This is BezierPlot.m in view mode; [Download] [Up]
(* Author: Silvio Levy *)
BeginPackage["BezierPlot`"]
BezierPatch::usage = "\n
BezierPatch[ 4 by 4 array ] describes a bicubic Bezier patch\n
to be plotted using OOGL.m, for example. The elements of the\n
array are usually 3D vectors, but the function doesn't care."
BezierPlot::usage = "\n
BezierPlot[f,{t,tmin,tmax},{u,umin,umax}] \"plots\" the function f\n
of two variables t and u, using Bezier patches. (Usually f returns\n
a 3D vector.) BezierPlot returns an array of BezierPatch'es.\n
Options:\n
Epsilon is the increment used to compute derivatives (default: 10^-4)\n
PlotPoints is a number or pair of numbers indicating the fineness\n
of the subdivision (default: 5)";
BezierPlot::baditer = "bad iterator";
BezierPlot::badpp = "requested number of plot points is < 1";
Options[BezierPlot] = {Epsilon -> .0001, PlotPoints->5}
Begin["`private`"]
BezierPlot[f_,{t_,tmin_,tmax_},{u_,umin_,umax_},options___]:=
Block[{it,iu,nt,nu,dt,du,loc,dfdt,dfdt0,dfdu,dfdu0,dboth,all,
plotPoints=PlotPoints/.{options}/.Options[BezierPlot],
eps=Epsilon/.{options}/.Options[BezierPlot]},
If[Length[plotPoints]==2,{nt,nu}=plotPoints,nt=plotPoints;nu=plotPoints];
If[nx<1 || ny<1,Message[BezierPlot::badpp];Return[{}]];
dt=N[(tmax-tmin)/nt]; du=N[(umax-umin)/nu];
If[!(NumberQ[dt]&&dt>0&&NumberQ[du]&&du>0),
Message[BezierPlot::baditer];Return[{}]];
loc=Table[f/.{t->tmin+dt it,u->umin+du iu},{iu,0,nu},{it,0,nt}];
dfdt0=-loc+Table[f/.{t->tmin+dt(it+If[it<nt,1,-1]eps),u->umin+du iu},
{iu,0,nu},{it,0,nt}];
dfdt=MapAt[-1#&,#,-1]& /@ dfdt0/(3 eps);
dfdu0=-loc+Table[f/.{t->tmin+dt it,u->umin+du(iu+If[iu<nu,1,-1]eps)},
{iu,0,nu},{it,0,nt}];
dfdu=MapAt[-1#&,#,-1]& @ dfdu0/(3 eps);
dboth=MapAt[-1#&,#,-1]& /@ MapAt[-1#&,#,-1]& @
(-loc-dfdt0-dfdu0+Table[f/.{t->tmin+dt(it+If[it<nt,1,-1]eps),
u->umin+du(iu+If[iu<nu,1,-1]eps)},
{iu,0,nu},{it,0,nt}])/(9 eps^2);
all=Transpose[{loc,dfdt,dfdu,dboth},{3,1,2}]//N;
Map[
BezierPatch[
{{#[[1,1]],#[[1,1]]+#[[1,2]],#[[2,1]]-#[[2,2]],#[[2,1]]},
{#[[1,1]]+#[[1,3]],#[[1,1]]+#[[1,2]]+#[[1,3]]+#[[1,4]],
#[[2,1]]-#[[2,2]]+#[[2,3]]-#[[2,4]],#[[2,1]]+#[[2,3]]},
{#[[3,1]]-#[[3,3]],#[[3,1]]+#[[3,2]]-#[[3,3]]-#[[3,4]],
#[[4,1]]-#[[4,3]]-#[[4,2]]+#[[4,4]], #[[4,1]]-#[[4,3]]},
{#[[3,1]],#[[3,1]]+#[[3,2]],#[[4,1]]-#[[4,2]],#[[4,1]]}}]&,
Transpose[{Drop[#,-1]&/@ Drop[#,-1]& @ all, Rest/@Drop[#,-1]& @ all,
Drop[#,-1]&/@ Rest @ all, Rest/@Rest @ all}, {3,1,2}],{2}]
]
Format[x_BezierPatch]:="-BezierPatch-"
End[]
EndPackage[]
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.