Fast Approach for Computing the Minimum Distance between a Point and a NURBS Curve

Point projection problem of NURBS curves has a wide application in geometric modeling system.A fast approach is presented for computing the minimum distance between a point and a NURBS curve.It combines a control-polygon-based method for searching the subdivision position,the classification based clipping method with progressive root-finding technique.It firstly translates the square distance function into Bézier form; and then,estimates the subdivision positions by using the control polygon,and does the clippings based on classification; finally it computes the minimum distance by using progressive root-finding technique.It can achieve a better clipping effect than the circle-clipping methods.Numerical examples show that the new method can achieve better clipping efficiency and better computational efficiency than those of circle clipping method and other prevailing methods.