Re: Intersection of surfaces

*To*: mathgroup at smc.vnet.net*Subject*: [mg88692] Re: Intersection of surfaces*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Tue, 13 May 2008 07:07:45 -0400 (EDT)*References*: <fvs2jg$en2$1@smc.vnet.net> <fvudl0$eak$1@smc.vnet.net> <g07grj$8qu$1@smc.vnet.net>

Hi, if you got the same result all is ok. Regards Jens ahallam at iastate.edu wrote: > On May 8, 3:29 am, Jens-Peer Kuska <ku... at informatik.uni-leipzig.de> > wrote: >> Hi, >> >> 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}]; >> >> and >> >> eqn = Eliminate[{TUBE == {x, y, z} // Thread, >> BOWL == {x, y, z} // Thread} // Flatten, {p, q, U}]; >> >> and >> sol = Solve[eqn, {x, y, z}]; >> >> gives >> >> {{y -> 0.02 (100.+ 9. Cos[V]^2 + 60. Sin[V] + 9. Sin[V]^2), >> x -> 0.6 Cos[V], z -> 0.2 (10.+ 3. Sin[V])}} >> >> and >> >> ll = ParametricPlot3D[{x, y, z} /. sol[[1]], {V, 0, 2 Pi}]; >> >> Show[bowl, tube, >> ll /. l_Line :> {AbsoluteThickness[4], RGBColor[1, 0, 0], l}] >> >> show that the result is right. >> >> Regards >> Jens >> >> Narasimham wrote: >>> 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 > > > So saw this post and found if useful for something I was doing. > > But as I looked at the suggested code, I was not sure why thread and > flatten were used in this particular case. > > > So I deleted them one at a time and still got the same answer. > > What is the difference then between. > > > > 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}]; > > eqn = Eliminate[{TUBE == {x, y, z} // Thread, > BOWL == {x, y, z} // Thread} // Flatten, {p, q, U}] > eqn1 = Eliminate[{TUBE == {x, y, z}, BOWL == {x, y, z}} // > Flatten, {p, q, U}] > eqn2 = Eliminate[{TUBE == {x, y, z}, BOWL == {x, y, z}}, {p, q, U}] > > > > sol = Solve[eqn, {x, y, z}] > sol1 = Solve[eqn1, {x, y, z}] > sol2 = Solve[eqn2, {x, y, z}] > > ll = ParametricPlot3D[{x, y, z} /. sol[[1]], {V, 0, 2 Pi}]; > l11 = ParametricPlot3D[{x, y, z} /. sol1[[1]], {V, 0, 2 Pi}]; > l12 = ParametricPlot3D[{x, y, z} /. sol2[[1]], {V, 0, 2 Pi}]; > > > Show[bowl, tube, > ll /. l_Line :> {AbsoluteThickness[4], RGBColor[1, 0, 0], l}] > > Show[bowl, tube, > l11 /. l_Line :> {AbsoluteThickness[4], RGBColor[1, 0, 0], l}] > > Show[bowl, tube, > l12 /. l_Line :> {AbsoluteThickness[4], RGBColor[1, 0, 0], l}] > > > > > > > > >