Differential Geometry

  • Jakob Andreas BærentzenEmail author
  • Jens Gravesen
  • François Anton
  • Henrik Aanæs


The chapter gives a short overview of the concepts from differetial geometry that are used in geometry processing: normal, area, first and second fundamental form, the Gauß and Weingarten map, normal and geodesic curvature, principal curvatures and directions, the Gaußian and mean curvature, the Gauß–Bonnet theorem and the Laplace–Beltrami operator. We end by a brief study of implicitly defined surfaces.

It is not meant as a course in differential geometry, but as a brush up and a handy point of reference. For the reader who wishes to know more there is a vast literature to which we refer.


Tangent Space Tangent Vector Fundamental Form Principal Curvature Principal Direction 
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Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Jakob Andreas Bærentzen
    • 1
    Email author
  • 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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