二维图形的集合运算算法研究

A New Algorithm for Set Operation of 2D Drawings

二维图形的并、交、差等集合运算是二维图形的设计、图形消隐处理、零件的三维造型及数控加工编程中刀具轨迹生成等的重要基础。文中借助于ＡＣＩＳ几何平台，提出了在线架、曲面和实体集成数据环境下，将二维线架图形转换为实体的数据结构，利用实体的布尔运算实现二维图形的集合运算的算法。避免了传统的集合运算中所必需的线段求交、裁剪、交点的有效性判断等．降低了算法的复杂度，从而提高了算法的可靠性。该算法已在南京航空航天大学ＣＡＤ／ＣＡＭ工程研究中心开发的ＣＡＤ／ＣＡＭ系统中实现。

The set operation of 2D drawings (union, intersection and subtraction) is an important foundation of design and hiding of 2D drawings, modeling of mechanical parts and generation of the tool path. In this paper, a new algorithm for the set operation of 2D drawings based on the data environment of integrating wireframe, surface and solid is proposed. According to the ideas of ACIS model topology and geometry, Boolean operation is introduced to the set operation of 2D drawings by converting the 2D wireframes into sheet bodies. With this algorithm, the complicated and error-prone procedures, such as edge intersection, trimming, and validity judgement of intersecting points, are avoided. As a result, the complexity of the algorithm is decreased and the reliability increased. The algorithm has been implemented in a CAD/CAM system developed by the Research Center of CAD/CAM Engineering, Nanjing University of Aeronautics & Astronautics.