Accurate and Efficient Algorithm for the Closest Point on a Parametric Curve

This paper presents an accurate and efficient method for computation of the closest point on parametric curves. This problem is firstly formulated in terms of solution of a polynomial equation expressed in Bernstein basis, and then based on subdivision relying on the convex hull property of Bezier curve and the recursive bintree decomposition on the parameter domain, a novel solution method is proposed. The computation of closest point is shown to be equivalent to the geometrically intuitive intersection of a curve with the parameter line. Finally, by comparing the distances between the test point and the candidate points, the closest point is found. An example illustrates the feasibility of this method.