[comp.graphics] Triangularization

garry@ithaca.uucp (Garry Wiegand) (04/24/91)

I am looking for references on the subject of transforming an
arbitrary polyhedron or polyhedral mesh into a "nice" 6-connected
triangular mesh, by introducing a minimal number (or near-minimal)
number of extra (redundant) edges and vertices and perhaps a
zero-width hole or two. 

The construct, if I had it, I think would lend itself to some
pleasant graphics rendering optimizations.

It seems like work must already have been done on this subject,
among the triangle-strip people or the finite-element people, or
even the mathematicians, but so far I'm totally spinning my wheels
in the library trying to find it. Help would be appreciated - a
recent reference or two to get me started on the right track is all
I need.
 
(If there's related code on-line somewhere, far be it from me to
turn that down either.) 

Thanks. Followups to comp.graphics.

Garry Wiegand --- Ithaca Software, Alameda, California
...!uunet!ithaca!garry, 415 523-5900 x219

rodent@netcom.COM (Ben Discoe) (04/25/91)

garry@ithaca.uucp (Garry Wiegand) writes:

>ctransforming an
>arbitrary polyhedron or polyhedral mesh into a "nice" 6-connected
>triangular mesh, by introducing a minimal number (or near-minimal)
>number of extra (redundant) edges and vertices and perhaps a
>zero-width hole or two. 

If I understand this correctly, you simply want to to subdivide
your triangular mesh into smaller triangles?  This isn't too hard -
the only slightly tricky part is being sure to eliminate redundant
edges.  If anyone wants the code, it's part of a 3D editor of mine
that you're welcome to.  The user-interface code is meant to run on
the Amiga, although the code is pretty generic.

>even the mathematicians, but so far I'm totally spinning my wheels
>in the library trying to find it.

I had the same trouble when I wanted this stuff, which is why I wrote it.
(if I understand your intent correctly)

One possible difficulty in using my code would be if you use a different
representation for your mesh.  I use the tried-and-true list of points
plus list of face vertices.

>Garry Wiegand --- Ithaca Software, Alameda, California
>...!uunet!ithaca!garry, 415 523-5900 x219

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Ben Discoe in San Jose.  Take my advice - you DON'T want to live here.