Ruixiong Tian, Zhe Xiang, et al.
Qinghua Daxue Xuebao/Journal of Tsinghua University
On a tilted plane T in three-space, skew distances are defined as the Euclidean distance plus a multiple of the signed difference in height. Skew distances may model realistic environments more closely than the Euclidean distance. Voronoi diagrams and related problems under this kind of distances are investigated. A relationship to convex distance functions and to Euclidean Voronoi diagrams for planar circles is shown, and is exploited for a geometric analysis and a plane-sweep construction of Voronoi diagrams on T. An output-sensitive algorithm running in time O(n log h) is developed, where n and h are the numbers of sites and non-empty Voronoi regions, respectively. The all nearest neighbors problem for skew distances, which has certain features different from its Euclidean counterpart, is solved in O(n log n) time.
Ruixiong Tian, Zhe Xiang, et al.
Qinghua Daxue Xuebao/Journal of Tsinghua University
Jianke Yang, Robin Walters, et al.
ICML 2023
A. Skumanich
SPIE OE/LASE 1992
Shashanka Ubaru, Lior Horesh, et al.
Journal of Biomedical Informatics