May 2015
Intermediate to advanced
246 pages
6h 33m
English
book
A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing
by Daniel Cohen-Or, Chen Greif, Tao Ju, Niloy J. Mitra, Ariel Shamir, Olga Sorkine-Hornung, Hao Zhang
Content preview from A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing
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Curvatures: A Differential Geometry Tool 127
κ
min
< 0 κ
min
= 0 κ
min
> 0
κ
max
< 0 peak ridge saddle
κ
max
= 0 ridge flat valley
κ
max
> 0 saddle valley pit
Table 8.1: Locally categorizing surfaces based on the principal curvatures
signs.
The two principal curvatures can be combined into a single
number, known as the shape index [KvD92], which is defined by
S = −
2
π
arctan
κ
max
− κ
min
κ
max
+ κ
min
. (8.4)
With the shape index, each local shape is associated with a value
in the range of [−1, 1], where all convex shapes have positive shape
indices and all concave shapes have negative shape indices. Sad-
dle points are mapped close to the zero value, where the minimal
saddle
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