Anisotropic polygonal remeshing

TLDR

The paper proposes a polygonal remeshing method that leverages the intrinsic anisotropy of surfaces. The method extracts and smooths a curvature tensor field on a genus‑0 surface patch, then uses its minimum and maximum curvature lines to guide edge placement in anisotropic areas while sampling points in spherical regions. The technique produces meshes composed mainly of quads in anisotropic regions and triangles in spherical areas, offering adjustable granularity and curvature adaptation from isotropic to highly anisotropic.

Abstract

In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or man-made geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input genus-0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply point sampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.