Efficient PRAM and Practical GPU Algorithms for Large Polygon Clipping with Degenerate Cases

Abstract

Polygonal geometric operations are fundamental in domains such as Computer Graphics, Computer-Aided Design, and Geographic Information Systems. Handling degenerate cases in such operations is important when real-world spatial data are used. The popular Greiner-Hormann (GH) clipping algorithm does not handle such cases properly without perturbing vertices leading to inaccuracies and ambiguities. In this work, we parallelize the $O$(n2)-time general polygon clipping algorithm by Foster et al., which can handle degenerate cases without perturbation. Our CREW PRAM algorithm can perform clipping in O (log n) time using $n$ + $k$ number of processors with simple polygons, where $n$ is the number of input edges and $k$ is the number of edge intersections. For efficient GPU implementation, we employ three effective filters which have not been used in prior work on polygon clipping: 1) Common-minimum-bounding-rectangle filter, 2) Count-based filter, and 3) Line-segment-minimum-bounding-rectangle filter. They drastically reduce O($n$2) candidate edge pairs comparisons by 80% - 99%, leading to significantly faster parallel execution. In our experiments, C++ CUDA-based implementation yields up to 40X speedup over real-world datasets, processing two polygons with a total of 174K vertices on an Nvidia Quadro RTX 5000 GPU compared to the sequential Foster's algorithm running on an Intel Xeon Silver 4210R CPU.