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07-Jul-2015
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In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on &#x27;closeness&#x27; to points in a specific subset of the plane. In this presentation you will seen definitions of Voronoi Diagrams and also computing Voronoi Diagrams ways. Proofs are explained in details and easiest way. Attention!: This presentation has animation effects to describe problems better and visually, so you should download it and then view it with Microsoft PowerPoint, or you can&#x27;t see parts of some pages. Also this file has first two parts of subjects: "Definition and Basic Properties" &"Computing the Voronoi Diagram". Feel free to ask your questions.

Transcript of Voronoi Diagrams

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2. 2 3. http://lpetrich.org/Science/GeometryDemo/GeometryDemo_GMap.html 4. p1, p2, . . . , pnpi pi pjpj 5. pipipi 6. epi pjpk 7. pipi 8. mv me + mf =2 9. Mv-Me+Mf=2let call Mv as nv , (nv+1) ne+n = 2Me as ne ,(number of sites)Mf as n(sum of all degrees) 2ne, 2ne 3(nv+1), 2ne 3(2+ne-n)3(nv+1)2ne 6+3ne-3n ne 3n-6, n-2+(nv+1) 3n-6 nv 2n-5 10. Cp 11. Cppi pjCp pi pj 12. Cppi pj pkpi pjpkpi pjpkpipj pkpi pj pk 13. pi pjpi pjpi pj pkpi pjpipj 14. 26 15. T(n) = O(n log n)pipi pj 16. l+l+l+ 17. ` 18. pj 19. ly pj pj,x pj,ypi,y pj,y ly 20. pi pk 21. 55