Intersect offsets of parametric surfaces with branch analysis

Based on the methods for solving contouring problem, we present an algorithm to compute the intersection of offsets of parametric surfaces robustly, accurately and efficiently. By first determining the topology of intersection, the algorithm makes tracing process smoothly. Resulting intersection curves is given inform of the trajectory of the parametric domains of the original surfaces, no approximation of offset surface is needed. The algorithm also does not need to inverse the 3D intersection to 2D parametric domains. The intersection is defined by a single parameter in interval [0,1]. The algorithm have been implemented and tested. It can overcome the degenerate conditions such as loop leaking, branch jumping, and disorder tracing, and it can also calculate the intersection robustly and accurately.