Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
On the geodesic Voronoi diagram of point sites in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Nonoverlap of the star unfolding
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Approximation of generalized Voronoi diagrams by ordinary Voronoi diagrams
CVGIP: Graphical Models and Image Processing
Three-dimensional convex hull as a fruitful source of diagrams
Theoretical Computer Science
Discrete Applied Mathematics
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
On the Triangle-Perimeter Two-Site Voronoi Diagram
ISVD '09 Proceedings of the 2009 Sixth International Symposium on Voronoi Diagrams
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This paper proposes a new generalization of the Voronoi diagram. Consider two kinds of facilities located in a city, for example, restaurants and bookstores. We want to visit both and return to our house. To each pair of a restaurant and a bookstore is assigned a region such that a resident in this region can visit them in a shorter round tour than visiting any other pair. The city is partitioned into these regions according to which pair of a restaurant and bookstore permits the shortest round tour. We call this partitioning a "round-tour Voronoi Diagram" for the restaurants and bookstores. We study the basic properties of this Voronoi diagram and consider an efficient algorithm for its approximate construction.