Gary L. Miller

Department of Computer Science

Carnegie Mellon University

Pittsburgh, PA 15213

Department of Computer Science

Carnegie Mellon University

Pittsburgh, PA 15213

Steven E. Pav

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

and

Noel J. Walkington

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

**Abstract**: The classical meshing problem is to
construct a triangulation of a region that conforms to the boundary,
is as coarse as possible, and is constructed from simplices having
bounded aspect ratio. In this paper we present an implementation of a
class of algorithms introduced by Ruppert and establish their
correctness. This class of algorithms solves the meshing problem in
two dimensions, and partiall y solve it in three dimensions. Since
geometric degeneracies frequently cause such algorithms to fail, care
is taken to accommodate these in the proofs.

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