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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
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(1) |
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(2) |
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(3) |
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(4) |
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(5) | |
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(6) |
See also Fundamental Forms, Shape Operator
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.