I'm relatively new to Mathematica (v11.2) and aim to plot some superqaudrics-glyphs(see http://www.cs.utah.edu/~gk/papers/vissym04/vissym04kindlmann.pdf).This plots are a generalisation of spheres and are controlled by the parameters $a$ and $b$.
Therefore I've create a little function using the cartesian coordinates of the glyph parametrisized in polar angle $\theta$ and azimut angle $\varphi$.
Numm[x_, b_] := Module[{s}, s = Sign[x]; s*Abs[x]^b]
PlotSQ[a_, b_] := Module[{x1, x2, x3, x}, (
x1 = Numm[Cos[phi], a]*Numm[Sin[theta], b];
x2 = Numm[Sin[phi], a]*Numm[Sin[theta], b];
x3 = Numm[Cos[theta],b];
x = {x1, x2, x3};
ParametricPlot3D[x, {theta, 0, Pi}, {phi, -2 Pi, Pi},
PlotRange -> All, Exclusions -> None, PlotPoints -> 200,
Mesh -> {20, 20}, PlotTheme -> "Classic", Boxed -> False,
ImageSize -> Medium, Axes -> None, PlotStyle -> Opacity[.7]]
)];
If I choose $a=1$ and $b=0.1$, my function should plot a cylinder-like glyph, but in Mathematica I get a hole normal to the z-axis (see picture below):
Entering lower bounds $\varphi = 0$ and $\theta = 0$ results in $<x,y,z>^\top = <0,0,1>^\top $. So there should be at least a point on the z-axis.
Can someone explain this akward behaviour or even have a solution?
TIA
ParametricPlot3D
apparently thinks it's not a good idea to put a point there $\endgroup$