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