Overlapping Area Computation between Irregular Polygons for Its Evolutionary Layout Based on Convex Decomposition

Low efficiency of interference calculation has become the bottleneck that restricts further development of the performance of evolutionary algorithm for the polygon layout. To solve the problem, in this paper, we propose an algorithm of calculating overlapping area between two irregular polygons. For this algorithm, at first, two irregular polygons are respectively decomposed into the minimum number of convex polygons; afterwards, each pair of the overlapping convex polygons from two resulting partitions is clipped and their overlapping area is calculated. Because through a fast non-overlapping test to all pairs of convex polygons to be clipped, invalid computation is decreased; by making use of simple internal vertex judgment and sheartransformation based on intersecting test and intersection calculation between a line segment and any convex broken line segment, its speed of clipping overlapping convex polygons is improved. The time complexity analysis and numerical experiments indicate that the performance of our presented algorithm superiors to the existing algorithms.