Re: 3D surface plots - non deletion of data inside undesirable

*To*: mathgroup at smc.vnet.net*Subject*: [mg116361] Re: 3D surface plots - non deletion of data inside undesirable*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Sat, 12 Feb 2011 05:17:19 -0500 (EST)*References*: <201102110919.EAA08103@smc.vnet.net>

Narasimham wrote: > a=2;b=1;c=3;gl={a Cos[ph-th],b Sin[ph-th],c Sin[ph+th]}/Cos[ph+th]; > GL1=ParametricPlot3D[gl,{th,-Pi/4,Pi/4},{ph,-Pi/4,Pi/4},PlotRange- >> {{-3,3},{-3,3},{-3,3}}] > GL2=ParametricPlot3D[gl,{th,-Pi/3,Pi/3},{ph,-Pi/3,Pi/3},PlotRange- >> {{-3,3},{-3,3},{-3,3}}] > Show[GL1,GL2] > > Extended plot limits in GL2 beyond those of GL1 result in 3D plot that > fail to delete undesired spurious tracing/tracking data between points > not lying on the required surface.Like 'pen up' data in earlier > graphing s/w. What leads you to believe it is spurious? > It is OK may be to plot an enclosed solid, but not for a > surface. The difficulty also appeared in earlier Mathematica versions. > Is there then, no work around possible? > > Best Regards > Narasimham Your denominator can vanish in the larger range. And there will be sampled points where it is quite small. So values will be huge. To see this, try eps = .01; GL1 = Table[ gl, {th, -Pi/4 - eps, -Pi/4 + eps, eps/10}, {ph, -Pi/4 - eps, -Pi/4 + eps, eps/10}] So the plotting routine will be interpolating between values quite far apart. Sure, there may be a real pen-up situation e.g. getting points that go toward opposite infinities in a neighborhood of a singularity. But I think your surface will cause trouble even without that happening. Set the plot range a bit larger, as below, to see what I mean. GL1 = ParametricPlot3D[ gl, {th, -Pi/4 - eps, Pi/4 + eps}, {ph, -Pi/4 - eps, Pi/4 + eps}, PlotRange -> {{-10, 10}, {-10, 10}, {-10, 10}}] I don't think what I see is a "pen up" effect. Daniel Lichtblau Wolfram Research

**References**:**3D surface plots - non deletion of data inside undesirable Range***From:*Narasimham <mathma18@hotmail.com>