Guaranteed-quality triangular mesh generation for domains with curved boundaries

Guaranteed-quality unstructured meshing algorithms facilitate the development of automatic meshing tools. However, these algorithms require domains discretized using a set of linear segments, leading to numerical errors in domains with curved boundaries. We introduce an extension of Ruppert’s Delaunay re nement algorithm to two-dimensional domains with curved boundaries and prove that the same quality bounds apply with curved boundaries as with straight boundaries. We provide implementation details for two-dimensional boundary patches such as lines, circular arcs, cubic parametric curves, and interpolated splines. We present guaranteed-quality triangular meshes generated with curved boundaries, and propose solutions to some problems associated with the use of curved boundaries