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Intersection of 2D Surfaces in 3D

• To: mathgroup at smc.vnet.net
• Subject: [mg86892] Intersection of 2D Surfaces in 3D
• From: Narasimham <mathma18 at hotmail.com>
• Date: Tue, 25 Mar 2008 01:17:19 -0500 (EST)

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

• Follow-Ups:
  • Re: Intersection of 2D Surfaces in 3D
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Intersection of 2D Surfaces in 3D
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>