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MathGroup Archive 2002

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Re: Parametric surface

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35264] Re: [mg35241] Parametric surface
  • From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
  • Date: Fri, 5 Jul 2002 02:20:10 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Yes, you are right of course. I was confused by your use of the phrase 
"parametric surface" and had inm mind the system of three equations:

F(x,y,z,a,b)==0,G(x,y,z,a,b)==0,H(x,y,z,a,b)==0

meaning three equations with two parameters. Under favorable conditions 
this gives a "parametric surface" that may be found by the method I 
described. In principle the method may also work in your cases. Of 
course your
your two surfaces are not given by parametric equations, so even if you 
could get interpolating functions for them you would still need to use 
CountourPlot3D function form the Graphics`ContourPlot3D package, which 
does nto work well. It might be necessary to use something like J.P. 
Kuska's MathGL3d, which has a much better function of this kind 
(MVContourPlot3D).

Andrzej


On Thursday, July 4, 2002, at 01:43  AM, Jun Lin wrote:

> Thanks for the message. Solving F(x,y;a,b)=0 and
> G(x,y;a,b)=0 simultaniously for x and y, in principle,
> gives x=fx(a,b) and y=fy(a,b). x=x(a,b) defines one
> surface, and y=y(a,b) defines another one. So, we have
> two surfaces by setting: f(x,a,b)=x-fx(a,b)=0 and
> g(y,a,b)=y-fy(a,b)=0, respectively.
>
> Sincerely,
>
> Jun Lin
>
> --- Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
> wrote:
>> 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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