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Intersection of two surfaces in 3D

• To: mathgroup at smc.vnet.net
• Subject: [mg52822] Intersection of two surfaces in 3D
• From: "Narasimham" <mathma18 at hotmail.com>
• Date: Tue, 14 Dec 2004 05:59:09 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

There are threads currently on sci.math  on this topic. How do we find
space intersection curve of two  parameterized surfaces? One needs to
solve for two unknown functions f1(t1,t2)=0 and f2(s1,s2)=0 to print
out/output coordinates of intersection. I do believe it is within the
capability of Mathematica, at least when surfaces are algebraically
generatable. An example/approach considered is:

Clear[x,y,z,t1,t2,s1,s2];
x1=4*t2* Cos[t1]; y1=4Sin[t1]; z1=3t2;
x2=s2 Sin[s1];y2=s2 Cos[s1];z2=(s2^2/4);
pp1=ParametricPlot3D[{x1,y1,z1},{t1,0,2 Pi},{t2,0,1}];
pp2=ParametricPlot3D[{x2,y2,z2},{s1,0,2 Pi},{s2,0,4}];
Show[pp1,pp2];
S1={x-x1,y-y1,z-z1}; S2={x-x2,y-y2,z-z2};
NSolve[Join[S1,S2],{x,y,z},{t1,t2,s1,s2}];

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