       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}];

```

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