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ParametricPlot3D is buggy


Can anyone explain this bug that appears in ParametricPlot3D
in my version of Mathematica 4.0.2 on Windows 2000?

-----------------------------------------------------------

This works fine:

ParametricPlot3D[{Cos[t]Cos[u], Sin[t]Cos[u], Sin[u]},
{t, 0, 2Pi}, {u, -Pi/2, Pi/2}, PlotPoints -> {8, 3}]

But this doesn't give a picture:

ParametricPlot3D[{Cos[t]Cos[u], Sin[t]Cos[u], Sin[u]},
{t, 0, 2Pi}, {u, -Pi/2, Pi/2}, PlotPoints -> {7, 3}]

This works fine:

ParametricPlot3D[{Cos[t]Cos[u], Sin[t]Cos[u], Sin[u]},
{t, 0, 2Pi}, {u, -Pi/2, Pi/2}, PlotPoints -> {6, 3}]

But this doesn't give a picture:

ParametricPlot3D[{Cos[t]Cos[u], Sin[t]Cos[u], Sin[u]},
{t, 0, 2Pi}, {u, -Pi/2, Pi/2}, PlotPoints -> {5, 3}]

In this last case, not only do I not get a picture, if I go
back and change the PlotPoints option to anything at all,
in the same cell, I still get no picture.

With PlotPoints set to {4, 3} I again get no picture, but
surprisingly, with PlotPoings set to {3,3} I get a picture.
Of course in this case the "sphere" has gone flat.

Do other people experience this same phenomenon? I find it
amazing and frustrating that ordinary things that have been part
of Mathematica for a long time do not work correctly.

Will Self


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