Anisotropic quadrangulation

Denis Kovacs, Ashish Myles, Denis Zorin
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/d7m3pqsgunbsrmcxdnyqqx2uxm" style="color: black;">Computer Aided Geometric Design</a> </i> &nbsp;
Quadrangulation methods aim to approximate surfaces by semi-regular 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; featurealigned quadrangulation algorithms reduce the remeshing error by aligning isotropic quads with principal curvature directions. A complementary approach is to allow
more &raquo; ... r 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.
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