球、圆柱和圆锥几何特征参数提取方法

GEOMETRIC PARAMETERS EXTRACTION OF SPHERE, CYLINDER AND CONE

空间任意位置球、圆柱和圆锥的几何特征参数提取问题,在逆向工程等工程实践中具有广泛的应用。为较好地求解该问题,以边界约束BFGS算法(L-BFGS-B)为基础,针对上述二次曲面几何特征参数边界约束或无约束两种情况,提出以点到曲面几何距离的均方和为目标函数,其中对圆柱和圆锥,采用球坐标表示其轴线方向矢量,从而将其目标函数转化为多变量边界约束优化问题,然后应用L-BFGS-B算法进行迭代求解。试验结果表明该方法具有易于使用和计算高效等特点。

Extracting geometric parameters of spheres, cylinders and cones in space has extensive engineering applications practically, such as reverse engineering and object recognition. A new approach is presented to solve this kind of problems based on the L-BFGS-B algorithm, where L-BFGS-B is a limited memory algorithm for solving large-scale nonlinear optimization problems subjected to simple bound-constrained or unconstrained on the variables. The method aims to discuss the geometric parameters extraction of the quadric surfaces under the bound-constrained or unconstrained, by taking the meansquared geometric distance between a set of points and quadric surfaces as objective function. For the objective function of a cylinder or cone, its axis direction vectors are expressed in terms of spherical coordinates. This can make its objective function into a multi-variables, non-linear and bound-constrained optimization problem. Finally, the L-BFGS-B algorithm is used to iteratively minimize the objective function. Experimental results show this method is effectively and easy to use for the geometric parameters extraction of spheres, cylinders and cones.