A Condition Guaranteeing the Existence of Higher-Dimensional Constrained Delaunay Triangulations

http://www.cs.cmu.edu/~quake-papers/cdt.ps, 1998

MESHING
RESEARCH
CORNER

School of Computer Science
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
Email:jrs@cs.cmu.edu

Abstract
Let X be a complex of vertices and piecewise linear constraining facets embedded in Ed. X has a d-dimensional constrained Delaunay triangulation if each k- dimensional constraining facet in X with k < d ^ 2 is a union of strongly Delaunay k-simplices. A simplex is strongly Delaunay if its vertices are in X and there exists a sphere that passes through its vertices but passes through and encloses no other vertex.

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