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Extrude along a curve?

Suppose you have a curve in space, and you wish to thicken it so that the cross section is a regular n-gon. There are many ways to do this, but the input below provides a really simple approach. Unfortunately, the PlotPoints setting inside Tube is colored red. It is not documented or supported, but it works quite nicely provided the tube radius doesn't get too big.

ParametricPlot3D[{Cos[x], Sin[x], 0}, {x, 0, \[Pi]}, 
  PlotStyle -> Tube[.5, PlotPoints -> 6], 
  PlotRange -> All] // DiscretizeGraphics

enter image description here

Does anyone know if there is a better way to accomplish this? I'm aware of more comprehensive approaches to extruding along a curve, e.g., using FrenetSerretSystem or Bishop Frames for differentiable curves, such as those shown at https://mathematica.stackexchange.com/questions/3051/extruding-along-a-path/

I'm just wondering if there is a simple, robust method for getting Tube to do this.

POSTED BY: Bruce Torrence
2 Replies

I'm looking for an alternative to the PlotPoints->6 option within Tube, because it is an undocumented option that may cease to work in future versions of Mathematica. If someone can tell me that this option will continue to work, I am happy to accept the sample code I submitted. But if there is/will be a different syntax that will accomplish the same result, I would love to know what it is.

POSTED BY: Bruce Torrence
Anonymous User
Anonymous User
Posted 6 years ago

what would you consider simpler? if the form above is the given and the problem is to transform it to an easier form, could you show us the easier form which is your goal?

POSTED BY: Anonymous User
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