| (************** Content-type: application/mathematica ************** |
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| Mathematica-Compatible Notebook |
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| *******************************************************************) |
| |
| (*CacheID: 232*) |
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| StyleBox["Mathematica", |
| FontWeight->"Plain", |
| FontSlant->"Italic"], |
| StyleBox[" and cddmathlink\nUsing cddmathlink to compute complex convex \ |
| hulls and drawing with ", |
| FontWeight->"Plain"], |
| StyleBox["Mathematica", |
| FontWeight->"Plain", |
| FontSlant->"Italic"], |
| StyleBox["\nby Komei Fukuda\nwith \na nice zonotope example\nof Russell \ |
| Towle\n (April 17, 2001)", |
| FontWeight->"Plain"] |
| }], "Title", |
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| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell["\<\ |
| |
| (* Russell Towle's codes to create projections (zonotopes) of |
| hypercubes. *) |
| |
| cross[ {ax_, ay_, az_}, {bx_, by_, bz_} ] := (*cross product*) |
| {ay bz - az by, az bx - ax bz, ax by - ay bx} |
| |
| mag[v_]:= Sqrt[Plus@@(v^2)] (*magnitude of a vector*) |
| |
| unit[v_]:= v/Sqrt[v.v] (*make unit vector*) |
| |
| tolerance=0.000001; |
| collinear[ v1_, v2_ ] := (*test for collinearity*) |
| Apply[And, Map[Abs[#]<tolerance&, cross[v1,v2]]] |
| |
| setStar[vlist_] := (*discard collinear vectors*) |
| Module[{selected={}}, |
| Scan[Function[v, If[v!={0,0,0} && |
| Select[selected, |
| collinear[v,#]&]=={}, |
| AppendTo[selected,v]] ], |
| vlist]; |
| |
| Print[Length[selected],\" zonal directions.\"]; |
| gStar=selected] (*gStar is global, list of non-collinear vectors*) |
| |
| \ |
| \>", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
| |
| Cell[CellGroupData[{Cell["\<\ |
| (* Here I set to a directory where I store |
| the packages I need *) |
| |
| SetDirectory[\"~/Math\"]\ |
| \>", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
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| Cell["<<UnfoldPolytope.m", "Input", |
| InitializationCell->True, |
| ImageRegion->{{0, 1}, {0, 1}}], |
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| InitializationCell->True, |
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| Cell["<<IOPolyhedra.m", "Input", |
| InitializationCell->True, |
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| Cell["\<\ |
| (*the vectors which determine an n-merous polar zonohedron*) |
| (*3<=n, 0<=pitch<=90 degrees*) |
| |
| vectors[n_Integer,pitch_]:= |
| Table[N[{Cos[Degree pitch] Cos[2Pi i/n], |
| \tCos[Degree pitch] Sin[2Pi i/n], |
| \t-Sin[Degree pitch]},15], |
| \t{i,n}] (* modified by KF, precision 15 added *)\ |
| \>", "Input", |
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| (*the pitch at which a polar zonohedron is |
| an isometric shadow of an n-cube*) |
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| N[1/Degree * ArcTan[(1/2)^(1/2)],15]; |
| \ |
| \>", "Input", |
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| |
| Cell["\<\ |
| (*Here, we obtain the vectors for an isometric projection of |
| a d-cube into cyclic symmetry*) |
| |
| dim=8; |
| gen=Zonotope[vectors[dim, N[ 1/Degree * ArcTan[(1/2)^(1/2)],15 ] ] ]; |
| genc = Chop[gen,10^(-12)];\ |
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| p |
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| P |
| p |
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| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
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| p |
| .02 w |
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| p |
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| p |
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| p |
| .02 w |
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| P |
| p |
| .02 w |
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| p |
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| p |
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| p |
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| p |
| .02 w |
| .51272 .66527 Mdot |
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| p |
| .02 w |
| .70275 .4721 Mdot |
| P |
| p |
| .02 w |
| .2899 .66405 Mdot |
| P |
| p |
| .02 w |
| .55419 .56715 Mdot |
| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
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| p |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| p |
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| p |
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| P |
| p |
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| p |
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| p |
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| P |
| p |
| .02 w |
| .4231 .65222 Mdot |
| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
| .46514 .55228 Mdot |
| P |
| p |
| .02 w |
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| P |
| p |
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| P |
| p |
| .02 w |
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| P |
| p |
| .02 w |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| P |
| p |
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| p |
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| p |
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| p |
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