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>