In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on 'closeness' 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'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.

1. 1

2. 2

4. http://lpetrich.org/Science/GeometryDemo/GeometryDemo_GMap.html

11. p1, p2, . . . , pn
pi pi pj
pj ≠

12. pi
pi
pi

16. e
pi pj
pk

17. pi
pi

19. mv – me + mf =2

21. Mv-Me+Mf=2
let call Mv as nv , (nv+1) – ne+n = 2
Me 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

22. Cp

23. Cp
pi pj
Cp pi pj

24. Cp
pi pj pk
pi pj
pk
pi pj
pk
pi
pj pk
pi pj pk

25. pi pj
pi pj
pi pj pk
pi pj
pi
pj

26. 26

27. T(n) = O(n² log n)
pi
pi pj ≠

31. • l+
l+
l+

32. `

35. pj

36. ly
• pj pj,x pj,y
pi,y pj,y ly

38. pi pk

55. 55