基于杆件变形理论的空间曲线插值算法

An Interpolation Methods Based on Bar Elastic Distortion Theory

为解决空间点列曲线插值问题,提出了一种基于杆件小挠度变形理论的空间曲线插值算法。根据插值理论的要求,将杆件弹性变形理论中的挠度、弹性模量赋予数学含义,修改变形理论的限制条件,将小变形理论移植到空间曲线插值算法中,通过求解插值系数g(gyi,gzi)确定插值方程。此算法具有明确的物理意义,数学模型简单,生成的曲线结构紧凑,弥补了B样条插值法的不足,能够生成形态复杂的空间曲线,在计算机造型、反求工程及运动轨迹描述等工程领域有重要的实用价值。

To resolve linear interpolation questions in three-dimension, a new interpolation methods using bar elastic distortion theory was presented. According to the definition of interpolation, the equations of the bar elastic distortion can be used as a interpolation methods to make the flexibility and elastic coefficient have the means of mathematics and modify the qualifications. The interpolation equations can be fixed by the parameters g（gyi ,gzi） This methods has specific means in physics and the arithmetic of it is simple. The curves produced by the methods have compact forms. It optimizes the B-spline methods and can be used in many fileds such as CAD and converse project.