Reload
Voronoi
diagrams
(Automatic
version)
OrdinaryMultiplicatively Weighted
/Area
Additively W
/Area
PW(additively Weighted Power)Compoundly WLW(L_{weight} norm)
Higher-order HMWHAWHPWHCWHLW
EllipticManhattanSupremumKarlsruheFarthest-point
HEllipticHManhattan
Farthest-Point Manhattan
HSupremumHKarlsruheHigher-order Farthest-point
line-segmentline-segments sometimes cross each otherline-segments need to cross each otherlargest empty circle in a polygon
Higher order line-segmentHigher order line-segment
(segnebts sometimes cross each other)
Higher order line-segment
(segments need to cross each other)
Area of Voronoi Region
/MW Area
/AW Area
Delaunay Tessellationorder-2 DelaunayOrder-3 DelaunayFarthest Delaunay
Delaunay
some edges deleted
--Extended Voronoi Edges--
Voronoi area game
for two
for threefor fourfor fivefor six-
Voronoi
diagrams
(Click
version)
Ordinary-Largest Empty circle in a polygon
Higher-order
-ManhattanSupremumKarlsruheFarthest-point
HManhattan
Farthest-Point Manhattan
HSupremumHKarlsruhe
Area of Voronoi RegionDelaunay Tessellationorder-2 DelaunayOrder-3 DelaunayFarthest Delaunay
Voronoi area game
for two
for threefor fourfor fivefor six-
CW, LW and Karlsruhe are very heavy.
Screensaver for Win 95,98

Automatic versionCenter problemEmpty circle, Largest empty circleLargest empty ellipse
Click versionCenter problemEmpty circle, Largest empty circle-
Voronoi diagram(Automatic version)EVoronoi diagram(Click version)
Farthest point Voronoi diagram(Automatic version)EFarthest point Voronoi diagram(Click version)
Elliptic Voronoi diagram(Automatic version)
Farthest-point Voronoi diagram(Open 5/Sep/2000 : The 4th Revision Saturday, 19-Jun-2010 22:55:41 JST)


If we use Farthest-point Voronoi diagram, we can find out the farthest facility.

Algorithm
i=1,...,N-1
    j=i+1,...,N
        Consider a bisector of p(i) and p(j)
        k=1,...,N except for i and j
            Consider a bisector of p(i) and p(k)
            Calculate the points of intersection of bisector(i,j) and bisector(i,k)
        next k
        Add the points x=0 and x=(the width of screen) of the bisector (i,j) into the points of intersections
        Sort the points of intersections in terms of x coordinates
        k=1,...,the number of intervals of the points of intersections
            Let c be a midpoint of the interval of the points of intersection.
            Let d be d(c,p(i))
            cnt=0
            h=1,...,N except for i and j
                Let d' be d(c,p(h))
                If d'<d then shout cnt=cnt+1
            next h
            If cnt=N-2, then draw the interval of the points of intersection
         next k
    next j
next i

Java(fpvoro.java)

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