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» Computing the Implicit Voronoi Diagram in Triple Precision
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WADS
2009
Springer
267views Algorithms» more  WADS 2009»
13 years 9 months ago
Computing the Implicit Voronoi Diagram in Triple Precision
In a paper that considered arithmetic precision as a limited resource in the design and analysis of algorithms, Liotta, Preparata and Tamassia defined an “implicit Voronoi diagr...
David L. Millman, Jack Snoeyink
CAD
2005
Springer
13 years 4 months ago
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Despite its important applications in various disciplines in science and engineering, the Euclidean Voronoi diagram for spheres, also known as an additively weighted Voronoi diagr...
Deok-Soo Kim, Youngsong Cho, Donguk Kim
SODA
2003
ACM
131views Algorithms» more  SODA 2003»
13 years 6 months ago
Root comparison techniques applied to computing the additively weighted Voronoi diagram
This work examines algebraic techniques for comparing quadratic algebraic numbers, thus yielding methods for deciding key predicates in various geometric constructions. Our motiva...
Menelaos I. Karavelas, Ioannis Z. Emiris
CCCG
2006
13 years 6 months ago
An O(n log n) Algorithm for the All-Farthest-Segments Problem for a Planar Set of Points
In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n log n) algorithm for th...
Asish Mukhopadhyay, Robert L. Scot Drysdale
COMPGEOM
2001
ACM
13 years 8 months ago
PRECISE: efficient multiprecision evaluation of algebraic roots and predicates for reliable geometric computation
: Many geometric problems like generalized Voronoi diagrams, medial axis computations and boundary evaluation involve computation and manipulation of non-linear algebraic primitive...
Shankar Krishnan, Mark Foskey, Tim Culver, John Ke...