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

Multiplicatively weighted Voronoi diagram is drawn by using distance function d(p,p(i))
d(p,p(i))=dis(p,p(i))/w(i)
where dis is Euclidean distance and w(i) is the weight of p(i).
An edge are generally circular arc.

Algorithm
```Multiplicatively weighted Voronoi diagram
Sort generators such that w<w<...<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

```
Java(mwvoro.java)
VB code(voromwexe.lzh)

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