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 > > >