基于动态参数化的二次B样条插值曲线  

Quadratic B-Spline Interpolation Curves Based on Dynamic Parametrization

作　　者：潘日晶[1] 姚志强[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福州350007

出　　处：《计算机学报》2005年第3期334-342,共9页Chinese Journal of Computers

基　　金：福建省自然科学基金(A0210016)资助~~

摘　　要：参数化为构造B样条插值曲线提供了自由度,但在以往的研究中,这些自由度并未得到充分利用.该文给出的二次B样条曲线插值方法充分利用了参数化的自由度,直接利用插值曲线直观的几何约束条件如曲线在数据点处的切向、曲线段的相对高度等进行参数化,使得构造出的插值曲线不仅在两端,而且在中间各段具有预期的几何性质.该文的方法比起以往的参数化方法来,能更直观有效地控制插值曲线的形状.而且,所构造的插值曲线具有局部性质或近似局部性质,即当改变某个数据点的位置时,插值曲线的形状只作局部改变或除局部范围外,曲线形状改变很小或完全不变.不同于以往的插值方法,该文的方法在构造插值曲线的过程中根据曲线的几何约束条件动态地递推确定参数值、节点向量和控制顶点,整个过程不必解方程组,计算简便.该文还给出了相应的算法和应用例子.实验结果表明,该文的方法十分有效.Parametrization provides degree of freedom for B-spline interpolation curves. But this degree of freedom has not been fully utilized in the past researches. In this paper, a interpolation method for quadratic B-spline curves is given which fully utilizes the degree of freedom of parametrization. With this method, the intuitive geometric constrained conditions of the interpolation curve such as the tangents of the curve on data points and the relative heights of curve segments are directly used in parametrization and the resulted interpolation curve possesses the expectant geometric properties. Hence the shapes of the interpolation curves can be controlled more intuitively and effectively by this method than by the existing B-spline interpolation methods. In addition, the resulted interpolation curves have localness or nearly localness properties for the data points. Differing from the other interpolation methods which need solve equation sets, the method proposed in this paper simply recursively calculates parameters, knots and control points dynamically according to the given geometric constrained conditions of the interpolation curve in the process of constructing interpolation curve. Two algorithms and some examples for this method are also given and the results show that this method is very effective.

关 键 词：B样条曲线 插值 参数化 节点向量 几何约束 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]