Voronoi diagrams—a survey of a fundamental geometric data structure
- F. Aurenhammer
- Computer ScienceCSUR
- 1 September 1991
Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer…
Power Diagrams: Properties, Algorithms and Applications
- F. Aurenhammer
- MathematicsSIAM journal on computing (Print)
- 1 February 1987
The close relationship to convex hulls and arrangements of hyperplanes is investigated and exploited, and efficient algorithms that compute the power diagram and its order-k modifications are obtained.
Voronoi Diagrams
- F. Aurenhammer, R. Klein
- PhysicsHandbook of Computational Geometry
- 2000
A Novel Type of Skeleton for Polygons
- O. Aichholzer, F. Aurenhammer, David Alberts, B. Gärtner
- Computer ScienceJournal of universal computer science (Online)
- 1995
A new internal structure for simple polygons, the straight skeleton, is introduced and discussed. It is composed of pieces of angular bisectores which partition the interior of a given n-gon P in a…
Minkowski-Type Theorems and Least-Squares Clustering
- F. Aurenhammer, F. Hoffmann, B. Aronov
- MathematicsAlgorithmica
- 1998
The concept of a constrained least-squares assignment is extended to continuous distributions of points, thereby obtaining existence results for power diagrams with prescribed region volumes and related to Minkowski's theorem for convex polytopes.
Straight Skeletons for General Polygonal Figures in the Plane
- O. Aichholzer, F. Aurenhammer
- Computer ScienceInternational Computing and Combinatorics…
- 17 June 1996
It is shown that the concept of S(G) is exible enough to allow an individual weighting of the edges and vertices of G, without changes in the maximal size ofS(G), or in the method of construction.
An optimal algorithm for constructing the weighted voronoi diagram in the plane
- F. Aurenhammer, H. Edelsbrunner
- MathematicsPattern Recognition
- 1984
Enumerating Order Types for Small Point Sets with Applications
- O. Aichholzer, F. Aurenhammer, H. Krasser
- MathematicsOrder
- 1 September 2002
A complete and reliable data base for all possible order types of size n=10 or less is established and substantiate the usefulness of the data base by applying it to several problems in computational and combinatorial geometry.
Farthest line segment Voronoi diagrams
- F. Aurenhammer, R. Drysdale, H. Krasser
- Computer ScienceInformation Processing Letters
- 31 December 2006
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