Ridge (differential geometry)
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In differential geometry, a smooth surface in three dimensions has a ridge point when a line of curvature has a local maximum or minimum of principal curvature. The set of ridge points form curves on the surface called ridges.
The ridges of a given surface fall into two families, typically designated red and blue, depending on which of the two principal curvatures has an extremum.
At umbilical points the colour of a ridge will change from red to blue. There are two main cases: one has three ridge lines passing through the umbilic, and the other has one line passing through it.
Ridge lines correspond to cuspidal edges on the focal surface.
See also
- Ridge detection
References
- Porteous, Ian R. (2001). "Ridges and Ribs". Geometric Differentiation. Cambridge University Press. pp. 182–197. ISBN 0-521-00264-8. https://books.google.com/books?id=BNrW0UJ_UFcC&pg=PA182.
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