Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids

doi:10.1145/3388540

	Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids
	Jia, Xiaohong 3,5; Tu, Changhe 4; Mourrain, Bernard 1; Wang, Wenping 2
刊名	ACM TRANSACTIONS ON GRAPHICS
	2020-06-01
卷号	39 期号:3 页码:12
关键词	Arrangements ellipsoids collision detection
ISSN号	0730-0301
DOI	10.1145/3388540
英文摘要	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.
资助项目	National Natural Science Foundation of China[61872354] ; National Natural Science Foundation of China[61772318] ; Beijing Natural Science Foundation[Z190004] ; Intelligent Science and Technology Advanced subject project of University of Chinese Academy of Sciences[115200S001] ; Alibaba Group through Alibaba Innovative Research Program
WOS研究方向	Computer Science
语种	英语
出版者	ASSOC COMPUTING MACHINERY
WOS记录号	WOS:000577126000010
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52316]
专题	中国科学院数学与系统科学研究院
通讯作者	Jia, Xiaohong
作者单位	1.Univ Cote dAzur, Inria Mediterranee, Aromath, F-06902 Nice, France 2.Univ Hong Kong, Dept Comp Sci, Hong Kong, Peoples R China 3.Univ Chinese Acad Sci, Beijing, Peoples R China 4.Shandong Univ, Sch Comp Sci & Technol, Qingdao 266237, Peoples R China 5.Chinese Acad Sci, KLMM, AMSS, 55 Zhongguancun East Rd, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Jia, Xiaohong,Tu, Changhe,Mourrain, Bernard,et al. Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids[J]. ACM TRANSACTIONS ON GRAPHICS,2020,39(3):12.
APA	Jia, Xiaohong,Tu, Changhe,Mourrain, Bernard,&Wang, Wenping.(2020).Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids.ACM TRANSACTIONS ON GRAPHICS,39(3),12.
MLA	Jia, Xiaohong,et al."Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids".ACM TRANSACTIONS ON GRAPHICS 39.3(2020):12.