       Re: Parametric surface

• To: mathgroup at smc.vnet.net
• Subject: [mg35261] Re: [mg35241] Parametric surface
• From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
• Date: Fri, 5 Jul 2002 02:19:31 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```First of all this situation defines at best one surface, not two. It may
be possible to obtain a graph of this surface but it depends very much
on what the equations are. The best approach I can think of has been
described on this list on on several occasions by Carl Woll: it is based
on turning the equations into a system of partial differential equations
and then using NDSolve to obtain  solutions in terms of interpolating
functions. One has to guess suitable initial conditions and the range of
values of a and b you want to use in your plot. Finally, Mathematica
must be able to solve these equations, whihc is by no means guaranteed.
Once that has been done one can get the graph using ParametricPlot3D. I
think there is little more that can be said without knowing what the
equations are.

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/

On Wednesday, July 3, 2002, at 06:15  PM, Jun Lin wrote:

> Given functions F=F(x,y;a,b) and G=G(x,y;a,b), where x and y are
> coordinates and a and b are parameters. So,
>
>  F(x,y;a,b)=0,
> {
>  G(x,y;a,b)=0
>
> defines two 3D surfaces:
>
>  x=x(a,b),
> {
>  y=y(a,b).
>
> Suppose the functions F and G are implicit and transcendental, so they
> are cumbersome to be solved directly to give x=x(a,b) and y=y(a,b). My
> question is whether it is possible to draw these two surfaces from
> relations F=0 and G=0.
>
> I appreciate with your help!
>
> Jun Lin
>
>
>

```

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