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Cropping a surface to a sphere

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88172] Cropping a surface to a sphere
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Sun, 27 Apr 2008 04:58:05 -0400 (EDT)
  • Organization: University of Bergen

Is there a simple way to crop a surface to a sphere?

For example, consider the surface

ContourPlot3D[
   -x^4*y^2 + x^2*y^4 + x^4*z^2 - y^4*z^2 -
    x^2*z^4 + y^2*z^4 == 1,
   {x, -3, 3}, {y, -3, 3}, {z, -3, 3},
   Mesh -> False]

It is cropped to a cube (the bounding box) by default.  I would like to 
crop it to a sphere of radius 3 (or some other region).

Is there an easy way to do this?  I guess that if there really isn't a 
better way, I could write a polygon cropping function, convert the 
graphic to Normal[] form, and crop/remove each polygon one by one, but I 
was hoping for a simpler solution ... (built-in function or existing 
package).


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