third_party/cddlib/examples-ml/cddml-Zonotope.m

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Off[General::spell1];Off[General::spell]


(* 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*)



(* Here I set to a directory where I store
the packages I need *)

SetDirectory["~/Math"]

cddml=Install["~/Math/cddmathlink"]

Needs["ExtendGraphics`View3D`"];

<<UnfoldPolytope.m

<<Combinatorica5.m

<<PolytopeSkeleton.m

<<IOPolyhedra.m

(*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],
	Cos[Degree pitch] Sin[2Pi i/n],
	-Sin[Degree pitch]},15],
	{i,n}]      (* modified by KF, precision 15 added *)

(*the pitch at which a polar zonohedron is
an isometric shadow of an n-cube*)

N[1/Degree * ArcTan[(1/2)^(1/2)],15];


(*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)];

extlist=Map[Prepend[#,1]&,genc];
{n,d}=Dimensions[extlist]