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Voronoi diagrams (Automatic version)	Ordinary	Multiplicatively Weighted /Area	Additively W /Area	PW(additively Weighted Power)	Compoundly W	LW(L_{weight} norm)
	Higher-order	HMW	HAW	HPW	HCW	HLW
	Elliptic	Manhattan	Supremum	Karlsruhe	Farthest-point
	HElliptic	HManhattan Farthest-Point Manhattan	HSupremum	HKarlsruhe	Higher-order Farthest-point
	line-segment		line-segments sometimes cross each other		line-segments need to cross each other	largest empty circle in a polygon
	Higher order line-segment		Higher 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 Tessellation	order-2 Delaunay	Order-3 Delaunay	Farthest Delaunay
	Delaunay some edges deleted	-	-	Extended Voronoi Edges	-	-
	Voronoi area game for two	for three	for four	for five	for six	-
Voronoi diagrams (Click version)	Ordinary	-				Largest Empty circle in a polygon
	Higher-order
	-	Manhattan	Supremum	Karlsruhe	Farthest-point
		HManhattan Farthest-Point Manhattan	HSupremum	HKarlsruhe
	Area of Voronoi Region	Delaunay Tessellation	order-2 Delaunay	Order-3 Delaunay	Farthest Delaunay
	Voronoi area game for two	for three	for four	for five	for six	-

CW, LW and Karlsruhe are very heavy.

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Multiplicatively weighted Voronoi diagram(Open 5/Sep/2000 : The 4th Revision Wednesday, 30-Jun-2010 23:04:07 JST)

Multiplicatively weighted Voronoi diagram
Sort generators such that w[1]<w[2]<...<w{N]
i=1,...,N-1
    j=i+1,...,N
        Consider a bisector of p(i) and p(j) Apporonius' circle; they mean that points are the rate of distance from i and distance from j is same.
        for x=left edge of circle to right edge of circle
            compute y for x, upper arc of the circle
            compute d from (x,y) to i
            set cnt=0
            k=1,...,N except for i and j
                compute d_k from (x,y) to k
                if d_k<d then cnt=1 and break
            next k
            if cnt=0 then plot (x,y)
            compute y for x, lower arc of the circle
            compute d from (x,y) to i
            set cnt=0
            k=1,...,N except for i and j
                compute d_k from (x,y) to k
                if d_k<d then cnt=1 and break
            next k
            if cnt=0 then plot (x,y)
        next x
        for y=bottom of circle to top of circle
            same logic of x
        next y
    next j
next i



Ordinary Voronoi diagram
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))
            h=1,...,N except for i and j
                Let d' be d(c,p(h))
                If d'<d then shout (Out!)
            next h
            If we did not shout, then draw the interval of the points of intersection
         next k
    next j
next i

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