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Curvature in Triangle Meshes

  • Jakob Andreas Bærentzen
  • Jens Gravesen
  • François Anton
  • Henrik Aanæs

Abstract

In many cases notions from differential geometry can be usefully extended to piecewise planar surfaces, and this chapter covers curvature measures on triangle meshes. A frequently used principle is to obtain a smooth surface approximation and to estimate the curvature from this approximation. Alternatively, the integral of some curvature measures can be computed from a small region of the mesh and then normalized by dividing by the area of that region.

Following these principles, we first discuss how to extend the definition of a surface normal to the edges and vertices of a triangle mesh. Next, we cover the estimation of Gaußian and mean curvature on a triangle mesh. Finally, techniques for computing the shape operator are discussed—followed by a discussion on how to obtain the principal curvatures from the shape operator.

Keywords

Smooth Surface Principal Curvature Principal Direction Curvature Measure Shape Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Jakob Andreas Bærentzen
    • 1
  • Jens Gravesen
    • 2
  • François Anton
    • 1
  • Henrik Aanæs
    • 1
  1. 1.Department of Informatics and Mathematical ModellingTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark

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