Mesh generation for domains with small angles

Abstract

Nonmanifold geometric domains having small angles present special problems for triangular and tetrahedral mesh generators. Although small angles inherent in the input geometry cannot be removed, 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 creates a mesh with no new angle smaller than arcsin[sin( =2)=p2], where 60 is the smallest angle separating two segments of the input domain. Furthermore, new angles smaller than 20:7 appear only near input angles smaller than 60 . In practice, the algorithm’s performance is better than these bounds suggest. A threedimensional 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).