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
- References:
- Intersection of 2D Surfaces in 3D
- From: Narasimham <mathma18@hotmail.com>
- Intersection of 2D Surfaces in 3D