Anisotropic triangular meshing using metric-adapted embeddings

Abstract

We propose a novel method to generate high-quality triangular meshes with specified anisotropy. Central to our algorithm is to present metric-adapted embeddings for converting the anisotropic meshing problem to an isotropic meshing problem with constant density. Moreover, the orientation of the input Riemannian metric forms a field, enabling us to use field-based meshing techniques to improve regularity and penalize obtuse angles. To achieve such metric-adapted embeddings, we use the cone singularities, which are generated to adapt to the input Riemannian metric. We demonstrate the feasibility and effectiveness of our method over various models. Compared to other state-of-the-art methods, our method achieves higher quality on all metrics in most models.