On computing translational swept volumes

A swept volume is a nice tool for solving various types of interference problems. Previous investigations have concentrated on sweeping an object along an arbitrary path that results in complex algorithms. We study the most fundamental motion, which is translation along a linear path. After analyzing the structure of the swept volume, we present an incremental algorithm for constructing a swept volume. Our algorithm takes O(n²α(n)+T_c) time where n is the number of vertices in the original object and T_c is the time for handling face cycles. When the object is monotone with respect to the sweeping path, we show that its swept volume can be calculated in O(n) time after O(n log n+k) time preprocessing, where k is the number of regions in the arrangement of the projected image of the object.