
Chapter 8
Curvatures: A Differential
Geometry Tool
Niloy J. Mitra and Daniel Cohen-Or
The term curvature simply refers to the amount of bending of a
curve or a surface. In simple terms, curvature at a point indicates
how quickly a curve or a surface bends away from its local tangent
line or tangent plane, respectively. While tangent planes are useful
for studying first-order behavior of surfaces, curvatures deal with
second-order behavior. However, a rigorous study of curvatures
can be quite involved, and in general, there are different notions
of curvatures depending on the context. The interested reader is
referred to the comprehensive survey of curvature ...