       Intersection of surfaces

• To: mathgroup at smc.vnet.net
• Subject: [mg88513] Intersection of surfaces
• From: Narasimham <mathma18 at hotmail.com>
• Date: Wed, 7 May 2008 07:07:18 -0400 (EDT)

```How to find the space curve formed by intersecting 3D patches in
simple cases like:

TUBE = {.6  Cos[V], 2 U + 3, .6 Sin[V] + 2};
tube = ParametricPlot3D[TUBE, {U, -1.2, .2}, {V, 0, 2 Pi}, PlotPoints -
> {10, 25}]
BOWL = {p Cos[q], p^2/2, p Sin[q]};
bowl = ParametricPlot3D [ BOWL, {p, 1, 2.75}, {q, 0, 2 Pi}, PlotPoints
-> {20, 35}]
Show[bowl, tube]

or in slightly more complicated surface cases like:

terr = ParametricPlot3D[{Cos[u + 1] Cos[v + 2.1], 0.6 + u^2/3,Exp[-v/
4] }, {v, -3, 3}, {u, -3, 3}, PlotPoints -> {45, 30}]
Show[terr, tube]

How to solve for x,y and z from {0.6 Cos[V] == p Cos[q], 3 + 2 U ==
p^2/2, 2 + 0.6 Sin[V] == p Sin[q]} obtaining t as a function of (U,V,p
and q) so as to be able to Show with

ParametricPlot3D[{x[t], y[t], z[t]},{t,tmin,tmax}]?

Regards
Narasimham

```

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