Constructing iterative non-uniform B-spline curve and surface to fit data points

摘要: In this paper, based on the idea of profit and loss modification, we present iterative non-uniform B-spline curve surface to settle a key problem in computer aided geometric design reverse engineering, that is, constructing (surface) fitting (interpolating) given ordered point set without solving linear system. We start with piece initial which takes as its control set. Then by adjusting points gradually formula, can get group curves (surfaces) higher precision. using modern matrix theory, strictly prove limit iteration interpolates The generated have many advantages, such satisfying NURBS standard, having explicit expression, gaining locality, convexity preserving, etc.