Isotropic Surface Remeshing without Large and Small Angles

Abstract

We introduce a novel algorithm for isotropic surface remeshing which progressively eliminates obtuse triangles and improves small angles. The main novelty of the proposed approach is a simple vertex insertion scheme that facilitates the removal of large angles, and a vertex removal operation that improves the distribution of small angles. In combination with other standard local mesh operators, e.g., connectivity optimization and local tangential smoothing, our algorithm is able to remesh efficiently a low-quality mesh surface. Our approach can be applied directly or used as a post-processing step following other remeshing approaches. Our method has a similar computational efficiency to the fastest approach available, i.e., real-time adaptive remeshing [1]. In comparison with state-of-the-art approaches, our method consistently generates better results based on evaluations using different metrics.

Anisotropic Surface Remeshing without Obtuse Angles

“…Also, similar to previous works on isotropic meshes [YW16, HYB∗17,WYL∗19], our method has no hard guarantee for complete obtuse angle removal. However, with carefully designed connectivity and geometry optimization, it is empirically effective to eliminate all obtuse angles (see Table ).…”

Valence optimization and angle improvement for molecular surface remeshing

“…2 Electrostatic potential on molecular surface, calculated with AFMPB [7] shows an example of the molecular surface mesh in the downstream applications, i.e., the electrostatic potentials calculated with AFMPB [7] mapped on the molecular surface. Typically, a triangle with an angle smaller than 30 • or obtuse angle (i.e., ≥ 90 • ) is called a bad triangle [8]. Similarly, it has been shown in the previous research that valence optimization can speed up the convergence.…”

“…Researches reveal that small and large triangles badly affect the simulation results, and even a single bad triangle can affect the results [1,8,18]. To the best of our knowledge, a recent method of non-obtuse remeshing [8] in computer graphics better performs for angle improvement achieving an angle bound [30 • 90 • ]. However, for molecular surface remeshing, there is no significant achievement in angle improvement with consideration of their area and volume preservations, valence optimization, and features preservations.…”

“…of adjacent edges) equal to four for a boundary vertex and valence 6 for an interior vertex is called optimal or regular vertex, while the others are non-optimal. Generally, valence 5, valence 6, and valence 7 vertices are treated as optimal valences and are found easy for surface remeshing [1,8,9]. In generic surface remeshing, the state-of-the-art methods have a significant improvement in the mesh quality.…”

A Robust Local Spectral Descriptor for Matching Non-Rigid Shapes With Incompatible Shape Structures

“…All models in FAUST have the same triangulation and resolution with 6890 vertices. We refer to [10,33] for details on remeshing and generate multi-resolution shapes with irregular triangulation while ensuring that each shape contains user-specified vertices.…”