
6
Differential Geometric Principles and
Operators
Differential geometry constitutes of a set of mathematical methods and opera-
tors which are useful in computing geometric quantities of discrete continuous
structures using differential calculus as discussed by Koenderink [28],[29]. It
can be described as a mathematical tool box for describing shape through
derivatives. The assumption made in differential geometry is that the geo-
metrical structures such as curves, surfaces, lattices etc. are everywhere dif-
ferentiable and there are no sharp discontinuities such as corners or cuts. In
differential geometry of shape measures, there is no global coordinate ...