THREE-DIMENSIONAL TOPOLOGICAL SWEEP FOR COMPUTING ROTATIONAL SWEPT VOLUMES OF POLYHEDRAL OBJECTS
Nakhoon Baek, Sung-Yong Shin, Kyung‐Yong Chwa · International Journal of Computational Geometry & Applications · 2000
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(n 2 ·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.