Re: Re:ParametricPlot3D

*To*: mathgroup at smc.vnet.net*Subject*: [mg18080] Re: [mg17695] Re:ParametricPlot3D*From*: Blimbaum Jerry DLPC <BlimbaumJE at ncsc.navy.mil>*Date*: Tue, 15 Jun 1999 01:43:36 -0400*Delivery-date*: Tue Jun 15 03:16:59 1999*Sender*: owner-wri-mathgroup at wolfram.com

E. Goris wrote (basically) " I have a problem using ParametricPlot3D. Suppose I have the following: ParametricPlot3D[{f1(x,y),f2(x,y),f3(x,y)},{x,-10,10},{y,-10,10}] and I want to tell Mathematica to take more space between the sample points as (x,y) gets further away from the origin and less if (x,y) gets closer to the origin." One solution given was, since the coordinate mesh chosen by ParametricPlot3D is equidistant you have to the refinement yourself, namely: X[x_]:=x^2; Y[x_]:=y^2; ParametricPlot3D[{f1(X[x],Y[y]),f2(X[x],Y[y]),f3(X[x],Y[y])},{x,-10,10},{y,- 10,10}]] I am confused on several accounts, however, both by the question and the answer. First, in the Mathematica book, ParametricPlot3D is of the form ParametricPlot3D[x[t] y[t] z[t], {t,min,max}], x, y, z are specified by limits on a single variable (not x and y), namely t. So does the questionner really want ParametricPlot3D or Plot3D?? Here is sample code for what I think would be a solution for a Plot3D example. I have broken up the x, y plane into an inner and 4 outer sections. p1= Block[{$DisplayFunction =Identity}, Plot3D[Cos[x y],{x,-2 Pi,2 Pi},{y,-2 Pi,2 Pi},PlotPoints->20]]; p2= Block[{$DisplayFunction =Identity}, Plot3D[Cos[x y],{x,-2 Pi,-8 Pi},{y,-8 Pi,8 Pi},PlotPoints->10]]; p3= Block[{$DisplayFunction =Identity}, Plot3D[Cos[x y],{x,2 Pi,8 Pi},{y,-8 Pi,8 Pi},PlotPoints->10]]; p4= Block[{$DisplayFunction =Identity}, Plot3D[Cos[x y],{x,-2 Pi,2 Pi},{y,-2 Pi,8 Pi},PlotPoints->10]]; p5= Block[{$DisplayFunction =Identity}, Plot3D[Cos[x y],{x,-2 Pi,2 Pi},{y,2 Pi,8 Pi},PlotPoints->10]]; Show[p1,p2,p3,p4,p5]; Secondly, w.r.t. the response, suppose f[x_}:=Sin[x]. Now if you Plot[f[x^2],{x,-10,10}]] vs. Plot[f[x],{x,-10,10}] you dont get the same result. thanks. Jerry Blimbaum NSCW Panama City, Fl