Approximate computation of curves on B-spline surfaces

Abstract : Curves on surfaces play an important role in computer-aided geometric design. Because of the considerably high degree of exact curves on surfaces, approximation algorithms are preferred in CAD systems. To approximate the exact curve with a reasonably low degree curve which also lies completely on the B-spline surface, an algorithm is presented in this paper. The Hausdorff distance between the approximate curve and the exact curve is controlled under the user-specified distance tolerance. The approximate curve is ɛT –G1 continuous, where ɛT is the user-specified angle tolerance. Examples are given to show the performance of our algorithm.