Abstract
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.
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© 2012 Springer-Verlag London
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Bærentzen, J.A., Gravesen, J., Anton, F., Aanæs, H. (2012). Differential Geometry. In: Guide to Computational Geometry Processing. Springer, London. https://doi.org/10.1007/978-1-4471-4075-7_3
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DOI: https://doi.org/10.1007/978-1-4471-4075-7_3
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4074-0
Online ISBN: 978-1-4471-4075-7
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