Parameter Estimation of Point Projection on NURBS Curves and Surfaces

This paper proposes an algorithm for estimation of point projection parameters, based on pruning on the explicit convex hull of the squared distance function. The explicit expression of the squared distance function is deduced. According to the special requirement of point projection, the convex hull of the squared distance function is incrementally constructed. In each step, regions that obviously contain no projection points are eliminated from the base curve or surface, by intersecting the current nearest distance line with the convex hull. When the user-defined tolerances are satisfied, iteration algorithms are used to get the precise projection points. Experimental results show that compared with existing algorithms using clipping circle/sphere or line/plane, this algorithm possesses higher elimination rate and computation speed.