Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

TL;DR

This paper introduces a surface remeshing algorithm that balances geometric fidelity, mesh simplicity, and element quality by optimizing for approximation error, minimal interior angle, and complexity within user-defined bounds.

Contribution

The proposed algorithm simultaneously addresses multiple remeshing goals with a novel optimization framework that prioritizes local operators under error constraints.

Findings

Produces high-quality meshes with preserved features

Balances fidelity, complexity, and element quality effectively

Outperforms state-of-the-art methods in experiments

Abstract

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error {\delta}, minimal interior angle {\theta} and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound {\delta} as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. In this way our optimization framework greedily searches for the coarsest mesh with minimal interior angle above {\theta} and approximation error bounded by {\delta}. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.