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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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Supremum-metric Voronoi diagram(Open 5/Sep/2000 : The 4th Revision Thursday, 03-Jun-2010 22:12:50 JST)

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 at x=0 and x=(the width of the screen) of the bisector of i and 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

but the bisector of supremum-metric Voronoi diagram is not line.
it is conbination of diagonal half-line, horizontal line segment and diagonal half-line (type 1) or
                     diagonal half-line, vertical line segment and diagonal half-line (type 2)
           (See Okabe et al. Soatial tessellations 2nd ed. Fig. 3.7.4)
  this conbination type is decided by the difference of x-coordinate and difference of y-coordinate.
 that is, if difference of x-coordinates is larger than the difference of y-coordinates then type 2 and
         if difference of y-coordinates is larger than the difference of x-coordinates then type 1
         (I don't consider the case that the differences are exactly same because the probability is 0 since generators are made from random variables.)

By the way, I set y=400 x+? instead of the vertical line segment (x=?) of the type-2, sorry.

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