Swept Volume Computation with Enhanced Geometric Detail Preservation

2025-09-11

AI Summary

Existing swept-volume computation methods suffer from poor robustness in explicit surface tracking and struggle to balance geometric fidelity with optimization efficiency in implicit representations. This paper proposes a multi-field tetrahedral framework based on inverse kinematic modeling: objects are held fixed while spatial points are traced backward along their trajectories, transforming complex rigid-body motions—including translation and screw motion—into linearizable point-trajectory problems. Each tetrahedral element maintains multiple signed distance fields to accurately capture fine-grained geometric features such as trajectory intersections and self-intersections. By overcoming the limitations of single-field modeling, the method achieves both high geometric fidelity and significantly improved numerical stability and computational efficiency. Experiments demonstrate high-accuracy, robust swept-volume reconstruction across diverse complex motion scenarios, effectively supporting downstream applications including path planning and collision detection.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Motion & Tracking
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Computing swept volumes with high geometric detail preservation
• Addressing robustness issues in complex motion interactions
• Overcoming limitations of single field methods at intersections

Innovation

• Inverts motion perspective to trace points backward
• Uses multi-field tetrahedral framework for detail preservation
• Maintains multiple distance fields per element