Quad-Dominant Mesh Adaptation Using Specialized Simplicial Optimization

Abstract

Summary. The proposed quad-dominant mesh adaptation algorithm is based on simplicial optimization. It is driven by an anisotropic Riemannian metric and uses specialized local operators formulated in terms of an L ∞ instead of the usual L2 distance. Furthermore, the physically-based vertex relocation operator includes an alignment force to explicitly minimize the angular deviation of selected edges from the local eigenvectors of the target metric. Sets of contiguous edges can then be effectively interpreted as active tensor lines. Those lines are not only packed but also simultaneous networked together to form a layered rectangular simplicial mesh that requires little postprocessing to form a cubical-dominant one. Almost all-cubical meshes are possible if the target metric is compatible with such a decomposition and, although presently only two-dimensional tests were performed, a three-dimensional extension is feasible.

A frontal Delaunay quad mesh generator using the L ∞ norm

“…This simple test case has been used for benchmarking quad meshers in . We therefore compare our results with the results of those two papers.…”

“…In their paper , Tchon and Camarero have already proposed a method for generating quad‐dominant meshes on the basis of the use of the L ∞ norm. In their approach, they start from a standard triangular mesh and apply vertex relocation that aim at aligns vertices on prescribed directions.…”

“…Because they rely on the minimization of complex and stiff functionals, both smoothing approaches of Tchon and Lévy are not CPU efficient (101 s for generating 972 quads and 322 s for generating a surface mesh of about 1000 elements). Here, our approach allows to generate quads at the speed of triangle mesh generation, that is, tens of thousands of elements a minute.…”

Feature aligned quad dominant remeshing using iterative local updates

“…This post optimization could be applied to our quad meshes if this property is desired. Tchon and Cameredo [31] propose to use iterative, specialized local operators to produce quad-dominant meshes, which bears some similarity with our method, however, their method applies only to 2D meshes.…”

Connectivity Editing for Quad‐Dominant Meshes

“…There is a large variety of algorithms that are often driven by curvature [ACSD*03, MK04, RLL*06]. Other approaches work by vertex alignment [TC06, LKH08], space partitioning (octree [Mar09] or quadtree [FM98]), or use segmentation as an important ingredient [MK06]. The generated meshes can also satisfy additional requirements, e.g.…”