Re: Ragged region boundary
- To: mathgroup at smc.vnet.net
- Subject: [mg123439] Re: Ragged region boundary
- From: Christopher Young <cy56 at comcast.net>
- Date: Wed, 7 Dec 2011 06:15:40 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201111281054.FAA19792@smc.vnet.net> <1322557751.1684.47.camel@warp>
Thanks very much, that sped things up quite a bit.
On Nov 29, 2011, at 4:09 AM, Patrick Scheibe wrote:
> Hi,
>
> first you could compile your torus-function and compare the runtimes
>
> torus[c_, a_, u_, v_] := {(c + a Cos[v]) Cos[u], (c + a Cos[v]) Sin[u],
> a Sin[v]};
> torusCompiled =
> Compile[{{c, _Real}, {a, _Real}, {u, _Real}, {v, _Real}},
> {(c + a Cos[v]) Cos[u], (c + a Cos[v]) Sin[u], a Sin[v]},
> CompilationTarget -> "C"];
>
> In[38]:= First[
> AbsoluteTiming[Do[#[1.3, 0.3, 2.3, 4.5], {1000000}]]] & /@ {torus,
> torusCompiled}
>
> Out[38]= {5.190318, 0.863473}
>
> and then you could set MaxRecursion to a higher value. Since then the
> runtime drops further, you could use ControlActive to use a very fast
> version, when you use the sliders. See the code at the end.
>
> Your "equator" is not the only unwanted boundary, but you don't see the
> other one. These are the lines where your PlotRange ends. The doc to
> BoundaryStyle says
>
> "For 3D graphics, it is also used at the boundary of regions defined by
> PlotRange."
>
> So these lines are at 0 and 2Pi for both of your variables. I have no
> idea how to turn them off.
>
> Cheers
> Patrick
>
> Manipulate[
> ParametricPlot3D[
> torusCompiled[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,
> MaxRecursion -> ControlActive[0, 5],
> MeshStyle -> {Lighter[Yellow], Tube[tubeR]},
> BoundaryStyle -> {Lighter[Red], Tube[tubeR]},
> PlotStyle -> {Orange, Opacity[opac]},
> PlotPoints -> ControlActive[10, 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, 0}, 0, 16, 1},
> {{tilt, N[ArcSin[a/c]]}, 0, \[Pi]/2, \[Pi]/36},
> {{plotPts, 50}, 0, 200, 5},
> {{viewR, 100}, 0, 100, 5},
> {{view\[Theta], \[Pi]/2}, 0, 2 \[Pi], \[Pi]/36},
> {{view\[Phi], \[Pi]/2}, 0, \[Pi], \[Pi]/36}
> ]
>
> On Mon, 2011-11-28 at 05:54 -0500, Chris Young wrote:
>> 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}
>> ]
>>
>>
>
>
Chris Young
cy56 at comcast.net
