Applied Calculus of Variations for Engineers, 2nd Edition

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. ...