Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Exact geometric computation in LEDA
Proceedings of the eleventh annual symposium on Computational geometry
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Efficient algorithms for line and curve segment intersection using restricted predicates
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Robust Proximity Queries: An Illustration of Degree-Driven Algorithm Design
SIAM Journal on Computing
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Further results on arithmetic filters for geometric predicates
Computational Geometry: Theory and Applications
Robust Plane Sweep for Intersecting Segments
SIAM Journal on Computing
Reporting curve segment intersections using restricted predicates
Computational Geometry: Theory and Applications
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
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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 diagram" supporting logarithmic-time proximity queries using predicates of twice the precision of the input and query coordinates. They reported, however, that computing this diagram uses five times the input precision. We define a reduced-precision Voronoi diagram that similarly supports proximity queries, and describe a randomized incremental construction using only three times the input precision. The expected construction time is O (n (logn + logμ )), where μ is the length of the longest Voronoi edge; we can construct the implicit Voronoi from the reduced-precision Voronoi in linear time.