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}
]

```

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