Next: 8.2.3 Principal curvatures
Up: 8.2 Stationary points of
Previous: 8.2.1 Gaussian curvature
Contents Index
8.2.2 Mean curvature
Similarly to the Gaussian curvature, we have the following equations
to evaluate the stationary points of mean curvature
given by
(convention (b) (see Fig.
3.7 (b) and Table 3.2) is
employed) within the domain [255]:
(8.48)
where
(8.49)
(8.50)
Polynomial
and its partial
derivatives are given by
(8.51)
(8.52)
(8.53)
where
(8.54)
(8.55)
(8.56)
Since
, (8.48) reduce to two
simultaneous bivariate polynomial equations
(8.57)
of degree
and
in
and
. For a
bicubic Bézier patch input, the degrees of the governing equations
are (21, 22) and (22, 21) in
and
, respectively. The system
(8.57) can be solved robustly with the IPP algorithm
described in Chap. 4 (see [255] for
details).
The stationary points of mean curvature along the domain boundary can
be obtained by solving the following four univariate polynomial equations:
(8.58)
(8.59)
These equations can be solved robustly with the IPP algorithm
described in Chap. 4 (see [255] for
details).
Next: 8.2.3 Principal curvatures
Up: 8.2 Stationary points of
Previous: 8.2.1 Gaussian curvature
Contents Index
December 2009