A divide-and-conquer algorithm for computing voronoi diagram
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A divide-and-conquer algorithm for computing voronoi diagram
VD
Voronoi
G. F. Voronoi (1868~1908) Voronoi
(Subdivision)(region),
DCEL
DCEL ()
Doubly-Connected Edge List
e->twin->oriV
plane sweep(divide-and-conquer).
VD(S1), VD(S2), VD(S3), …, VD(Sn)
DCEL VD pS p
DCEL VD(Sn)
O(n2logn)
2
Plane sweep
() sweep line
()Voronoi
3:
VD(S)
return(dacVD(S, 1, n))
return (j-i < 3) ?
trivialVD(S, i, j) :
x 2 3
2-3 VD VDSL VD(SR)merge
merge contour contour
:
1:, site ,, 2;,
3: voronoi .
2
6:.
1:.
2:.
face, face .
1:,.
site LSite2 RSite2.
2: site1 site2 ,,
site Line1 , voronoi .
,, 3; 4;
face ..
4:, face , face
. face ,
Original_Halfedge,
site1. site1 LSite2,site2 RSite2,
merge . 2;, 6.
6:,LSite2 RSite2 ,
n
Voronoi O(n)
O(n)
2
O(nlogn)
Voronoi
[1] M. I. Shamos and D. Hoey. Closest-point problems. In Proc. 16 th
Annu. IEEE Symbos. Found. Comput. Sci. ,pages 151-162, 1975.
[2] L. J. Guibas and J. Stolfi, Primitives for the manipulation of general
subdivisions and the computions of Voronoi diagrams, ACM Trans.
Graph. 4 (1985), 74-123.
[3] A. Okabe, B. Boots, and K. Sugihara, Spatial Tessellations, Concepts
and Applications of Voronoi diagrams, John Wiley & Sons Ltd.
England (1992)
.
Voronoi
G. F. Voronoi (1868~1908) Voronoi
(Subdivision)(region),
DCEL
DCEL ()
Doubly-Connected Edge List
e->twin->oriV
plane sweep(divide-and-conquer).
VD(S1), VD(S2), VD(S3), …, VD(Sn)
DCEL VD pS p
DCEL VD(Sn)
O(n2logn)
2
Plane sweep
() sweep line
()Voronoi
3:
VD(S)
return(dacVD(S, 1, n))
return (j-i < 3) ?
trivialVD(S, i, j) :
x 2 3
2-3 VD VDSL VD(SR)merge
merge contour contour
:
1:, site ,, 2;,
3: voronoi .
2
6:.
1:.
2:.
face, face .
1:,.
site LSite2 RSite2.
2: site1 site2 ,,
site Line1 , voronoi .
,, 3; 4;
face ..
4:, face , face
. face ,
Original_Halfedge,
site1. site1 LSite2,site2 RSite2,
merge . 2;, 6.
6:,LSite2 RSite2 ,
n
Voronoi O(n)
O(n)
2
O(nlogn)
Voronoi
[1] M. I. Shamos and D. Hoey. Closest-point problems. In Proc. 16 th
Annu. IEEE Symbos. Found. Comput. Sci. ,pages 151-162, 1975.
[2] L. J. Guibas and J. Stolfi, Primitives for the manipulation of general
subdivisions and the computions of Voronoi diagrams, ACM Trans.
Graph. 4 (1985), 74-123.
[3] A. Okabe, B. Boots, and K. Sugihara, Spatial Tessellations, Concepts
and Applications of Voronoi diagrams, John Wiley & Sons Ltd.
England (1992)
.
