# Ridge (differential geometry)

Ridge (differential geometry)

For a smooth surface in three dimensions a ridge point occurs 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.

Ridges fall into two types typically designated "red" and "blue" depending on which of the two principal curvatures have 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 line line passing through it.

Ridge lines correspond to cuspidal edges on the focal surface.

References

*

ee also

*Ridge detection

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