The Weingarten equations express the derivatives of the Normal using derivatives of the position vector. Let
be a Regular Patch, then the Shape Operator of **x** is given in terms of the basis
by

(1) | |||

(2) |

where is the Normal Vector, , , and the coefficients of the first Fundamental Form

(3) |

(4) | |||

(5) | |||

(6) |

**References**

Gray, A. ``Calculation of the Shape Operator.'' §14.3 in *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 274-277, 1993.

© 1996-9

1999-05-26