| 摘要: |
| 插值运动物体给定活动标架(原点位置和3个坐标轴朝向)是计算机图形学、机器人等领域的一个重要问题.该文提出一种采用B样条曲线插值与逼近运动物体活动标架的新方法.采用4个欧拉参数对正交活动标架的旋转变换矩阵进行参数化,得到了一个简单的优化方程.采用迭代法求解该优化方程来逼近运动轨迹任意处伪活动标架的旋转变换矩阵.还证明了插值和逼近所引起的误差是可控的.由于活动标架的计算只涉及2阶或3阶线性方程组,所以此方法具有很高的运行效率. |
| 关键词: 运动设计,插值与逼近,活动标架,B样条. |
| DOI： |
| 分类号: |
| 基金项目:本文研究得到国家自然科学基金(No.69973043)和国家杰出青年基金(No.69625304)资助. |
|
| A New Method to Interpolate and Approximate Moving Frames of Moving Object |
|
JIANG Zhong-ding,MA Li-zhuang
|
| Abstract: |
| The interpolation of some given moving frames (origin position+orientations of three coordinate axes) of a moving object is an important problem in the fields of computer graphics, robotics, etc. In this paper, a new method is presented to interpolate and approximate the moving frames of moving object by employing B-splines. By parameterizing the rotation transformation part of the orthogonal moving frame with four Euler parameters, a simplified optimization function is derived. An iteration method is presented to solve the optimization function for approximating the rotation transformation part of the pseudo moving frame at any position of the motion trajectory. The error caused by interpolation and approximation is proven to be controllable. Since the computation of moving frame is only related with order 2 or 3 linear equations, the proposed approach can be implemented with high efficiency. |
| Key words: Motion design, interpolation, approximation, moving frame, B-spline. |
