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

*To*: mathgroup at smc.vnet.net*Subject*: [mg116460] Re: 3D surface plots - non deletion of data inside undesirable*From*: Narasimham <mathma18 at hotmail.com>*Date*: Wed, 16 Feb 2011 04:34:57 -0500 (EST)*References*: <201102110919.EAA08103@smc.vnet.net> <ij5mnb$jgq$1@smc.vnet.net>

On Feb 12, 3:17 pm, Daniel Lichtblau <d... at wolfram.com> wrote: > 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 undesiredspurioustracing/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 isspurious? > > > 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 Thanks. GL3=ParametricPlot3D[gl,{th,-Pi,Pi},{ph,-Pi/4,Pi/4},PlotRange->{{-3,3}, {-3,3},{-3,3}}] ep=1.73205;hb={Cos[t],Sin[t]}/(1-ep Cos[t]); HB=ParametricPlot[hb,{t,0,2Pi},PlotRange->{{-3,3},{-3,3}}] In 2-D plots we see a neat pair of asymptotic lines between the two branches of a hyperbola where all the infinitely remote points are effectively removed. In 3-D by the same token we can't see a single neat asymptotic cone, but what appear as remnants of a clutter of packed planes.It may be tougher to handle the 3-D though. Regards, Narasimham

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