【摘要】 针对现有的实体构造模型计算复杂、无法满足实时性要求较高的仿真任务问题，提出一种用于球头刀具仿真的十字网格拓扑结构二维映射算法，以提高布尔求差运算效率．基于仿真模型底层拓扑提出一种十字网格拓扑结构，将节点元素作为十字网格数据对象存放在动态邻接表中，以节约内存；此外，基于非均匀有理B样条(NURBS)曲面细分网格点，构造复杂表面的十字网格数据，拓展该方法的实用性．利用数控插补指令简化球头刀具的运动轨迹，提出一种追踪轮廓线法以构建工件与刀具的相交轮廓线，加快相交点搜索过程；引入网格参数化法将相交轮廓线的三维数据映射至二维数组，以快速生成工件与刀具的相交面．结果表明：该方法的布尔求差运算效率比主流方法提升10倍以上，内存占用平均减少46%，追踪轮廓线和二维映射法能够大幅度加快计算，十字网格拓扑结构可以显著提升内存利用率，所提出的算法能够明显改善边界表示法的计算效率，有助于计算机辅助系统的实时应用．更多还原

【Abstract】 As the existing solid construction model is complex in calculation,and cannot meet the high real-time requirements of the simulation task,a two-dimensional mapping algorithm of cross mesh topology was proposed to improve the efficiency of Boolean difference calculation. A cross mesh topology was proposed for the bottom topology of the simulation model,and node elements were stored in the dynamic adjacency table as cross mesh data objects to save memory.In addition,the cross mesh data of complex surfaces was constructed based on non-uniform rational B-splines(NURBS) surface subdivision,which expanded the practicability of the method. Numerical control(NC) interpolation instructions were used to simplify the trajectory of the ball-end tool,and a tracing contour method was proposed to construct the intersecting contour of the workpiece and the tool,and speed up the intersecting point search process.Mesh parameterization was introduced to map the three-dimensional data of intersecting contour lines to a two-dimensional array to quickly generate the intersecting surfaces of workpiece and tool.Experimental results show that the efficiency of the proposed method is more than 10 times higher than that of the mainstream method,and the average memory usage is reduced by 46%,which indicates that the tracing contour and two-dimensional mapping can effectively accelerate the calculation,and the cross mesh topology can significantly improve the memory utilization. The proposed algorithm can obviously improve the computational efficiency of boundary representation and is helpful to the real-time application of computer aided systems.更多还原