Re: Intersection of 2D Surfaces in 3D

• To: mathgroup at smc.vnet.net
• Subject: [mg86896] Re: [mg86892] Intersection of 2D Surfaces in 3D
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 26 Mar 2008 04:46:42 -0500 (EST)
• References: <200803250617.BAA10628@smc.vnet.net>

On 25 Mar 2008, at 07:17, Narasimham wrote:
> Following is an example (slightly altered) given in intersection of 2-
> D curves with one real root.
>
> c1  =  {x - (t^2 - 1), y - (s^3 + s - 4) };
> c2  =  {x - (s^2 + s + 5),  y - (t^2 + 7 t - 2) };
>
> It uses NSolve[Join[c1, c2], {x, y}, {s, t}]  for supplying real roots
> of 2D curves in 2D itself.
>
> Next, how to generalize further to Solve and find real intersection
> curves of two parameter surfaces in 3-D by extending the same
> Mathematica Join procedure?
>
> And how to Show the one parameter 3D space curve of intersection so
> obtained ? The following attempt of course fails.
>
> c3 = {x - (t^2 - 1), y - (s^3 + s - 4), z -  (t  + s)};
> c4 = {x - (s^2 + s + 5), y - (t^2 + 7 t - 2),z  -( t + s^2/2)};
> NSolve[Join[c3, c4], {x, y, z}, {t,s}];
>
> FindRoot also was not successful.
>
> Regards,
> Narasimham
>
>

Your two surfaces do not interesect:

In[58]:= GroebnerBasis[Join[c3, c4], {x, y, s, t}]
Out[58]= {1}

So what do you mena by "fails"? What would constitute a "success" here?

Andrzek Kozlowski

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