scholarly journals On delaunay oriented matroids for convex distance functions

1996 ◽  
Vol 16 (2) ◽  
pp. 197-210 ◽  
Author(s):  
F. Santos
Keyword(s):  
Oriented Matroids ◽  
Distance Functions ◽  
Convex Distance Functions

CONVEX DISTANCE FUNCTIONS IN 3-SPACE ARE DIFFERENT

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

scholarly journals Voronoi Diagrams of Lines in 3-Space Under Polyhedral Convex Distance Functions

1998 ◽  
Vol 29 (2) ◽  
pp. 238-255 ◽  
Author(s):  
L.Paul Chew ◽  
Klara Kedem ◽  
Micha Sharir ◽  
Boaz Tagansky ◽  
Emo Welzl
Keyword(s):  
Voronoi Diagrams ◽  
Distance Functions ◽  
Polyhedral Convex ◽  
Convex Distance Functions

SKEW VORONOI DIAGRAMS

1999 ◽  
Vol 09 (03) ◽  
pp. 235-247 ◽  
Author(s):  
OSWIN AICHHOLZER ◽  
FRANZ AURENHAMMER ◽  
DANNY Z. CHEN ◽  
D. T. LEE ◽  
EVANTHIA PAPADOPOULOU
Keyword(s):  
Euclidean Distance ◽  
Voronoi Diagrams ◽  
Nearest Neighbors ◽  
Distance Functions ◽  
Plane Sweep ◽  
Voronoi Regions ◽  
Convex Distance Functions ◽  
Tilted Plane ◽  
Three Space

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.

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