参数B样条曲线的非均匀离散细分算法

Self-Adaptive Non-Uniform Subdivision Algorithm for Generating B-Spline Curve

利用差商算子给出一种参数 B样条曲线的非均匀离散细分算法。为了便于工程实际应用 ,在算法中分别考虑了 B样条的均匀细分算法和非均匀细分算法 ,并将其应用在自由型曲线生成和函数逼近上 ,通过计算比较表明 ,B样条的非均匀离散细分算法在某些方面比均匀离散细分算法有更好的效果。

Existing subdivision algorithms are mostly uniform. Though Chinese engineers engaged in CAGD(computer aided geometric design) still have misgivings about the increased computation cost of non uniform subdivision for generating Bspline curve, they are still quite interested in a subdivision algorithm that is self adaptive under certain conditions such as the case of a curve whose curvature varies very rapidly. We propose a non uniform subdivision algorithm that can be self adaptive . Section 1 describes our self adaptive non uniform subdivision algorithm for generating Bspline curve. Eqs.(12) and (13) are the important mathematical expressions used in our algorithm. Section 2 gives two numerical examples, corresponding to the two sets of numerical data in Table 1. Figs.1 and 2 give the results of curve fitting based on our self adaptive subdivision algorithm and on uniform subdivision algorithm respectively. In both figures, self adaptive subdivision algorithm's curve fitting is better.