反求建模中常见二次曲面拟合方法

Research on Algorithm of Quadric Surface Fitting in Reverse Modeling for Mechanical Parts

针对机械零件反求建模过程中常见二次曲面的表面重建问题,提出了曲面拟合分步计算法.该算法根据数字化离散点的三维坐标及各点的法矢量,利用零件表面的几何特征建立拟合计算目标函数,把二次曲面拟合问题转化为线性最小二乘计算问题;通过拟合计算提取曲面的几何参数,为建立机械零件实体及特征模型打下基础.

To solve the problem of quadric surface reconstruction in reverse modeling for mechanical parts, a two-step fitting algorithm was presented. With this fitting algorithm, the objective function is built based on the coordinates of measuring points, the normal vector of each point and the geometrical features of mechanical part surfaces, and as a result, the nonlinear calculation of quadric fitting can be changed into a linear least square problem. Furthermore, the geometrical parameters of mechanical part surfaces can be gained through fitting calculation to provide a basis for building solid model and feature model in the reverse engineering for mechanical parts.