Stationary points of surface curvature are important in methods for
the correct topological decomposition of the surface on the basis of
curvature
[255]. Let the curvature in question of a parametric
surface
defined over
be
denoted by a scalar function
, then the following (see also
Sect. 7.2.1), need to be evaluated to locate all the
stationary points of curvature and to find the global maximum and
minimum values of
to provide a correct topological
decomposition of the surface [255].
The four values of curvature at the parameter domain corners
(8.27)
Stationary points along parameter domain boundaries
(roots of the four equations)
(8.28)
Stationary points within the parameter domain (roots
of the two simultaneous equations)
(8.29)
The curvature values at the
parameter domain corners are readily computed.
The classification of stationary points of functions of two variables
is given in Theorem 7.3.1. The formulations for the
stationary points of the Gaussian, mean and principal curvatures for
parametric surfaces are derived in Sect.
8.2.
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Up: 8.1.4 Third-order interrogation methods
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December 2009