Thickness in ParametricPlot3D

Questions
,
1

How is the thickness defined in ParametricPlot3D? For 2D plots, the thickness “is given as a fraction of the horizontal plot range,” but how does that work in 3D for the following example? Also, it doesn’t seem that AbsoluteThickness works.

Moebius[R_, a_, b_] := {(R + a Cos[b/2]) Cos[b], (R + a Cos[b/2]) Sin[b], a Sin[b/2]}

MBand = ParametricPlot3D[Moebius[5, a, b], {a, -1, 1}, {b, 0, 2 Pi},
Mesh → None, PlotPoints → {20, 100}, MaxRecursion → 0,
PlotRange → All,
PlotStyle → Directive[{Thickness[1], Opacity[0.5]}]]

2

Hi,

stackexchange link

Moebius[R_, a_, b_] := {(R + a Cos[b/2]) Cos[b], (R + a Cos[b/2]) Sin[b], a Sin[b/2]}
MBand = ParametricPlot3D[
	Moebius[5, a, b], {a, -1, 1}, {b, 0, 2 Pi}, Mesh -> None, PlotPoints -> {20, 100}, MaxRecursion -> 0, PlotRange -> All, 
	PlotStyle -> {Thickness[.2],Opacity[0.5]} ]

I.M.

3

Thanks Ivan. I’d happened on the link you sent as well. My question though is whether the thickness in 3D is defined relative to a plot range or is rather a nondimensional height corresponding to a particular number of units.

Regards,

Russell