A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations

1 January 1998

proceedings article
Published by Association for Computing Machinery (ACM)

p. 76-85
https://doi.org/10.1145/276884.276893

Abstract

Let be a complex of vertices and piecewise linear constraining facets embedded in . Say that a simplex is strongly Delaunay if its vertices are in and there exists a sphere that passes through its vertices but passes through and encloses no other vertex. Then has a -dimensional constrained Delaunay triangulation if each -dimensional constraining facet in with is a union of strongly Delaunay -simplices. This theorem is especially useful in for forming tetrahe- dralizations that respect specified planar facets. If the bounding segments of these facets are subdivided so that the subsegments are strongly Delaunay, then a constrained tetrahedralization exists. Hence, fewer vertices are needed than in the most common practice in the literature, wherein additional vertices are inserted in the rel- ative interiors of facets to form a conforming (but unconstrained) Delaunay tetrahedralization.

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