Size-optimal Steiner points for Delaunay-refinement on curved surfaces

TL;DR

This paper introduces a new surface mesh generation algorithm that uses off-centre Steiner points to improve element quality, combining Delaunay-refinement and advancing-front techniques for better surface tessellations.

Contribution

It presents a size-optimal Steiner point placement scheme for Delaunay-refinement on curved surfaces, enhancing mesh quality and robustness.

Findings

Significant improvements in shape and size quality of surface tessellations.

The new method produces smooth, high-quality surface triangulations.

Experimental results confirm robustness and practical performance.

Abstract

An extension of the restricted Delaunay-refinement algorithm for surface mesh generation is described, where a new point-placement scheme is introduced to improve element quality in the presence of mesh size constraints. Specifically, it is shown that the use of off-centre Steiner points, positioned on the faces of the associated Voronoi diagram, typically leads to significant improvements in the shape- and size-quality of the resulting surface tessellations. The new algorithm can be viewed as a Frontal-Delaunay approach -- a hybridisation of conventional Delaunay-refinement and advancing-front techniques in which new vertices are positioned to satisfy both element size and shape constraints. The performance of the new scheme is investigated experimentally via a series of comparative studies that contrast its performance with that of a typical Delaunay-refinement technique. It is shown that the new method inherits many of the best features of classical Delaunay-refinement and advancing-front type methods, leading to the construction of smooth, high quality surface triangulations with bounded radius-edge ratios and convergence guarantees. Experiments are conducted using a range of complex benchmarks, verifying the robustness and practical performance of the proposed scheme.