DISCRETE CLOTHOID SPLINE SURFACES ON OPEN MESHES

By introducing a discrete Frenet frame, this paper first proposes 3D discrete clothoid splines to extend the planar discrete clothoid splines of Schneider and Kobbelt. On the basis of 3D discrete clothoid spline curves, discrete clothoid spline surfaces for arbitrary meshes are defined as a generalization of their closed discrete clothoid spline surfaces. Moreover, a discrete mean curvature normal operator instead of the conic surface fitting method is employed to compute curvature values. This induces a new iteration algorithm for generating the discrete clothoid spline surfaces. Since the curvature at a vertex is an area average over a region around this vertex and no linear system needs to be settled, the algorithm works more steadily and efficiently. Besides being directly used to produce fair mesh surfaces, the approach can also be employed to smooth control nets of spline surfaces.