convex distance functions
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1999 ◽  
Vol 09 (03) ◽  
pp. 235-247 ◽  
Author(s):  
OSWIN AICHHOLZER ◽  
FRANZ AURENHAMMER ◽  
DANNY Z. CHEN ◽  
D. T. LEE ◽  
EVANTHIA PAPADOPOULOU

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 analysisis 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.


1998 ◽  
Vol 29 (2) ◽  
pp. 238-255 ◽  
Author(s):  
L.Paul Chew ◽  
Klara Kedem ◽  
Micha Sharir ◽  
Boaz Tagansky ◽  
Emo Welzl

1995 ◽  
Vol 22 (4) ◽  
pp. 331-352 ◽  
Author(s):  
Christian Icking ◽  
Rolf Klein ◽  
Ngoc-Minh Lé ◽  
Lihong Ma

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