Exact and approximate computation of B-spline curves on surfaces

Curves on surfaces are important elements in computer aided geometric design. After presenting a method to explicitly compute these curves in three-dimensions, practical algorithmic issues are discussed concerning the efficiency of the implementation. Good approximations are important because of the quite high degree of exact curves on surfaces. We present two approximate solutions to the problem. The first is derived from the exact representation, while the second extends conventional least-squares approximation by incorporating the geometry of the surface as well. The efficiency and behaviour of the algorithms are evaluated by means of examples.