  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.
