Re: Intersection of 2D Surfaces in 3D

*To*: mathgroup at smc.vnet.net*Subject*: [mg86933] Re: [mg86892] Intersection of 2D Surfaces in 3D*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 26 Mar 2008 04:56:15 -0500 (EST)*References*: <200803250617.BAA10628@smc.vnet.net> <46E32647-0187-4DF7-B920-62BBF4E39C61@mimuw.edu.pl>

On 25 Mar 2008, at 08:11, Andrzej Kozlowski wrote: > > 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 Actually, it should have been In[60]:= GroebnerBasis[Join[c3, c4], {x, y, z}, {s, t}] Out[60]= {1} But they still do not intersect. Andrzej

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