Re: Slow plotting of reflected parametric "butterflies"

*To*: mathgroup at smc.vnet.net*Subject*: [mg124458] Re: Slow plotting of reflected parametric "butterflies"*From*: Christopher Young <cy56 at comcast.net>*Date*: Fri, 20 Jan 2012 01:52:25 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201201191013.FAA03742@smc.vnet.net> <4F184BFC.4030104@math.umass.edu>

On Jan 19, 2012, at 11:59 AM, Murray Eisenberg wrote: > 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? I know I shouldn't name globals "C" or "D", and I try to avoid it, but isn't Mathematica now sophisticated enough to allow localized variables "C" and "D" as long as they don't have the same form as the functions? I.e., it allows "overloading" of those symbols. At any rate, I'll see if avoiding that speeds things up. Meanwhile, my guess is that using lists of functions in ParametricPlot3D is the main source of the slow-down, so I'm rewriting the curves as regular one-item functions. > > 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 Chris Young cy56 at comcast.net

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