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Austin Schuh405fa6c2015-09-06 18:13:55 -07001(************** Content-type: application/mathematica **************
2
3 Mathematica-Compatible Notebook
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36*******************************************************************)
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53Cell[TextData[{
54 StyleBox["Mathematica",
55 FontWeight->"Plain",
56 FontSlant->"Italic"],
57 StyleBox[" and cddmathlink\nUsing cddmathlink to compute complex convex \
58hulls and drawing with ",
59 FontWeight->"Plain"],
60 StyleBox["Mathematica",
61 FontWeight->"Plain",
62 FontSlant->"Italic"],
63 StyleBox["\nby Komei Fukuda\nwith \na nice zonotope example\nof Russell \
64Towle\n (April 17, 2001)",
65 FontWeight->"Plain"]
66}], "Title",
67 ImageRegion->{{0, 1}, {0, 1}}],
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70 InitializationCell->True,
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72
73Cell["\<\
74
75(* Russell Towle's codes to create projections (zonotopes) of
76hypercubes. *)
77
78cross[ {ax_, ay_, az_}, {bx_, by_, bz_} ] := (*cross product*)
79 {ay bz - az by, az bx - ax bz, ax by - ay bx}
80
81mag[v_]:= Sqrt[Plus@@(v^2)] (*magnitude of a vector*)
82
83unit[v_]:= v/Sqrt[v.v] (*make unit vector*)
84
85tolerance=0.000001;
86collinear[ v1_, v2_ ] := (*test for collinearity*)
87 Apply[And, Map[Abs[#]<tolerance&, cross[v1,v2]]]
88
89setStar[vlist_] := (*discard collinear vectors*)
90 Module[{selected={}},
91 Scan[Function[v, If[v!={0,0,0} &&
92 Select[selected,
93 collinear[v,#]&]=={},
94 AppendTo[selected,v]] ],
95 vlist];
96
97 Print[Length[selected],\" zonal directions.\"];
98 gStar=selected] (*gStar is global, list of non-collinear vectors*)
99
100\
101\>", "Input",
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104
105Cell[CellGroupData[{Cell["\<\
106(* Here I set to a directory where I store
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109SetDirectory[\"~/Math\"]\
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155Cell["\<\
156(*the vectors which determine an n-merous polar zonohedron*)
157(*3<=n, 0<=pitch<=90 degrees*)
158
159vectors[n_Integer,pitch_]:=
160Table[N[{Cos[Degree pitch] Cos[2Pi i/n],
161\tCos[Degree pitch] Sin[2Pi i/n],
162\t-Sin[Degree pitch]},15],
163\t{i,n}] (* modified by KF, precision 15 added *)\
164\>", "Input",
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169(*the pitch at which a polar zonohedron is
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173\
174\>", "Input",
175 InitializationCell->True,
176 ImageRegion->{{0, 1}, {0, 1}}],
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178Cell["\<\
179(*Here, we obtain the vectors for an isometric projection of
180a d-cube into cyclic symmetry*)
181
182dim=8;
183gen=Zonotope[vectors[dim, N[ 1/Degree * ArcTan[(1/2)^(1/2)],15 ] ] ];
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