
9
Computational geometry
The geodesic concept, introduced in the last chapter purely on variational
principles, has interesting engineering aspects. On the other hand, the an-
alytic solution of a geodesic curve by finding the extremum of a variational
problem may not be easy in practical cases.
It is reasonable to assume, however, that the quality of a curve in a geodesic
sense is related to its curvature. This observation proposes a strategy for cre-
ating good quality (albeit not necessarily geodesic) curves by minimizing the
curvature.
Since the curvature is difficult to compute, one can use the second derivative
of the curve in lieu of the curvature. ...