Mesh generation for domains with small angles

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Abstract
Nonmanifold geometric domains having small angles present spe- cial problems for triangular and tetrahedral mesh generators. Al- though small angles inherent in the input geometry cannot be re- moved, one would like to find a way to triangulate a domain without creating any new small angles. Unfortunately, this problem is not always soluble. I discuss how mesh generation algorithms based on Delaunay refinement can be modified to ensure that they always produce a mesh. A two-dimensional algorithm presented here cre- ates a mesh with no new angle smaller than , where is the smallest angle separating two segments of the input domain. Furthermore, new angles smaller than ap- pear only near input angles smaller than . In practice, the algo- rithm's performance is better than these bounds suggest. A three- dimensional algorithm presented here creates a mesh in which all tetrahedra have circumradius-to-shortest edge ratios no greater than two, except near acute input angles (angles separating segments and/or facets of the input domain).

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