RaPC：一种基于栅格化思想的多边形裁剪算法及其误差分析

摘要

Computational efficiencies of traditional vector computing‐based polygon clipping algorithms will decrease rapidly when handling polygons contain large amount of vertices .The computing flows of traditional polygon clipping algorithms are tightly coupled with special data structures ,which difficult to be optimized in the underlying of them .Under the premise of meeting a certain degree of area errors ,the polygonclippingproblemcanbesolvedbyintroducingtheideaofrasterizationprocessing.Inthisresearch, we proposed a new rasterization processing‐based polygon clipping algorithm:the RaPC algorithm ,on the basis of analyzing the characteristics of existing algorithms .The area errors of results of the new algorithm are also analyzed and discussed .Experimental results show that the efficiencies of the RaPC algorithm can be enhanced significantly when using l arge grid cells ,and it shows a linear trend growth with the increase of amount of polygon vertices .Compared with the Vatti algorithm ,the RaPC algorithm represents more efficiencies on dealing clipping issues between polygons with large amount of vertices ,the former shows lower time costs when handling polygons with less vertices .The area error of computing results of the RaPC algorithmiscloselyrelatedwiththegridsize,anderrorscanbereducedusingsmallergridsizes.Therefore the RaPC algorithm showed higher efficiencies on processing polygons with large amount of vertices than the Vatti algorithm and presented practical values to some degree .%传统的基于矢量计算的多边形裁剪算法的时间复杂度介于O（Nlog N ）～ O（N 2）之间，且计算过程与特定的复杂数据结构耦合紧密，难以进行底层优化和细粒度并行化。在满足一定误差要求的前提下，采用栅格化处理思想可以实现多边形快速裁剪。本文在已有多边形裁剪算法特征的基础上，提出了一种基于栅格化处理思想的多边形裁剪算法———R a PC算法，并对其误差进行了分析和讨论。试验结果显示，RaPC算法的计算效率随网格单元增大呈幂函数规律降低；当网格大小恒定时，RaPC算法效率随多边形顶点数量呈线性增长，计算时间复杂度为O（N）；在处理小数据集时Vatti算法表现出了较高效率，但是在处理包含大量顶点的多边形叠加时，RaPC算法更为高效；RaPC算法的面积误差与网格大小直接相关，提高网格空间分辨率可以有效地降低面积误差。R a PC算法在处理包含大量顶点的多边形叠加分析时比V atti算法更为高效。