I am learning lots by reading the Trott's Numerics Guidebook. I came across this PlotPoints spec, so I sent a note to the author. My note and his reply are excerpted below.
Regards..
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I am going through the Numerics guidebook and I have come across the following construct in one of the solutions (page 606-Clebsch surfaces):
PlotPoints -> {{8,4},{8,3},{22,3}}
I look at your code using V6 since the Notebook interface is some much more friendly to reading long code passages (otherwise I would not be inspecting this option). I look at my PlotPoints setting quite often since it is so closely related to the displayed output as well as the performance.
Anyway, V6 complains that this is an invalid specification. Of course it runs just fine under V5.
But in the PlotPoints help for V5, it does not explain this construct. It only describes a single scalar for sample points in each direction.
So, I have 2 questions about this.
- Is this documented somewhere?
- Is there a corresponding construct that is valid in V6?
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The V5 syntax indicated how to deal with the number of plotpoints in 3D contour plots at the various subdivision stages. In V6, after the initial sampling, always one point is added per dimensions.
So the approximate equivalent of PlotPoints -> {{8,4},{8,3},{22,3}} would be
PlotPoints -> {8, 8, 22}, MaxRecursion -> 1
But this will not make all of the code of this solution work.
In V5, ContourPlot3D returned a Graphics3D object that contained polygons.
In V6, a GraphicsComplex is returned. So one must apply Normal to resolve the GraphicsComplex into polygons. And one has potentially to remove the vertex normals.