Hello, I am running the following line of code for Mathematica 10 to visualize superquadrics (supertoroid):
Manipulate[
ParametricPlot3D[{a1*(a4 + Sign[Cos[u]]*Abs[Cos[u]]^eps1)*
Sign[Cos[t]]*Abs[Cos[t]]^eps2,
a2*(a4 + Sign[Cos[u]]*Abs[Cos[u]]^eps1)*Sign[Sin[t]]*
Abs[Sin[t]]^eps2, a3*Sign[Sin[u]]*Abs[Sin[u]]^eps1}, {t, -Pi,
Pi}, {u, -Pi, Pi}, MaxRecursion -> 5, ViewPoint -> {2, 2, 2},
PlotStyle -> Lighter[Red, op]],
{{op, 1, "Lightness"}, 0, 1, Appearance -> "Labeled"},
{{a1, 1, "Parameter a1"}, 0, 5,
Appearance -> "Labeled"}, {{a2, 1, "Parameter a2"}, 0, 5,
Appearance -> "Labeled"}, {{a3, 1, "Parameter a3"}, 0, 5,
Appearance -> "Labeled"}, {{a4, 1, "Parameter a4"}, 0, 5,
Appearance -> "Labeled"}, {{eps1, 1, "Parameter eps1"}, 0, 5,
Appearance -> "Labeled"}, {{eps2, 1, "Parameter eps2"}, 0, 5,
Appearance -> "Labeled"}]
Unfortunately, the image has several discontinuities (see Figure) and I do not know how to fix it. These discontinuities are more significant if parameters eps1 and eps2 are smaller (i.e. 0.25). Could anyone help with that? Thank you,
Wawosz