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Abstract:
The computation of the curvature of smooth surfaces has a long history
in differential geometry and is essential for many
geometric modeling applications such as feature detection. We present a novel
approach to calculate the
mean curvature from arbitrary normal curvatures. Then, we demonstrate how the
same method can be used to
obtain new formulae to compute the Gaussian curvature and the curvature
tensor.
The idea is to compute the curvature integrals by a weighted sum by making
use of the periodic
structure of the normal curvatures to make the quadratures exact.
Finally, we derive an approximation formula for
the curvature of discrete data like meshes and
show its convergence if quadratically converging normals are available.
