An Efficient Method for Computation of Geodesic on B-Spline Surfaces

Abstract

A new algorithm is presented to compute geodesic on B-spline surfaces. At first, the principle of the algorithm is introduced in detail. The geodesic on the surface is traced in a simple way with a starting point and a starting direction as initial values. Then, three examples are delivered to test accuracy and efficiency of our algorithm. Experimental results indicate that the accuracy of our algorithm is comparable with that of Beck's approach, and at the same time our algorithm is faster than it. Furthermore, we do not need to solve the differential equations of geodesic which are quite complicated for B-spline surfaces.