The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Power Diagrams: Properties, Algorithms and Applications
Abstract
The power pow $(x,s)$ of a point x with respect to a sphere s in Euclidean d-space $E^d $ is given by $d^2 (x,z) - r^2 $, where d denotes the Euclidean distance function, and z and r are the center and the radius of s. The power diagram of a finite set S of spheres in $E^d $ is a cell complex that associates each $s \in S$ with the convex domain $\{ x \in E^d | {\operatorname{pow}} (x,s) < {\operatorname{pow}} (x,t), {\text{ for all }} t \in S - \{ s\} \}$. The close relationship to convex hulls and arrangements of hyperplanes is investigated and exploited. Efficient algorithms that compute the power diagram and its order-k modifications are obtained. Among the applications of these results are algorithms for detecting k-sets, for union and intersection problems for cones and paraboloids, and for constructing weighted Voronoi diagrams and Voronoi diagrams for spheres. Upper space bounds for these geometric problems are derived.
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Cites
Voronoi, G. (1908) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.1908.134.198 · Cited by 2,248
Shamos, M. I., & Hoey, D. (1975) · 16th Annual Symposium on Foundations of Computer Science (sfcs 1975) · doi:10.1109/sfcs.1975.8 · Cited by 1,057
Convex hulls of finite sets of points in two and three dimensions
Preparata, F. P., & Hong, S. J. (1977) · Communications of the ACM · doi:10.1145/359423.359430 · Cited by 710
Lagerungen in der Ebene auf der Kugel und im Raum
Tóth, L. F. (1972) · Springer eBooks · doi:10.1007/978-3-642-65234-9 · Cited by 578
On k-Nearest Neighbor Voronoi Diagrams in the Plane
Lee, D.-T. (1982) · IEEE Transactions on Computers · doi:10.1109/tc.1982.1676031 · Cited by 331
Generalization of Voronoi Diagrams in the Plane
Lee, D. T., & Drysdale, III (1981) · SIAM Journal on Computing · doi:10.1137/0210006 · Cited by 312
An optimal algorithm for constructing the weighted voronoi diagram in the plane
Aurenhammer, F., & Edelsbrunner, H. (1984) · Pattern Recognition · doi:10.1016/0031-3203(84)90064-5 · Cited by 293
Self-citationVoronoi diagrams from convex hulls
Brown, K. Q. (1979) · Information Processing Letters · doi:10.1016/0020-0190(79)90074-7 · Cited by 289
Voronoui Diagrams in $L_1 (L_\infty )$ Metrics with 2-Dimensional Storage Applications
Lee, D. T., & Wong, C. K. (1980) · SIAM Journal on Computing · doi:10.1137/0209017 · Cited by 126
Boots, B. N. (1980) · Economic Geography · doi:10.2307/142716 · Cited by 109
Cited by
Voronoi diagrams—a survey of a fundamental geometric data structure
Aurenhammer, F. (1991) · ACM Computing Surveys · doi:10.1145/116873.116880 · Cited by 4,340
Self-citationComputational Optimal Transport
Peyré, G., & Cuturi, M. (2019) · now publishers, Inc. eBooks · doi:10.1561/9781680835519 · Cited by 847
Protein–protein interaction and quaternary structure
Janin, J., Bahadur, R. P., & Chakrabarti, P. (2008) · Quarterly Reviews of Biophysics · doi:10.1017/s0033583508004708 · Cited by 398
A Survey on Quantum Channel Capacities
Gyongyosi, L., Imre, S., & Nguyen, H. V. (2018) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2017.2786748 · Cited by 337
Olechnovič, K., & Grudinin, S. (2025) · Journal of Computational Chemistry · doi:10.1002/jcc.70178 · Cited by 3
Metadata
- Authors
- Aurenhammer, F.
- Venue
- SIAM Journal on Computing
- Published
- 1987-02
- Volume
- 16
- Issue
- 1
- Pages
- 78-96
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2048475323
- Cited by
- 832
- References
- 10
- FWCI
- 10.91
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
