ABSTRACT
The geodesic concept, introduced in the last chapter purely on variational principles, has interesting engineering aspects. On the other hand, the analytic 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 creating good quality (albeit not necessarily geodesic) curves by minimizing the curvature. This chapter discusses the harmonic equation, B-spline approximation, B-splines with tangent constraints, and tangent constrained B-spline. In practical applications, some heuristics, like setting the tangent at a certain point parallel to the chord between the two neighboring points, can be used successfully. Systematic and possibly interactive application of this concept should result in good shape preservation and general smoothness.
