# Reload Voronoidiagrams(Automaticversion)OrdinaryMultiplicatively Weighted/AreaAdditively W/AreaPW(additively Weighted Power)Compoundly WLW(L_{weight} norm) Higher-order HMWHAWHPWHCWHLW EllipticManhattanSupremumKarlsruheFarthest-point HEllipticHManhattanFarthest-Point ManhattanHSupremumHKarlsruheHigher-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 AreaDelaunay Tessellationorder-2 DelaunayOrder-3 DelaunayFarthest Delaunay Delaunaysome edges deleted--Extended Voronoi Edges-- Voronoi area gamefor twofor threefor fourfor fivefor six- Voronoidiagrams(Clickversion)Ordinary-Largest Empty circle in a polygon Higher-order -ManhattanSupremumKarlsruheFarthest-point HManhattanFarthest-Point ManhattanHSupremumHKarlsruhe Area of Voronoi RegionDelaunay Tessellationorder-2 DelaunayOrder-3 DelaunayFarthest Delaunay Voronoi area gamefor twofor threefor fourfor fivefor six- CW, LW and Karlsruhe are very heavy.Screensaver for Win 95,98 Manhattan-metric Voronoi diagram(Open 5/Sep/2000 : The 5th Revision Thursday, 03-Jun-2010 22:12:47 JST)

Manhattan-metric Voronoi diagram is drawn by using distance function d(p,p(i))
d(p,p(i))=|x-x(i)|+|y-y(i)|
where (x,y) is the coordinate of p, (x(i),y(i)) is the coordinate of p(i), |a| is a sign of absolute value.
Special case Manhattan Voronoi diagram for square lattice generators Manhattan Voronoi diagram for radial generators 1 Manhattan Voronoi diagram for radial generators 2 Manhattan Voronoi diagram for triangular lattice generators Manhattan Voronoi diagram for hexagonal lattice generators

Algorithm
the concept is very close to that of the ordinary Voronoi diagram
Following algorithm is for the 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 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 Manhattan Voronoi diagram is not line.
it is conbination of horizontal half-line, diagonal line segment and horizontal half-line (type 1) or
vertical half-line, diagonal line segment and vertical half-line(type 2)
(See Okabe et al. Soatial tessellations 2nd ed. Fig. 3.7.2)
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 half-line(x=?) of the type-2, sorry.
```

Java(man.java)

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