Discrete Distortion for Surface Meshes

  • Mohammed Mostefa Mesmoudi
  • Leila De Floriani
  • Paola Magillo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5716)

Abstract

Discrete distortion for two- and three-dimensional combinatorial manifolds is a discrete alternative to Ricci curvature known for differentiable manifolds. Here, we show that distortion can be successfully used to estimate mean curvature at any point of a surface. We compare our approach with the continuous case and with a common discrete approximation of mean curvature, which depends on the area of the star of each vertex in the triangulated surface. This provides a new, area-independent, tool for curvature estimation and for morphological shape analysis. We illustrate our approach through experimental results showing the behavior of discrete distortion.

Keywords

Gaussian curvature mean curvature discrete curvature estimators triangle meshes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mohammed Mostefa Mesmoudi
    • 1
  • Leila De Floriani
    • 1
  • Paola Magillo
    • 1
  1. 1.Department of Computer ScienceUniversity of GenovaGenovaItaly

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