Swept Volume Computation with Enhanced Geometric Detail Preservation

Abstract: Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex interactions, or employ implicit representations that trade off geometric fidelity and face optimization difficulties. We propose a novel inversion of motion perspective: rather than tracking object motion, we fix the object and trace spatial points backward in time, reducing complex trajectories to efficiently linearizable point motions. Based on this, we introduce a multi field tetrahedral framework that maintains multiple distance fileds per element, preserving fine geometric details at trajectory intersections where single field methods fail. Our method robustly computes swept volumes for diverse motions, including translations and screw motions, and enables practical applications in path planning and collision detection.