Curvature estimation for meshes via algebraic quadric fitting

TL;DR

This paper presents a new algebraic quadric fitting method for estimating mean and Gaussian curvature on polygonal meshes, demonstrating robustness and accuracy across various sampling conditions and mesh types.

Contribution

The novel AQFC method introduces a quadratic surface approximation for curvature estimation, improving accuracy and robustness over existing methods, especially on irregular and scanned meshes.

Findings

Approximates true curvatures with increasing sampling density.

Resilient to irregular mesh sampling.

Provides robust estimates on scanned, arbitrary meshes.

Abstract

We introduce the novel method for estimation of mean and Gaussian curvature and several related quantities for polygonal meshes. The algebraic quadric fitting curvature (AQFC) is based on local approximation of the mesh vertices and associated normals by a quadratic surface. The quadric is computed as an implicit surface, so it minimizes algebraic distances and normal deviations from the approximated point-normal neighbourhood of the processed vertex. Its mean and Gaussian curvature estimate is then obtained as the respective curvature of its orthogonal projection onto the fitted quadratic surface. Experimental results for both sampled parametric surfaces and arbitrary meshes are provided. The proposed method AQFC approaches the true curvatures of the reference smooth surfaces with increasing density of sampling, regardless of its regularity. It is resilient to irregular sampling of the mesh, compared to the contemporary curvature estimators. In the case of arbitrary meshes, obtained from scanning, AQFC provides robust curvature estimation.