       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

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
```

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