Reducing number of triangles in ParametricPlot3D STL file?

[bryanlettner]

r = 7;
R = 19;
ParametricPlot3D[{
{(u^Cos[(r t)/R]) Cos[t], (u^Cos[(r t)/R]) Sin[t], (-Log[u] Sin[(r t)/R])}
}, {t, 0, 2 R Pi}, {u, 1, E}, MaxRecursion → 0, Mesh-> All, PlotPoints → 300, PlotStyle → Thickness[0.02]]

The rendered object has far too many triangles. And to get a good rendering, PlotPoints must be much higher than 300, which will in turn create even more extra triangles. I’m exporting the part as an .stl for 3d printing. I prefer to solve this issue at the rendering and export stage, rather than reducing the number of triangles afterwards. I’ve looked into Mesh and MeshFunctions options, with no luck so far. Thanks in advance!
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=florp.jpg&userId=167076

[sghuisman (Sander Huisman)]

So you want high plotpoints but low triangles? Isn’t that a contradiction?

[bryanlettner]

I don’t think it is a contradiction. PlotPoints determines how many sample points to use to generate the plot, not how finely to divide up the mesh. In the above plot, we have redundant triangles. It can be reduced from 359,996 triangles to <50,000 without losing any detail:

reduces to

My issue is that the plot renders too precisely for how accurate it is. It is an overly precise depiction of a not-very accurate plot.

vs.

Of course we can get the more accurate plot by increasing PlotPoints, but it still gives an overly precise plot (far more triangles than necessary). This results in long computation times and huge files that are too big to open with my mesh manipulation software. I hope this clarifies.

[ghurst (Greg Hurst)]

You can choose to sample many points as t varies and few points as u varies. Choosing PlotPoints -> {2000, 3} gives good detail:

r = 7; R = 19;
ParametricPlot3D[{{(u^Cos[(r t)/R]) Cos[t], (u^Cos[(r t)/R]) Sin[t], (-Log[u] Sin[(r t)/R])}}, 
  {t, 0, 2 R Pi}, {u, 1, E}, MaxRecursion -> 0, Mesh -> All, PlotPoints -> {2000, 3}, PlotStyle -> Thickness[0.02]]

There are roughly 24000 triangles in this plot:

MeshCellCount[DiscretizeGraphics[%]]
(* {12000, 35994, 23996} *)

[bryanlettner]

This solves the issue 100%! Thank you so much.

[Vitaliyk (Vitaliy Kaurov)]

Also use PlotTheme → “ThickSurface” for a better visualization:

r=7;R=19;
ParametricPlot3D[{
	{(u^Cos[(r t)/R]) Cos[t],(u^Cos[(r t)/R]) Sin[t],(-Log[u] Sin[(r t)/R])}},
	{t,0,2 R Pi},{u,1,E},
	PlotPoints->500,
	PlotTheme->"ThickSurface"]