A Linear time algorithm for computing the Voronoi diagram of a convex polygon
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Voronoi diagrams of lines in 3-space under polyhedral convex distance functions
Journal of Algorithms - Special issue on SODA '95 papers
Discrete Applied Mathematics
3-Dimensional Euclidean Voronoi Diagrams of Lines with a Fixed Number of Orientations
SIAM Journal on Computing
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence
Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence
Proceedings of the twenty-fifth annual symposium on Computational geometry
On Voronoi Diagrams for Lines in the Plane
ICCSA '09 Proceedings of the 2009 International Conference on Computational Science and Its Applications
On the Triangle-Perimeter Two-Site Voronoi Diagram
ISVD '09 Proceedings of the 2009 Sixth International Symposium on Voronoi Diagrams
On Constructing the Voronoi Diagram for Lines in the Plane under a Linear-Function Distance
ICCSA '10 Proceedings of the 2010 International Conference on Computational Science and Its Applications
On 2-Site Voronoi Diagrams under Arithmetic Combinations of Point-to-Point Distances
ISVD '10 Proceedings of the 2010 International Symposium on Voronoi Diagrams in Science and Engineering
| Hi-index | 0.00 |
We describe a method based on the wavefront propagation, which computes a multiplicatively weighted Voronoi diagram for a set L of n lines in the plane in O(n2 log n) time and O(n2) space. In the process, we derive complexity bounds and certain structural properties of such diagrams. An advantage of our approach over the general purpose machinery, which requires computation of the lower envelope of a set of halfplanes in three-dimensional space, lies in its relative simplicity. Besides, we point out that the unweighted Voronoi diagram for n lines in the plane has a simple structure, and can be obtained in optimal θ(n2) time and space.