Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Ragged region boundary

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123269] Re: Ragged region boundary
  • From: Chris Young <cy56 at comcast.net>
  • Date: Tue, 29 Nov 2011 08:06:06 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <javpho$jct$1@smc.vnet.net> <jb2i3g$5hk$1@smc.vnet.net>

This looks like a great idea. Thanks very much. Unfortunately, I can't 
seem to find a C compiler on my Mac. Maybe Apple is charging for the 
development package now, I don't know. I'll look into it.

In[80]:= Needs["CCompilerDriver`"]
In[86]:= CCompilers[]
Out[86]= {}

On 2011-11-29 12:10:24 +0000, Patrick Scheibe said:

> 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}
>  ]




  • Prev by Date: Point light source penetrating through surfaces
  • Next by Date: Ploting a transformation of a set
  • Previous by thread: Re: Ragged region boundary
  • Next by thread: Re: Ragged region boundary