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Ragged region boundary

• To: mathgroup at smc.vnet.net
• Subject: [mg123240] Ragged region boundary
• From: Chris Young <cy56 at comcast.net>
• Date: Mon, 28 Nov 2011 05:54:41 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Would anyone have any tips on how to get a better region boundary here?
Maybe via CountourPlot3D?

Actually, if I use PlotPoints -> 200, it's OK, but it's extremely slow
to plot then, of course.

Also, I don't want the horizontal "boundary" line at the equator. Can't
see why this is considered a boundary line anyway.

http://home.comcast.net/~cy56/RegionBoundary.nb

http://home.comcast.net/~cy56/RegionBoundary.png


Manipulate[
 ParametricPlot3D[
  torus[c, a, u, v], {u, 0, 2 \[Pi]}, {v, 0, 2 \[Pi]},
  MeshFunctions -> {{x, y, z, \[Theta], \[Phi]} \[Function]
     z + Tan[tilt] x},
  RegionFunction -> ({x, y, z, \[Theta], \[Phi]} \[Function]
     z <= -Tan[tilt] x),
  Mesh -> mesh,
  MeshStyle -> {Lighter[Yellow], Tube[tubeR]},
  BoundaryStyle -> {Lighter[Red], Tube[tubeR]},
  PlotStyle -> {Orange, Opacity[opac]},
  PlotPoints -> plotPts,
  Axes -> True,
  AxesLabel -> {"x", "y", "z"},
  PlotRange -> {{-4, 4}, {-4, 4}, {-3, 3}},
  BoxRatios -> {8, 8, 6},
  ViewPoint ->
   {
    viewR Cos[view\[Theta]] Sin[view\[Phi]],
    viewR Sin[view\[Theta]] Sin[view\[Phi]],
    viewR Cos[view\[Phi]]
    },
  PerformanceGoal -> "Quality"
  ],

 {{c, 3}, 0, 4},
 {{a, 1}, 0, 3},
 {{sphereR, 0.1}, 0, 0.5},
 {{tubeR, 0.05}, 0, 0.5},
 {{opac, 0.5}, 0, 1},
 {{mesh, 1}, 0, 16, 1},
 {{tilt, N[ArcSin[a/c]]}, 0, \[Pi]/2, \[Pi]/36},
 {{plotPts, 50}, 0, 100, 5},
 {{viewR, 100}, 0, 100, 5},
 {{view\[Theta], \[Pi]/2}, 0, 2 \[Pi], \[Pi]/36},
 {{view\[Phi], \[Pi]/2}, 0, \[Pi], \[Pi]/36}
 ]