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Summary: COMPACT REPRESENTATIONS OF SIMPLICIAL
MESHES IN TWO AND THREE DIMENSIONS
Daniel K. Blandford
dkb1@cs.cmu.edu
Guy E. Blelloch
blelloch@cs.cmu.edu
David E. Cardoze
cardoze@cs.cmu.edu
Clemens Kadow
kadow@cmu.edu
Carnegie Mellon University, Pittsburgh, PA, U.S.A.
ABSTRACT
We describe data structures for representing simplicial meshes compactly while supporting online queries and updates
eÆciently. Our representation requires about a factor of ve less memory than the most eÆcient standard represen-
tations of triangular or tetrahedral meshes, while eÆciently supporting traversal among simplices, storing data on
simplices, and insertion and deletion of simplices.
Our implementation of the data structures uses about 5 bytes/triangle in two dimensions (2D) and 7.5
bytes/tetrahedron in three dimensions (3D). We use the representations to implement 2D and 3D incremental algo-
rithms for generating a Delaunay mesh. The 3D algorithm can generate 100 Million tetrahedrons with 1 Gbyte of
memory, including the space for the coordinates and all data used by the algorithm. The runtime of the algorithm is
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