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 refinement 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.