Sometimes there are empty regions in power diagram. It looks like some regions are smaller compared to the normal Voronoi diagram. How is this possible and how is this useful?
http://en.wikipedia.org/wiki/Voronoi_diagram
In mathematics, a Voronoi diagram is a way of dividing space into a number of regions. A set of points (called seeds, sites, or generators) is specified beforehand and for each seed there will be a corresponding region consisting of all points closer to that seed than to any other. The regions are called Voronoi cells. It is dual to the Delaunay triangulation.
Voronoi diagrams can be found in a large number of fields in science and technology, even in art, and they have found numerous practical and theoretical applications
Refer to the Article: How Are "Empty" Regions Implemented?
Link: https://blogs.oracle.com/DavidGiammona/entry/how_are_empty_regions_implemen
P.S.
Pisupati gave an excellent answer, I can also recommenmd this paper by Liebling http://www.math.uiuc.edu/documenta/vol-ismp/60_liebling-thomas.pdf
Prof. Gerro Prinsloo,
Thank you for the appreciation of my answer to the question as applicable to the Oracle Application Development Framework (ADF) controller in computer Science. .If you feel my answer is good you may Upvote my answer.I find it was downvoted, by whom,I do not know.
P.S.
Power diagram:
In computational geometry, a power diagram is a partition of the Euclidean plane into polygonal cells defined from a set of circles, where the cell for a given circle C consists of all the points for which the power distance to C is smaller than the power distance to the other circles. It is a form of generalized Voronoi diagram, and coincides with the Voronoi diagram of the circle centers in the case that all the circles have equal radii.
Link: http://en.wikipedia.org/wiki/Power_diagram
Also Please Refer to my Data Set in R.G. " Voronoi Diagrams and Delaunay Tringulations-Their Aplications in Computer Science"
ABSTRACT: Voronoi Diagrams and Delaunay Tringulations(Power Diagrams) are the latest trend in not only Computer Science,but in many other Areas. Delaunay Triangulations is Dual of Voronoi Diagrams. Delaunay implies Optimization. Locally Delaunay everywhere ⇐⇒ Globally Delaunay. These Diagrams get the Optimal Solutions in one Stretch. The Presentation had been given by the Author to the Faculty of C.S.E. and I.T. Departments of V.B.I.T.,Hyderabad and was well Received. It is only a Compilation done by the Author from different Resources and not a Original Work. It will help a Peep into this New Area of Research.
Link: https://www.researchgate.net/publication/272033927_Voronoi_Diagrams__Delaunay_Triangulations_-_Their_Applications_in_Computer_Science
P.S.
Data Voronoi Diagrams & Delaunay Triangulations - Their Applicati...
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Inorganic Materials
- Ceramics
- Glass