| 摘要: |
| 本文给出了求２次和３次非均匀有理Ｂ样条（ＮＵＲＢＳ）曲线的相关积分量，例如它所包围区域的面积、旋转体体积、面积矩、形心等的算法．对于２次曲线，本文推导了一系列精确的积分公式，由此，所有积分量可用曲线的控制顶点坐标和权因子一步代入直接求得而没有逼近误差；对于３次曲线，本文展示了一种近似算法，与通常的数值积分法相比，它具有误差界估计简单，高精度下收敛速度快等优点． |
| 关键词: 计算机辅助几何设计 非均匀有理B样条 积分 面积 旋转体体积 面积矩 |
| DOI： |
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| 基金项目:本文研究得到国家自然科学基金和曹光彪科学研究基金资助. |
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| COMPUTING INTEGRAL VALUES INVOLVING NURBS CURVES |
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Wang Guojin
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| Abstract: |
| This paper presents an algorithm for computing quantities involving integration of NURBS curves, such as areas, volumes of revolution, first moments of area, centroids etc., of regions bounded by plane NURBS curves. For quadratic NURBS curves,closed form integral solutions are derived, thus all integral values can be directly obtaind by the coordinates of control points and weights without approximation error. For cubic NURBS curves, an approximation method is given, which provides a simple error bound and has a speed advantage for small tolerance. |
| Key words: Computer aided geometric design NURBS integration area volume of revolution moments of area. |
