计算机工程与应用 ›› 2009, Vol. 45 ›› Issue (35): 157-160.DOI: 10.3778/j.issn.1002-8331.2009.35.048

• 图形、图像、模式识别 • 上一篇    下一篇

B样条乘积计算的区间跳跃算法及应用

车翔玖1,高占恒1,车 娜1,2   

  1. 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
  • 收稿日期:2009-10-15 修回日期:2009-11-15 出版日期:2009-12-11 发布日期:2009-12-11
  • 通讯作者: 车翔玖

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

CHE Xiang-jiu1,GAO Zhan-heng1,CHE Na1,2   

  1. 1.College of Computer Science and Technology,Jilin University,Changchun 130012,China
    2.Department of Computer Animation,College of Fine-Art,Changchun University,Changchun 130024,China
  • Received:2009-10-15 Revised:2009-11-15 Online:2009-12-11 Published:2009-12-11
  • Contact: CHE Xiang-jiu

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。

Abstract: 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.

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