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Re: Slow plotting of reflected parametric "butterflies"

• To: mathgroup at smc.vnet.net
• Subject: [mg124447] Re: Slow plotting of reflected parametric "butterflies"
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 20 Jan 2012 01:48:36 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201191013.FAA03742@smc.vnet.net>
• Reply-to: murray at math.umass.edu

I don't have any suggestions, at least yet, on speeding up your code. 
However, you should avoid naming things "C" and "D", since those names 
stand for objects already built into Mathematica. In fact, didn't you 
notice that running your code gives Shadowing warning messages?

On 1/19/12 5:13 AM, Chris Young wrote:
> I'm wondering if there's anyway I can speed this up. It's basically
> just some sections of a parabolic hyperboloid, with the outer edges
> curves. I'm porting it from another program, where it ran much faster.
> I had to chop it up into parts for that program, but maybe this isn't
> the best way to do it in Mathematica.
>
> http://home.comcast.net/~cy56/Mma/ReflectedButterflies.nb
> http://home.comcast.net/~cy56/Mma/ReflectedButterfliesPic.png
>
> Chris Young
> cy56 at comcast.net
>
>
> \[HorizontalLine]CurvedButterfly[A_, B_, C_, D_, u_,
>    v_, \[ScriptC]_] :=
>
>   Table[
>      (A + B + C + D)/4 +
>       j Sqrt[1 - \[ScriptC] v] u/2 ((A + C)/2 - (B + D)/2) +
>       k u/2 v (((C + D)/2 + j u (C - D)/2) - ((A + B)/2 +
>            j u (A - B)/2)),
>      {j, {-1, 1}}, {k, {-1, 1}}
>      ] // FullSimplify  // Flatten[#, 1]&
> Putting Butterfly into a Manipulate module:
> Manipulate[
>   With[
>    {
>     A = {Ax, Ay, Az},
>     B = {Bx, By, Bz},
>     C = {Cx, Cy, Cz},
>     D = {Dx, Dy, Dz}
>     },
>    Show[
>     ParametricPlot3D[
>      Table[
>       ( {
>            {\[ScriptI], 0, 0},
>            {0, \[ScriptJ], 0},
>            {0, 0, \[ScriptK]}
>           } ). #&   /@  \[HorizontalLine]CurvedButterfly[A, B, C, D, u,
>          v, wingCurve],
>       {\[ScriptI], {-1, 1}}, {\[ScriptJ], {-1, 1}}, {\[ScriptK], {-1,
>         1}}],
>      {u, 0, 1}, {v, 0, 1},
>
>      PlotRange ->  2.5,
>      Lighting ->  "Neutral",
>      ColorFunctionScaling ->  False,
>      ColorFunction ->  ({x, y, z, u, v} \[Function]
>         Hue[\[LeftFloor]5 v\[RightFloor]/10]),
>      Mesh ->  None,
>      PlotPoints ->  plotPts,
>      AxesLabel ->  {"x", "y", "z"}
>      ],
>     Graphics3D[
>      {
>       With[{pts = {A, B, C, D}},
>        Table[{Hue[(k - 1)/4], Sphere[pts[[k]], ptRad]}, {k, 1, 4}]
>        ]
>       }
>      ]
>     ]
>    ],
>   {{Ax, 1.25}, -2.5, 2.5, 0.03125},
>   {{Ay, 2}, -2.5, 2.5, 0.03125},
>   {{Az, 0.75}, -2.5, 2.5, 0.03125},
>
>   {{Bx, 1.75}, -2.5, 2.5, 0.03125},
>   {{By, 0.5}, -2.5, 2.5, 0.03125},
>   {{Bz, 0.125}, -2.5, 2.5, 0.03125},
>
>   {{Cx, 0.5}, -2.5, 2.5, 0.03125},
>   {{Cy, 0.375}, -2.5, 2.5, 0.03125},
>   {{Cz, 0.25}, -2.5, 2.5, 0.03125},
>
>   {{Dx, 0.375}, -2.5, 2.5, 0.03125},
>   {{Dy, 0.125}, -2.5, 2.5, 0.03125},
>   {{Dz, 1.25}, -2.5, 2.5, 0.03125},
>
>   {{plotPts, 4}, 2, 30, 1},
>   {{ptRad, 0.1}, 0, 0.3},
>   {{wingCurve, 0}, 0, 1}
>   ]
>
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • Slow plotting of reflected parametric "butterflies"
    • From: Chris Young <cy56@comcast.net>