Ridge (differential geometry)

A ridge

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.