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Exact and interpolatory quadratures for curvature tensor estimation

Authors
Journal
Computer Aided Geometric Design
0167-8396
Publisher
Elsevier
Publication Date
Volume
24
Identifiers
DOI: 10.1016/j.cagd.2006.09.006
Keywords
  • Mean Curvature
  • Curvature Tensor
  • Discretization
  • Convergence Analysis
  • Exact Quadrature
Disciplines
  • Mathematics

Abstract

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.

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