多义线及其偏移算法研究

摘要

Offset of planar curves has many applications in CAD/CAM. Line segments and arcs are the most common curve style in many engineering fields. In order to store and dispose of these kinds of curves, we present the concepts of convex rate and polyline to describe line segments and arcs by the same format. Considering the characteristic of polyline, we propose an algorithm to get the accurate offset of polyline. By this algorithm, the offset of a polyline is also a polyline, and the result polyline has the same geometry continuity as the original one. As every planar curve can be approximated by polyline, the algorithm is useful for the offset calculation of general planar curves.%计算平面曲线的偏移线在计算机辅助设计和数控加工中具有十分广泛的应用。在许多工程应用领域中，直线段和圆弧是使用频率较高的线段元素。为了便于计算机存储和处理，给出了直线和圆弧的统一表示形式，并在此基础上给出了多义线的定义与存储结构。针对多义线的特点，提出了一套求其精确偏移线的算法，该算法能够保证偏移线在各处具有与原曲线相应点相同的几何连续性。由于任意平面曲线均可以用多义线近似表示，本算法还可用来近似计算任意平面曲线的偏移线。