Anisotropic quadrangulation

Quadrangulation methods aim to approximate surfaces by semiregular meshes with as few extraordinary vertices as possible. A number of techniques use the harmonic parameterization to keep quads close to squares, or fit parametrization gradients to align quads to features. Both types of techniques create near-isotropic quads; feature-aligned quadrangulation algorithms reduce the remeshing error by aligning isotropic quads with principal curvature directions. A complimentary approach is to allow for anisotropic elements, which are well-known to have significantly better approximation quality. In this work we present a simple and efficient technique to add curvature-dependent anisotropy to harmonic and feature-aligned parameterization and improve the approximation error of the quadrangulations. We use a metric derived from the shape operator which results in a more uniform error distribution, decreasing the error near features.