A regular patch is a Patch for which the Jacobian has rank 2 for all . A Patch is said to be regular at a point provided that its Jacobian has rank 2 at . For example, the points at in the standard parameterization of the Sphere are not regular.

An example of a Patch which is regular but not Injective is the Cylinder defined
parametrically by
with
and . However, if
is
an injective regular patch, then **x** maps diffeomorphically onto .

**References**

Gray, A. *Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, p. 187, 1993.

© 1996-9

1999-05-25