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Re: a question about intersection curve.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59846] Re: a question about intersection curve.
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 24 Aug 2005 06:30:12 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <deeort$3tv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

the simplest form would be to use the implicit 
equations
because than CSG opartiosn are easy

Ploting the contour surface
of

f[x_,y_,z_]:=If[(x^2 + y^2 + (z + 1)^2 < 1) && ((x 
+ 1)^2 + y^2 + z^2 < 1), 1, 0]

should do that otherwise you have to clip the 
polygons of one sphere
against the implicit form of the other sphere but
than you will get slits (cracks) alon the 
intersection curve.

Regards
  Jens

"Zhou Jiang" <jiangzhou_yz at yahoo.com> schrieb im 
Newsbeitrag news:deeort$3tv$1 at smc.vnet.net...
|
| Hi, Dear Group,
| I want to plot the intersection curve between 
two semispheres. The two semispheres are descriped 
by the following equations,
|
| x^2+y^2+(z+1)^2=1
| and
| (x+1)^2+y^2+z^2=1
|
| I am only interested in the halves that can 
intersect. I plot these two semi-spheres as
|
| f1=Sin[theta] Cos[phi];
| f2=Sin[theta] Sin[phi];
| f3=-1+Cos[theta];
| s1=ParametricPlot3D[{f1,f2,f3},{theta, -Pi/2, 
Pi/2}, {phi, 0, Pi}];
|
|
| f1=-1+Cos[theta];
| f2=Sin[theta] Cos[phi];
| f3=Sin[theta] Sin[phi];
| s2=ParametricPlot3D[{f1,f2,f3}, {theta, -Pi/2, 
Pi/2}, {phi, 0, Pi}];
|
| Show[s1,s2];
|
| I can see the intersection curve between these 
two spheres. But I do not know how to plot the 
intersection curve directly. Can anyone give me 
some help?
| Thanks a lot.
|
| 



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