B样条乘积计算的区间跳跃算法及应用  

Knot interval skipping method for multiplication of B-spline functions and the application

作　　者：车翔玖[1] 高占恒[1] 车娜[1,2] 

机构地区：[1]吉林大学计算机科学与技术学院,长春130012 [2]长春大学艺术学院计算机动画系,长春130024

出　　处：《计算机工程与应用》2009年第35期157-160,共4页Computer Engineering and Applications

基　　金：国家自然科学基金No.60773098;60673021;教育部博士学科点专项基金项目No.20060183041~~

摘　　要：利用B样条基函数节点区间的对应关系,首先给出了B样条基函数间的转换矩阵的计算方法,进而给出了计算B样条乘积的区间跳跃算法。该算法仅需计算部分节点区间上的转换矩阵,因此称其为区间跳跃算法。这一方法解决了分段多项式与B样条曲线乘积的计算问题,可应用到B样条曲线的升阶、曲面间光滑拼接等问题中。通过算例验证了该方法计算简捷、易于实现。By utilizing the relationship between the knot intervals,a method for calculating the transform matrix between different B-spline basis functions is presented.Furthermore,an interval skipping algorithm is given to calculate B-spline functions multiplication.This algorithm is so-called just as only part of knot intervals need to be considered to calculate rapidly B-spline functions multiplication.This algorithm partially solves the multiplication of piecewise polynomial and B-spline curve;and it can be applied into smooth B-spline surfaces blending and elevation of B-spline.Some examples are given to illustrate the efficiency of the presented algorithm.

关 键 词：B样条乘积 转换矩阵 区间跳跃算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]