Date: Sun, 06 Jan 2013 08:53:21 -0800 From: Marc LeBrun <mlb@well.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] stupid 3d graphics problem Message-ID: <CD0EEC01.E717%mlb@well.com> Content-Type: text/plain; charset="US-ASCII"

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="Henry Baker" <hbaker1@pipeline.com> A usual trick in modeling 3D surfaces is to "triangulate" them with triangles that could in principle be hooked together with hinges.

Q. Is it possible to "quadrangulate" a 3D surface with _only_ (planar) quadrilaterals "hinged" together ?

(A quadrilateral has to have 4 non-trivial sides, so no triangles as limiting cases.)

How would we quadrangulate a tetrahedron?

Quadrangulate each triangular face separately. To quadrangulate a face, pick a point in the center and draw a line from it to each side. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com