Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!rutgers!uwvax!tank!eecae!cps3xx!flynn
From: flynn@pixel.cps.msu.edu (Patrick J. Flynn)
Newsgroups: comp.graphics
Subject: Re: 3-D triangulation?
Message-ID: <4129@cps3xx.UUCP>
Date: 11 Aug 89 11:52:38 GMT
References: 
Sender: usenet@cps3xx.UUCP
Organization: Pattern Rec. & Image Processing Lab, CS, Michigan State U.
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In article  spencer@eecs.umich.edu (Spencer W. Thomas) writes:
>Can someone point me to a 3-D "triangulation" algorithm?  What we need
>is something equivalent to the 2-D Delauney triangulation.  I.e., we
>want to create a set of tetrahedra that fill the space within the
>convex hull of a set of randomly distributed 3-D points.
>
>I found reference to 3-D Voronoi diagrams in Preparata and Shamos, but
>not even an algorithm (although there seems to be reference to work
>that may contain an algorithm).  And, in any case, it's not obvious
>how to go from the Voronoi diagram to a triangulation.
>
>Reference to an accessible publication would be sufficient.

In 3D vision, work has been done by J.D. Boissonnat and colleagues at INRIA.

Boissonnat, ``Representation of Objects by Triangulating Points in 3D
Space,'' Proc. 6ICPR, 830-832, 1982.

Boissonnat, ``Representing 2D and 3D Shapes with the Delaunay triangulation,''
Proc. 7ICPR, 745-748, 1984.

O'Rourke also did some early work.

O'Rourke, ``Polyhedra of minimal area as 3D object models,'' Proc. 7th
IJCAI, 664-666, 1981.

Also see

De Floriani, ``Surface representations based on triangular grids,''
The Visual Computer, v.3, 27-50, 1987. (Pub. by Springer-Verlag)

Choi et al., ``Triangulation of Scattered Data in 3D Space,'' Comp. Aided
Des. v. 20, n. 5, 239-248, 1988. (Pub. by Butterworths)

Avis and ElGindy, ``Triangulating Point Sets in Space,'' Disc. Comput.
Geom., v.2, 99-111, 1987. (Pub. by Springer-Verlag)
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Patrick Flynn, CS, Mich. State Univ. -- flynn@cps.msu.edu -- uunet!frith!flynn

"                 " -- Marcel Marceau