依据有限个观测点的坐标分析空间曲线的弯曲程度  

Analysis of the Degree of Bending Degree of the Curve According to Limited Observation Points

作　　者：陈刚[1] 吴彬[1] 

机构地区：[1]南通职业大学基础课部,江苏南通226007

出　　处：《南通职业大学学报》2014年第2期59-62,70,共5页Journal of Nantong Vocational University

基　　金：江苏省高等教育教学改革研究课题重点项目(2011JSJG085)

摘　　要：空间曲线的方程未知,要依据曲线上有限个观测点的坐标,计算曲线的弯曲度。从曲率的原始定义出发,建立起直接利用原始坐标数据计算空间曲线各弧段弯曲度的方法,同时构造出具有最佳弯曲度逼近的光滑曲线,证明了直接方法的可靠性。经过深入剖析,厘清了某些流行算法的模糊认识,通过示例阐明了运用二次样条和三次样条插值方法计算曲线弯曲度的缺陷。With the space curve equation unknown, to calculate the curvature of the curve, we should use the coordinates of the limited observation points on the curve. According to the original definition of the curvature, this paper establishes the direct method using the original data to calculate the coordinates of each arc of curvature of the space curve segment, while smooth curves is constructed with the best approximation of curvature, which proves the reliability of the direct method. After in-depth analysis, this paper purifies the understanding of some popular algorithms, by illustrating the defects of using quadratic spline and cubic spline interpolation method to calculate the curve bending.

关 键 词：空间曲线的弯曲度 观测点坐标 曲率 曲线段的转角 弯曲度逼近 样条插值 

分 类 号：O29[理学—应用数学] TU196[理学—数学]