In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easy-to-implement but without loss of efficiency. Given two circular-arc polygons with m and n edges respectively, our method runs in O(m+n+(l+k) l) time, using O(m+n+k) space, where k is the number of intersections, and l is the number of edges. Our algorithm has the power to approximate to linear complexity when k and l are small. The superiority of the proposed algorithm is also validated through empirical study.