# 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 Higher order Voronoi diagram(Open 5/Sep/2000 : The 5th Revision Thursday, 03-Jun-2010 22:12:25 JST)

If we use Higher order Voronoi diagram, we can find out the 2nd or 3rd nearest facility.
White is the first order, green is 2nd, and blue is 3rd.
Algorithm for the higher order Voronoi diagrams (If you want draw the l-th order Voronoi diagram, then m=1,2,...,l)
```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 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 points of intersections
Sort points of intersections in turns of x coordinates
k=1,...,the number of interval of points of intersections
Let c be a middle point of interval of points of intersection
Let d be d(c,p(i))
label=0
h=1,...,N except for i and j
Let d' be d(c,p(h))
If d'<d then label=label+1
next h
If label=m-1, then draw the interval of points of intersection by m-th order's color.
next k
next j
next i
```
And the following is the algorithm of the ordinary Voronoi diagram. It is very similar.
```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 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 points of intersections
Sort points of intersections in turns of x coordinates
k=1,...,the number of interval of points of intersections
Let c be a middle point of interval of points of intersection
Let d be d(c,p(i))
label=0
h=1,...,N except for i and j
Let d' be d(c,p(h))
If d'<d then label=1
next h
If label=0, then draw the interval of points of intersection
next k
next j
next i
```
Java(hivoro.java)

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