Conforming restricted Delaunay mesh generation for piecewise smooth complexes

TL;DR

This paper introduces a novel Frontal-Delaunay refinement algorithm for generating high-quality meshes in piecewise smooth domains, effectively handling complex features and outperforming classical methods in 3D benchmarks.

Contribution

The paper presents a new unweighted, conforming restricted Delaunay mesh generation algorithm with advanced feature protection and off-centre refinement rules for complex geometries.

Findings

Outperforms classical restricted Delaunay refinement in 3D benchmarks

Handles non-manifold, piecewise smooth surface patches and curves

Achieves high-quality point placement along embedded features

Abstract

A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted, conforming restricted Delaunay representation for domains specified as a (non-manifold) collection of piecewise smooth surface patches and curve segments, (ii) a protection strategy for domains containing curve segments that subtend sharply acute angles, and (iii) a new class of off-centre refinement rules designed to achieve high-quality point-placement along embedded curve features. Experimental comparisons show that the new Frontal-Delaunay algorithm outperforms a classical (statically weighted) restricted Delaunay-refinement technique for a number of three-dimensional benchmark problems.