关键词: 逆向细分, 曲线细分, 简化与重构

Abstract: According to the problem of simplification and reconstruction methods of freedom curve, this paper presents a reverse subdivision scheme based on B-spline of degree three. If the new midpoint and new vertex are determined inappropriately, the simplified curve using the above-mentioned reverse subdivision will not properly retain the characteristic and shape of freedom curve. Thus this paper introduces extreme points and inflexion points as characteristic points of freedom curve, and then presents a kind of reverse subdivision which can retain the characteristic points of freedom curve on the basis of subdivision of B-spline of degree three. By using this reverse subdivision, conformal simplification of freedom curve can be achieved. The freedom curve can be reconstructed by establishing the error vectors while reversing. Finally, this paper presents a practical way of finding the curvature extreme points of discrete point set.

Key words: reverse subdivision, curve subdivision, simplification and reconstruction