A Clipping Method Applied in Subdivision to Solve Point Projection Problems

Point projection to a NURBS curve/surface is an essential operation in CAD. When computing the projection result, the curve/surface is usually subdivided into several patches to avoid being trapped in the local optima.In this paper, in order to improve the efficiency of the subdivision, a clipping method is proposed to eliminate the patches which are irrelevant to the result.In our projection algorithm, the curve/surface is subdivided recursively and the projection distance to the current curve/surface patch is computed in each step.We approximate the distance between the source point and the convex hull of the control points.If it is larger than the upper bound of the projection result, according to the convex hull property of NURBS curves/surfaces, the current projection distance is also larger than the upper bound and the current curve/surface patch can be ignored. Examples illustrate the performance improvement of the corresponding projection algorithms.