RE2L: An Efficient Output-sensitive Algorithm for Computing Boolean Operation on Circular-arc Polygons

The boundaries of conic polygons consist of conic segments or second degree curves. The conic polygon has two degenerate or special cases: the linear polygon and the circular-arc polygon. The natural problem — boolean operation on linear polygons, has been well studied. Surprisingly, (almost) no article focuses on the problem of boolean operation on circular-arc polygons, which actually can also find many applications, implying that if there is a targeted solution for boolean operation on circular-arc polygons, which should be favourable for potential users. In this article, we devise a concise data structure, and then develop a targeted algorithm called RE2L. Our method is surprisingly simple, easy-to-implement but without loss of efficiency. Given two circular-arc polygons with m and n edges respectively, we prove that the proposed method runs in O(m + n + (l + k) log l) time, using O(m + n + l + k) space, where k is the number of intersections, and l is the number of related edges. The experimental results show our proposed algorithm is significantly faster than the ones that are by directly appealing to the existing algorithms.