink)\ |
| \>", "Title", |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[TextData[StyleBox["Komei Fukuda, fukuda@ifor.math.ethz.ch\nSwiss Federal \ |
| Institute of Technology, Lausanne and Zurich\nDecember 17, 2002", |
| FontSize->17, |
| FontSlant->"Italic"]], "Subtitle", |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[CellGroupData[{ |
| |
| Cell["Preparation (reading Packages)", "Section", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell["Off[General::spell1]; Off[General::spell]", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell["$Path = Append[$Path,\"~/Math\"]; ", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[TextData[{ |
| "We use an extra graphics package available from ", |
| StyleBox["MathSource", |
| FontSlant->"Italic"], |
| ". It is called View3D which is a part of ExtendGraphics package wrtten \ |
| by Tom Wickham-Jones . The package is available at ", |
| StyleBox["http://www.mathsource.com/", |
| FontFamily->"Courier", |
| FontWeight->"Bold"], |
| ". If you install it in a directory which in not in the $Path, you need to \ |
| append the directory to $Path." |
| }], "Text", |
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| Cell["$Path", "Input", |
| InitializationCell->True, |
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| |
| Cell[BoxData[ |
| \({"/Users/fukuda/Library/Mathematica/4.1/Kernel", |
| "/Users/fukuda/Library/Mathematica/4.1/AddOns/Autoload", |
| "/Users/fukuda/Library/Mathematica/4.1/AddOns/Applications", |
| "/Library/Mathematica/Kernel/", "/Library/Mathematica/Autoload/", |
| "/Library/Mathematica/Applications/", "/Library/Mathematica/", ".", |
| "/Users/fukuda", |
| "/Applications/LocalApps/Mathematica 4.1.app/AddOns/StandardPackages", |
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| 4.1.app/AddOns/StandardPackages/StartUp", |
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| Cell["Needs[\"ExtendGraphics`View3D`\"];", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[TextData[{ |
| "cddmathlink is a ", |
| StyleBox["MathLink", |
| FontSlant->"Italic"], |
| " version of libcdd for doing the vertex enumeration and the facet \ |
| enumeration of a convex polyhedron. cddlib-080.tar.gz is available from \ |
| Fukuda's Homepage: http:///www.ifor.math.ethz.ch/staff/fukuda/fukuda.html \ |
| . Look for \"cdd Homepage\"." |
| }], "Text", |
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| |
| Cell["cddml=Install[\"~/Math/cddmathlink\"]", "Input", |
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| ImageRegion->{{0, 1}, {0, 1}}], |
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| Cell[BoxData[ |
| \(LinkObject["/Users/fukuda/Math/cddmathlink", 4, 3]\)], "Output"] |
| }, Open ]], |
| |
| Cell[TextData[{ |
| "The following packages come with libcdd package and should be installed in \ |
| your favorite directory. Here I assume it is in \"~/Math\" directory. They \ |
| are separately available from Fukuda's Homepage: \ |
| http:///www.ifor.math.ethz.ch/staff/fukuda/fukuda.html . Look for ", |
| StyleBox["Mathematica", |
| FontSlant->"Italic"], |
| " Projects." |
| }], "Text", |
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| |
| Cell["<< PolytopeSkeleton.m", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[CellGroupData[{ |
| |
| Cell["<< IOPolyhedra.m", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[BoxData[ |
| \(Syntax::"com" \(\(:\)\(\ \)\) |
| "Warning: comma encountered with no adjacent expression; the expression \ |
| will be treated as Null. \!\(\" (line 49 of \\\"IOPolyhedra.m\\\")\"\)"\)], \ |
| "Message"] |
| }, Open ]], |
| |
| Cell[CellGroupData[{ |
| |
| Cell["<< UnfoldPolytope.m", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[BoxData[ |
| \(Syntax::"com" \(\(:\)\(\ \)\) |
| "Warning: comma encountered with no adjacent expression; the expression \ |
| will be treated as Null. \!\(\" (line 90 of \ |
| \\\"UnfoldPolytope.m\\\")\"\)"\)], "Message"] |
| }, Open ]] |
| }, Open ]], |
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| Cell[CellGroupData[{ |
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| Cell["Compute theVertices of a Polytope by using cddmathlink", "Section", |
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| \({"~/Math/ine_3d/cube3a.ine", "~/Math/ine_3d/cube3b.ine", |
| "~/Math/ine_3d/cube3.ine", "~/Math/ine_3d/cubocta.ine", |
| "~/Math/ine_3d/cuboctaT.ine", "~/Math/ine_3d/denault1.ine", |
| "~/Math/ine_3d/dodeca.ine", "~/Math/ine_3d/dodecaT.ine", |
| "~/Math/ine_3d/grcubocta.ine", "~/Math/ine_3d/grcuboctaT.ine", |
| "~/Math/ine_3d/hexocta.ine", "~/Math/ine_3d/hexoctaT.ine", |
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| "~/Math/ine_3d/rhomtriaT.ine", "~/Math/ine_3d/scube3.ine", |
| "~/Math/ine_3d/zono3_10.ine"}\)], "Output"] |
| }, Open ]], |
| |
| Cell["\<\ |
| The file test.ine is the main output file of cdd+, which gives the \ |
| inequality (facet) representation of the polytope.\ |
| \>", "Text", |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[CellGroupData[{ |
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| Cell["\<\ |
| MatrixForm[inedata= |
| \tReadPolyhedraData[\"~/Math/ine_3d/hexocta.ine\"]];\ |
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| Cell[BoxData[ |
| InterpretationBox[\("m="\[InvisibleSpace]48\[InvisibleSpace]", n="\ |
| \[InvisibleSpace]4\[InvisibleSpace]" type="\[InvisibleSpace]"integer"\), |
| SequenceForm[ "m=", 48, ", n=", 4, " type=", "integer"], |
| Editable->False]], "Print"] |
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| |
| Cell["\<\ |
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| Cell[BoxData[ |
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| Cell["\<\ |
| {{extlist,linearity},ecdlist,eadlist,icdlist,iadlist}= |
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| \>", "Input", |
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| Cell["\<\ |
| invertpos[l_List, j_]:= |
| \tModule[{i,pos={}}, |
| \t\tDo[ |
| \t\t\tIf[Position[l[[i]],j]!={},AppendTo[pos,i]], |
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| \t\t]; |
| \t\tpos |
| \t]; |
| dualizeIndices[ecd_List, ineLen_Integer]:= |
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| }, Open ]] |
| }, Closed]], |
| |
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| |
| Cell["Draw a Polytope by a New VisibleSkeleton Graphics", "Subsection", |
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| |
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| |
| Cell["\<\ |
| Do[ uvp=circle[a,5,2]; |
| \tShow[skel3D[uvp], |
| \t\tBoxed->False, |
| \t\tViewPoint -> getMmaViewPoint[uvp,skel3D[uvp]], |
| \t\tSphericalRegion->True |
| \t], |
| \t{a,Pi/11,Pi,Pi/18} |
| ]\ |
| \>", "Input", |
| ImageRegion->{{0, 1}, {0, 1}}, |
| AnimationDisplayTime->1.33333, |
| AnimationCycleOffset->0.0625, |
| AnimationCycleRepetitions->Infinity], |
| |
| Cell[GraphicsData["PostScript", "\<\ |
| %! |
| %%Creator: Mathematica |
| %%AspectRatio: 1 |
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| Mgmatrix idtransform |
| Mtmatrix dtransform |
| } bind def |
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| 3 -1 roll add |
| 3 1 roll add |
| exch } bind def |
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