# Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

# 3D Conforming Delaunay Triangulation

• Siu-Wing Cheng
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_716-1

## Years and Authors of Summarized Original Work

1998; Shewchuk

2004; Cohen-Steiner, de Verdière, Yvinec

2006; Cheng, Poon

2012; Cheng, Dey, Shewchuk

## Problem Definition

A three-dimensional domain with piecewise linear boundary elements can be represented as a piecewise linear complex (PLC) of linear cells – vertices, edges, polygons, and polyhedra – that satisfy the following properties [ 4]. First, no vertex lies in the interior of an edge and every two edges are interior-disjoint. Second, the boundary of a polygon or polyhedra are union of cells in the PLC. Third, if two cells f and g intersect, the intersection is a union of cells in the PLC with dimensions lower than f or g. A triangulation of an input PLC is conformingif every edge and polygon appear as a union of segments and triangles in the triangulation. Additional Steiner vertices are often necessary. The 3D conforming Delaunay triangulation problem is to construct a triangulation of an input PLC that is both conforming and...

## Keywords

Delaunay refinement Protecting ball Radius-edge ratio Weighted Delaunay triangulation
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1. 1.
Cheng S-W, Dey TK (2003) Quality meshing with weighted Delaunay refinement. SIAM J Comput 33(1):69–93
2. 2.
Cheng S-W, Poon S-H (2006) Three-dimensional Delaunay mesh generation. Discret Comput Geom 36(3):419–456; conference version in Proceedings of the ACM-SIAM symposium on discrete algorithms (2003)Google Scholar
3. 3.
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4. 4.
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5. 5.
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