Two Simple Methods for Improving a Triangle Mesh Surface

Abstract

We present two simple and efficient local methods that reposition vertices of a triangle mesh surface with the goal of producing good triangle shapes while preserving the enclosed volume and sharp features. The methods involve minimizing a quadratic energy functional with respect to variations in a tangent plane (or in the direction of a crease) at each free vertex. One of the methods is aimed at producing uniform angles, while the other method is designed to produce uniform triangle areas, or more generally, to force relative triangle areas to conform to curvature estimates or estimates of local feature size so that vertex density is low in flat spots and relatively high in regions of large curvature. Test results demonstrate the effectiveness of both methods, especially when combined.

Field‐Aligned Isotropic Surface Remeshing

“…Isotropic surface remeshing has been extensively studied. Representative approaches include particle reactions [Tur92, MKW07, BLW10, AGY*17], Delaunay insertion [Che93, Boi05, CDS12], discrete local operators [HDD*93, BK04, AYZ12, DVBB13, HYB*17], randomized sampling [YW13, GYJZ15, ERA*16] and variational approaches, for example, centroidal Voronoi tessellation (CVT) [DFG99], optimal Delaunay triangulation (ODT) [Che04] and their variations [FAKG10, CCW12, Ren16]. CVT‐based approaches gain considerable attention due to their elegant theoretical background and the capability to generate high‐quality meshes.…”

A Constrained Resampling Strategy for Mesh Improvement

“…Mesh Improvement and Quality Remeshing: Smoothing methods represented by the Centroidal Voronoi Tessellation (CVT) [DFG99] and its variants [DGJ03,WHWB16,JFL14,DW03] work by moving vertices to optimize an energy function. Other optimization‐based smoothing techniques for various quality objectives including angle bounds, edge length and triangle areas compute locally optimal moves [ABE99, Ren16]. On the other hand, transformation methods may add or remove vertices and work by vertex clustering [LT97,SW03], vertex removal [SZL92], edge and half‐edge collapses [HDD*93, ATC*08], and incremental decimation [WK03, KCS98, EMA*13].…”