Paper Info
Title
Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids
Abstract
AbstractArrangements 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.
Year
DOI
Venue
2020
10.1145/3388540
ACM Transactions on Graphics
Keywords
DocType
Volume
Arrangements, ellipsoids, collision detection
Journal
39
Issue
ISSN
Citations 
3
0730-0301
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Xiaohong Jia141.91
Changhe Tu228834.47
Bernard Mourrain31074113.70
Wenping Wang42491176.19