Affiliation:
1. KLMM, AMSS, Chinese Academy of Sciences 8 University of Chinese Academy of Science, Beijing, China
2. School of Computer Science and Technology, Shandong University, Qingdao, China
3. Aromath, Inria Méditerranée, Université Côte d’Azur, France
4. The University of Hong Kong, Hong Kong
Abstract
Arrangements of geometric objects refer to the spatial partitions formed by the objects, and they serve as an underlining structure of motion design, analysis, and planning in CAD/CAM, robotics, molecular modeling, manufacturing, and computer-assisted radio-surgery. Arrangements are especially useful to collision detection, which is a key task in various applications such as computer animation, virtual reality, computer games, robotics, CAD/CAM, and computational physics.
Ellipsoids are commonly used as bounding volumes in approximating complex geometric objects in collision detection. In this article, we present an in-depth study on the arrangements formed by two ellipsoids. Specifically, we present a classification of these arrangements and propose an efficient algorithm for determining the arrangement formed by any particular pair of ellipsoids. A stratification diagram is also established to show the connections among all the arrangements formed by two ellipsoids. Our results, for the first time, elucidate all possible relative positions between two arbitrary ellipsoids and provide an efficient and robust algorithm for determining the relative position of any two given ellipsoids, therefore providing the necessary foundation for developing practical and trustworthy methods for processing ellipsoids for collision analysis or simulation in various applications.
Funder
Beijing Municipal Natural Science Foundation
National Natural Science Foundation of China
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Graphics and Computer-Aided Design
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献