A way to fix coloring

• To: mathgroup at smc.vnet.net
• Subject: [mg3201] A way to fix coloring
• From: Matthias Reinsch <reinsch at tops.lbl.gov>
• Date: Sat, 17 Feb 1996 14:15:19 -0500
• Organization: Lawrence Berkeley Laboratory, Berkeley CA
• Sender: owner-wri-mathgroup at wolfram.com

are colored incorrectly (see ProblemPlot below).  Enclosed in this message
is FastFixColoring, a solution to this problem.  I have already notified
sites so that users who need correctly colored plots can generate them.

======================================================================
An example of a plot in which the coloring has errors:
======================================================================

f = N @ ComplexExpand @ Expand[SphericalHarmonicY[6, 3, th, ph] -
SphericalHarmonicY[6,-3, th, ph] ]

ProblemPlot = ParametricPlot3D[ (1+.2 f Sin[6/11 Pi]) *
{Sin[th] Cos[ph],Sin[th] Sin[ph],Cos[th]}, {th,0,Pi},{ph,0,2 Pi}]

======================================================================
The corrected plot:
======================================================================

FastFixColoring[gr3D_] := (viewpt = ViewPoint /. gr3D[[2]];
Graphics3D[ Flatten @ Map[ (p4 = #[[1]];
p42=Drop[p4,{2}]; p44=Drop[p4,{4}]; m={viewpt,p4[[1]],p4[[1]]};
If[ Det[m-p44] Det[m-p42] < 0, {Polygon @ p44, Polygon @ p42}, {#}])&,
gr3D[[1]] ], gr3D[[2]] ] )

Show @ FastFixColoring @ ProblemPlot

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