{'fraction_non_alphanumeric': 0.017587939698492462, 'fraction_numerical': 0.002512562814070352, 'mean_word_length': 5.586776859504132, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Revisiting Delaunay Refinement Triangular Mesh Generation on Curve-bounded Domains

An extension of Shewchuk’s Delaunay Refinement algorithm to planar domains bounded by curves is presented. A novel method is applied to construct constrained Delaunay triangulations from such geometries. The quality of these triangulations is then improved by inserting vertices at carefully chosen locations. Amendments to Shewchuk’s insertion rules are necessary to handle cases resulting from the presence of curves. The algorithm accepts small input angles, although special provisions must be taken in their neighborhood. In practice, our algorithm generates graded triangular meshes where no angle is less than 30◦, except near small input angles. Such meshes are suitable for use in numerical simulations.