Three-dimensional topological sweep for computing rotational swept volumes of polyhedral objects

Plane sweep plays an important role in computational geometry. This paper shows that an extension of topological plane sweep to three-dimensional space can calculate the volume swept by rotating a solid polyhedral object about a fixed axis. Analyzing the characteristics of rotational swept volumes, we present an incremental algorithm based on the three-dimensional topological sweep technique. Our solution shows the time bound of O(n² · 2^α(n) + T_c), where n is the number of vertices in the original object and T_c is time for handling face cycles. Here, α(n) is the inverse of Ackermann's function.