基于扩展测地线的鞋楦围长测量

Shoe Last Girth Measuring by Extended Geodesic with Width

通过扩展测地线的定义,把鞋楦围长测量问题转化为求解鞋楦曲面上带宽度属性的测地线问题.首先以传统测地线为初始曲线在鞋楦曲面上构造具有一定宽度的子曲面,对子曲面进行离散点采样并构造弹簧质点系统;用带曲面约束的弹簧质点系统的运动能量作为子曲面的运动能量,再基于迭代优化的方法最小化子曲面能量,基于测地线思想计算出的鞋楦表面最短路径即为鞋楦围长;此外,对耗时较多的曲面约束计算采用GPU并行加速,进一步缩短了计算时间.实验结果表明,鞋楦围长测量结果达到了行业精度要求.

Measuring the girth of shoe last on polygonal mesh is an important problem in modern shoe- making CAD systems. In this paper we introduce a novel approach to measure the girth of digitized shoe last by extending the traditional geodesic with width. Firstly, it constructs a subsurface on shoe last based on a specified geodesic and its width. The energy of subsurface is defined in terms of a constrained mass-spring system. Secondly, an iterative optimization mechanism is employed to minimize the energy of this surface while it is moving on the shoe last. At last, the extended geodesic is extracted as the desired path of girth of the current shoe last after the convergence of aforementioned minimization. Furthermore, the time-consuming part of energy calculation is accelerated with a GPU implementation. Experimental results show that both precision and time performance of our approach can fulfill the requirements of shoe last measuring in the shoe-making industry.