Guaranteed-quality triangular mesh generation for domains with curved boundaries
Boivin, Charles; Ollivier-Gooch, Carl
International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 55, Num 10, pp.1185 - 1213, December 2002
Advanced Numerical Simulation Laboratory, Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada
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 Ruppertaposs 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.
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