Algorithm for Minimum Distance between Bézier Curves

An effective and straightforward algorithm is developed for computation of minimum distance between two Bézier curves．This problem is firstly formulated in terms of solutions of a polynomial equation expressed in Bernstein basis by means of the arithmetic for multivariate Bernsteinform polynomials,and a novel solution method is proposed by using the convex hull property of Bézier surface and the de Casteljau algorithm．The proposed method is geometrically intuitive,can avoid the choice of initial values and the solution of non-linear equation system,and can also be further generalized to compute the minimum distance between a Bézier curve and a Bézier surface． Experimental results demonstrate that the algorithm is steady and effective,and can further improve its efficiency when integrated with Newton-Raphson method．