Voronoi diagram

Voronoi diagram
You are encouraged to solve this task according to the task description, using any language you may know.

A Voronoi diagram is a diagram consisting of a number of sites. Each Voronoi site s also has a Voronoi cell consisting of all points closest to s.

The task is to demonstrate how to generate and display a Voroni diagram. See algo K-means++ clustering.

C

C code drawing a color map of a set of Voronoi sites. Image is in PNM P6, written to stdout. Run as a.out > stuff.pnm. <lang c>#include <stdio.h>

1. include <stdlib.h>
2. include <string.h>

1. define N_SITES 150

double site[N_SITES][2]; unsigned char rgb[N_SITES][3];

int size_x = 640, size_y = 480;

inline double sq2(double x, double y) { return x * x + y * y; }

1. define for_k for (k = 0; k < N_SITES; k++)

int nearest_site(double x, double y) { int k, ret = 0; double d, dist = 0; for_k { d = sq2(x - site[k][0], y - site[k][1]); if (!k || d < dist) { dist = d, ret = k; } } return ret; }

/* see if a pixel is different from any neighboring ones */ int at_edge(int *color, int y, int x) { int i, j, c = color[y * size_x + x]; for (i = y - 1; i <= y + 1; i++) { if (i < 0 || i >= size_y) continue;

for (j = x - 1; j <= x + 1; j++) { if (j < 0 || j >= size_x) continue; if (color[i * size_x + j] != c) return 1; } } return 0; }

1. define AA_RES 4 /* average over 4x4 supersampling grid */

void aa_color(unsigned char *pix, int y, int x) { int i, j, n; double r = 0, g = 0, b = 0, xx, yy; for (i = 0; i < AA_RES; i++) { yy = y + 1. / AA_RES * i + .5; for (j = 0; j < AA_RES; j++) { xx = x + 1. / AA_RES * j + .5; n = nearest_site(xx, yy); r += rgb[n][0]; g += rgb[n][1]; b += rgb[n][2]; } } pix[0] = r / (AA_RES * AA_RES); pix[1] = g / (AA_RES * AA_RES); pix[2] = b / (AA_RES * AA_RES); }

1. define for_i for (i = 0; i < size_y; i++)
2. define for_j for (j = 0; j < size_x; j++)

void gen_map() { int i, j, k; int *nearest = malloc(sizeof(int) * size_y * size_x); unsigned char *ptr, *buf, color;

ptr = buf = malloc(3 * size_x * size_y); for_i for_j nearest[i * size_x + j] = nearest_site(j, i);

for_i for_j { if (!at_edge(nearest, i, j)) memcpy(ptr, rgb[nearest[i * size_x + j]], 3); else /* at edge, do anti-alias rastering */ aa_color(ptr, i, j); ptr += 3; }

/* draw sites */ for (k = 0; k < N_SITES; k++) { color = (rgb[k][0]*.25 + rgb[k][1]*.6 + rgb[k][2]*.15 > 80) ? 0 : 255;

for (i = site[k][1] - 1; i <= site[k][1] + 1; i++) { if (i < 0 || i >= size_y) continue;

for (j = site[k][0] - 1; j <= site[k][0] + 1; j++) { if (j < 0 || j >= size_x) continue;

ptr = buf + 3 * (i * size_x + j); ptr[0] = ptr[1] = ptr[2] = color; } } }

printf("P6\n%d %d\n255\n", size_x, size_y); fflush(stdout); fwrite(buf, size_y * size_x * 3, 1, stdout); }

1. define frand(x) (rand() / (1. + RAND_MAX) * x)

int main() { int k; for_k { site[k][0] = frand(size_x); site[k][1] = frand(size_y); rgb [k][0] = frand(256); rgb [k][1] = frand(256); rgb [k][2] = frand(256); }

gen_map(); return 0; }</lang>

C++

<lang cpp>

1. include <windows.h>
2. include <vector>
3. include <string>

//-------------------------------------------------------------------------------------------------- using namespace std;

//-------------------------------------------------------------------------------------------------- class point { public:

   int x, y;

   point() { x = y = 0; }
   point( int a, int b ) { x = a; y = b; }
   int distanceSqrd( const point& p )
   {

int xd = p.x - x, yd = p.y - y;

return xd * xd + yd * yd;

   }

}; //-------------------------------------------------------------------------------------------------- class myBitmap { public:

   myBitmap() : pen( NULL ) {}
   ~myBitmap()
   {

DeleteObject( pen ); DeleteDC( hdc ); DeleteObject( bmp );

   }

   bool create( int w, int h )
   {

BITMAPINFO bi; void *pBits; ZeroMemory( &bi, sizeof( bi ) );

bi.bmiHeader.biSize = sizeof( bi.bmiHeader ); bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8; bi.bmiHeader.biCompression = BI_RGB; bi.bmiHeader.biPlanes = 1; bi.bmiHeader.biWidth = w; bi.bmiHeader.biHeight = -h;

HDC dc = GetDC( GetConsoleWindow() ); bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 ); if( !bmp ) return false;

hdc = CreateCompatibleDC( dc ); SelectObject( hdc, bmp ); ReleaseDC( GetConsoleWindow(), dc );

width = w; height = h;

return true;

   }

   void setPenColor( DWORD clr )
   {

if( pen ) DeleteObject( pen ); pen = CreatePen( PS_SOLID, 1, clr ); SelectObject( hdc, pen );

   }

   void saveBitmap( string path )
   {

BITMAPFILEHEADER fileheader; BITMAPINFO infoheader; BITMAP bitmap; DWORD* dwpBits; DWORD wb; HANDLE file;

GetObject( bmp, sizeof( bitmap ), &bitmap );

dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight]; ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) ); ZeroMemory( &infoheader, sizeof( BITMAPINFO ) ); ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );

infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8; infoheader.bmiHeader.biCompression = BI_RGB; infoheader.bmiHeader.biPlanes = 1; infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader ); infoheader.bmiHeader.biHeight = bitmap.bmHeight; infoheader.bmiHeader.biWidth = bitmap.bmWidth; infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );

fileheader.bfType = 0x4D42; fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER ); fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;

GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );

file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL ); WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL ); WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL ); WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL ); CloseHandle( file );

delete [] dwpBits;

   }

   HDC getDC()     { return hdc; }
   int getWidth()  { return width; }
   int getHeight() { return height; }

private:

   HBITMAP bmp;
   HDC	    hdc;
   HPEN    pen;
   int	    width, height;

}; //-------------------------------------------------------------------------------------------------- class Voronoi { public:

   void make( myBitmap* bmp, int count )
   {

_bmp = bmp; createPoints( count ); createColors(); createSites(); setSitesPoints();

   }

private:

   void createSites()
   {

int w = _bmp->getWidth(), h = _bmp->getHeight(), d; for( int hh = 0; hh < h; hh++ ) { for( int ww = 0; ww < w; ww++ ) { point bpt( ww, hh ); int ind = -1, dist = INT_MAX; for( int it = 0; it < points.size(); it++ ) { d = ( points[it] ).distanceSqrd( bpt ); if( d < dist ) { dist = d; ind = it; } }

if( ind > -1 ) SetPixel( _bmp->getDC(), ww, hh, colors[ind] ); else __asm nop // should never happen! }

       }
   }

   void setSitesPoints()
   {

for( vector<point>::iterator it = points.begin(); it < points.end(); it++ ) { int x = ( *it ).x, y = ( *it ).y; for( int i = -1; i < 2; i++ ) for( int j = -1; j < 2; j++ ) SetPixel( _bmp->getDC(), x + i, y + j, 0 ); }

   }

   void createPoints( int count )
   {

int w = _bmp->getWidth() - 20, h = _bmp->getHeight() - 20; for( int i = 0; i < count; i++ ) { point p( rand() % w + 10, rand() % h + 10 ); points.push_back( p ); }

   }

   void createColors()
   {

for( int i = 0; i < points.size(); i++ ) { DWORD c = RGB( rand() % 200 + 50, rand() % 200 + 55, rand() % 200 + 50 ); colors.push_back( c ); }

   }

   vector<point> points;
   vector<DWORD> colors;
   myBitmap* _bmp;

}; //-------------------------------------------------------------------------------------------------- int main(int argc, char* argv[]) {

   ShowWindow( GetConsoleWindow(), SW_MAXIMIZE );
   srand( GetTickCount() );

   myBitmap bmp;
   bmp.create( 512, 512 );
   bmp.setPenColor( 0 );

   Voronoi v;
   v.make( &bmp, 50 );

   BitBlt( GetDC( GetConsoleWindow() ), 20, 20, 522, 522, bmp.getDC(), 0, 0, SRCCOPY );
   bmp.saveBitmap( "f://rc//v.bmp" );

   system( "pause" );

   return 0;

} //-------------------------------------------------------------------------------------------------- </lang>

D

Translation of: Go

<lang d>import std.random, std.algorithm, std.range, bitmap;

struct Point { int x, y; }

Point[] randomPoints(in size_t nPoints, in size_t nx, in size_t ny) {

   immutable RndPt = (int) => Point(uniform(0, nx), uniform(0, ny));
   return iota(nPoints).map!RndPt().array();

}

Image!RGB generateVoronoi(in Point[] pts,

                         in size_t nx, in size_t ny) {
   // Generate a random color for each site.
   immutable RndRBG = (int) => RGB(cast(ubyte)uniform(0, 256),
                                   cast(ubyte)uniform(0, 256),
                                   cast(ubyte)uniform(0, 256));
   const colors = iota(pts.length).map!RndRBG().array();

   // Generate diagram by coloring pixels with color of nearest site.
   auto img = new typeof(return)(nx, ny);
   foreach (immutable x; 0 .. nx)
       foreach (immutable y; 0 .. ny) {
           immutable dCmp = (in Point a, in Point b) nothrow =>
               ((a.x - x) ^^ 2 + (a.y - y) ^^ 2) <
               ((b.x - x) ^^ 2 + (b.y - y) ^^ 2);
           img[x, y] = colors[pts.length - minPos!dCmp(pts).length];
       }

   // Mark each site with a black dot.
   foreach (immutable p; pts)
       img[p.x, p.y] = RGB.black;
   return img;

}

void main() {

   enum imageWidth = 640,
        imageHeight = 480;
   randomPoints(150, imageWidth, imageHeight)
   .generateVoronoi(imageWidth, imageHeight)
   .savePPM6("voronoi.ppm");

}</lang>

Go

Output png

<lang go>package main

import (

   "fmt"
   "image"
   "image/color"
   "image/draw"
   "image/png"
   "math/rand"
   "os"
   "time"

)

const (

   imageWidth  = 300
   imageHeight = 200
   nSites      = 10

)

func main() {

   writePngFile(generateVoronoi(randomSites()))

}

func generateVoronoi(sx, sy []int) image.Image {

   // generate a random color for each site
   sc := make([]color.NRGBA, nSites)
   for i := range sx {
       sc[i] = color.NRGBA{uint8(rand.Intn(256)), uint8(rand.Intn(256)),
           uint8(rand.Intn(256)), 255}
   }

   // generate diagram by coloring each pixel with color of nearest site
   img := image.NewNRGBA(image.Rect(0, 0, imageWidth, imageHeight))
   for x := 0; x < imageWidth; x++ {
       for y := 0; y < imageHeight; y++ {
           dMin := dot(imageWidth, imageHeight)
           var sMin int
           for s := 0; s < nSites; s++ {
               if d := dot(sx[s]-x, sy[s]-y); d < dMin {
                   sMin = s
                   dMin = d
               }
           }
           img.SetNRGBA(x, y, sc[sMin])
       }
   }
   // mark each site with a black box
   black := image.NewUniform(color.Black)
   for s := 0; s < nSites; s++ {
       draw.Draw(img, image.Rect(sx[s]-2, sy[s]-2, sx[s]+2, sy[s]+2),
           black, image.ZP, draw.Src)
   }
   return img

}

func dot(x, y int) int {

   return x*x + y*y

}

func randomSites() (sx, sy []int) {

   rand.Seed(time.Now().Unix())
   sx = make([]int, nSites)
   sy = make([]int, nSites)
   for i := range sx {
       sx[i] = rand.Intn(imageWidth)
       sy[i] = rand.Intn(imageHeight)
   }
   return

}

func writePngFile(img image.Image) {

   f, err := os.Create("voronoi.png")
   if err != nil {
       fmt.Println(err)
       return
   }
   if err = png.Encode(f, img); err != nil {
       fmt.Println(err)
   }
   if err = f.Close(); err != nil {
       fmt.Println(err)
   }

}</lang>

Icon and Unicon

The sample images to the right show the screen size, number of sites, and metric used in the title bar.

<lang Icon>link graphics,printf,strings

record site(x,y,colour) # site data position and colour invocable all # needed for string metrics

procedure main(A) # voronoi

&window := open("Voronoi","g","bg=black") | stop("Unable to open window")

WAttrib("canvas=hidden") # figure out maximal size width & height WAttrib(sprintf("size=%d,%d",WAttrib("displaywidth"),WAttrib("displayheight"))) WAttrib("canvas=maximal") height := WAttrib("height") width  := WAttrib("width")

metrics := ["hypot","taxi","taxi3"] # different metrics

while case a := get(A) of { # command line arguments

 "--sites"  | "-s" : sites  := 0 < integer(a := get(A)) | runerr(205,a)
 "--height" | "-h" : height := 0 < (height >= integer(a := get(A))) | runerr(205,a)
 "--width"  | "-w" : width  := 0 < (width  >= integer(a := get(A))) | runerr(205,a)
 "--metric" | "-m" : metric := ((a := get(A)) == !metrics) | runerr(205,a)
 "--help"   | "-?" : write("Usage:\n voronoi [[--sites|-s] n] ",

"[[--height|-h] pixels] [[--width|-w] pixels]", "[[--metric|-m] metric_procedure]", "[--help|-?]\n\n")

 }

/metric := metrics[1] # default to normal /sites := ?(r := integer(.1*width)) + r # sites = random .1 to .2 of width if not given

WAttrib(sprintf("label=Voronoi %dx%d %d %s",width,height,sites,metric)) WAttrib(sprintf("size=%d,%d",width,height))

x := "0123456789abcdef" # hex for random sites (colour) siteL := [] every 1 to sites do # random sites

 put(siteL, site(?width,?height,cat("#",?x,?x,?x,?x,?x,?x))) 

VoronoiDiagram(width,height,siteL,metric) # Voronoi-ize it WDone() end

procedure hypot(x,y,site) # normal metric return sqrt((x-site.x)^2 + (y-site.y)^2) end

procedure taxi(x,y,site) # "taxi" metric return abs(x-site.x)+abs(y-site.y) end

procedure taxi3(x,y,site) # copied from a commented out version (TCL) return (abs(x-site.x)^3+abs(y-site.y)^3)^(.3) end

procedure VoronoiDiagram(width,height,siteL,metric)

  /metric := hypot
  every y := 1 to height & x := 1 to width do {
     dist := width+height         # anything larger than diagonal
     every site := !siteL do {
        if dist < (dt :=  metric(x,y,site)) then next  # skip
        else if dist >:= dt then Fg(site.colour)       # site
        else Fg("#000000")                             # unowned
        DrawPoint(x,y)
        }
     }

  Fg("Black")
  every site := !siteL do                              # mark sites
     DrawCircle(site.x,site.y,1)     

end</lang>

Library: Icon Programming Library

printf.icn provides the printf family graphics.icn provides graphics support strings.icn provides cat

J

A straightforward solution: generate random points and for each pixel find the index of the least distance. Note that the square root is avoided to improve performance. <lang j>NB. (number of points) voronoi (shape) NB. Generates an array of indices of the nearest point voronoi =: 4 :0

 p =. (x,2) ?@$ y
 (i.<./)@:(+/@:*:@:-"1&p)"1 ,"0/&i./ y

) viewmat 25 voronoi 500 500</lang>

Another solution generates Voronoi cells from Delaunay triangulation. The page Voronoi diagram/J/Delaunay triangulation also contains a convex hull algorithm.

Liberty BASIC

For first site it fills the table with distances to that site. For other sites it looks at vertical lines left and right from its location. If no place on a vertical line is closer to the current site, then there's no point looking further left or right. Don't bother square-rooting to get distances.. <lang lb> WindowWidth =600 WindowHeight =600

sites = 100 xEdge = 400 yEdge = 400 graphicbox #w.gb1, 10, 10, xEdge, yEdge

open "Voronoi neighbourhoods" for window as #w

1. w "trapclose quit"
2. w.gb1 "down ; fill black ; size 4"
3. w.gb1 "font courier_new 12"

dim townX( sites), townY( sites), col$( sites)

for i =1 to sites

   townX( i) =int( xEdge *rnd( 1))
   townY( i) =int( yEdge *rnd( 1))
   col$( i) = int( 256 *rnd( 1)); " "; int( 256 *rnd( 1)); " "; int( 256 *rnd( 1))
   #w.gb1 "color "; col$( i)
   #w.gb1 "set "; townX( i); " "; townY( i)

next i

1. w.gb1 "size 1"

dim nearestIndex(xEdge, yEdge) dim dist(xEdge, yEdge)

start = time$("ms")

'fill distance table with distances from the first site for x = 0 to xEdge - 1

   for y = 0 to yEdge - 1
       dist(x, y) = (townX(1) - x) ^ 2 + (townY(1) - y) ^ 2
       nearestIndex(x, y) = 1
   next y

next x

1. w.gb1 "color darkblue"

'for other towns for i = 2 to sites

   'display some progress
   #w.gb1 "place 0 20"
   #w.gb1 "\computing: "; using("###.#", i / sites * 100); "%"
   'look left
   for x = townX(i) to 0 step -1
       if not(checkRow(i, x,0, yEdge - 1)) then exit for
   next x
   'look right
   for x = townX(i) + 1 to xEdge - 1
       if not(checkRow(i, x, 0, yEdge - 1)) then exit for
   next x
   scan

next i

for x = 0 to xEdge - 1

   for y =0 to yEdge - 1
       #w.gb1 "color "; col$(nearestIndex(x, y))
       startY = y
       nearest = nearestIndex(x, y)
       for y = y + 1 to yEdge
           if nearestIndex(x, y) <> nearest then y = y - 1 : exit for
       next y
       #w.gb1 "line "; x; " "; startY; " "; x; " "; y + 1
   next y

next x

1. w.gb1 "color black; size 4"

for i =1 to sites

   #w.gb1 "set "; townX( i); " "; townY( i)

next i print time$("ms") - start wait

sub quit w$

   close #w$
   end

end sub

function checkRow(site, x, startY, endY)

   dxSquared = (townX(site) - x) ^ 2
   for y = startY to endY
        dSquared = (townY(site) - y) ^ 2 + dxSquared
        if dSquared <= dist(x, y) then
            dist(x, y) = dSquared
            nearestIndex(x, y) = site
            checkRow = 1
        end if
   next y

end function </lang>

Mathematica

<lang Mathematica>Needs["ComputationalGeometry`"] DiagramPlot[{{4.4, 14}, {6.7, 15.25}, {6.9, 12.8}, {2.1, 11.1}, {9.5, 14.9}, {13.2, 11.9}, {10.3, 12.3}, {6.8, 9.5}, {3.3, 7.7}, {0.6, 5.1}, {5.3, 2.4}, {8.45, 4.7}, {11.5, 9.6}, {13.8, 7.3}, {12.9, 3.1}, {11, 1.1}}]</lang>

Prolog

Works with SWI-Prolog and XPCE.
3 Voronoi diagrams are given for the same sites, one with the Manhattan distance, one with the Euclidean distance and the last with the Minkowski distance (order 3).

<lang Prolog>:- dynamic pt/6. voronoi :- V is random(20) + 20, retractall(pt(_,_,_,_)), forall(between(1, V, I), ( X is random(390) + 5, Y is random(390) + 5, R is random(65535), G is random(65535), B is random(65535), assertz(pt(I,X,Y, R, G, B)) )), voronoi(manhattan, V), voronoi(euclide, V), voronoi(minkowski_3, V).

voronoi(Distance, V) :- sformat(A, 'Voronoi 400X400 ~w ~w', [V, Distance]), new(D, window(A)), send(D, size, size(400,400)), new(Img, image(@nil, width := 400, height := 400 , kind := pixmap)),

       % get the list of the sites

bagof((N, X, Y), R^G^B^pt(N, X, Y, R, G, B), L),

forall(between(0,399, I), forall(between(0,399, J), ( get_nearest_site(V, Distance, I, J, L, S), pt(S, _, _, R, G, B), send(Img, pixel(I, J, colour(@default, R, G, B)))))),

new(Bmp, bitmap(Img)), send(D, display, Bmp, point(0,0)), send(D, open).

% define predicatea foldl (functionnal spirit) foldl([], _Pred, R, R).

foldl([H | T], Pred, Acc, R) :- call(Pred, H, Acc, R1), foldl(T, Pred, R1, R).

% predicate for foldl compare(Distance, XP, YP, (N, X, Y), (D, S), R) :- call(Distance, XP, YP, X, Y, DT), ( DT < D -> R = (DT, N) ; R = (D, S)).

% use of a fake site for the init of foldl get_nearest_site(Distance, I, J, L, S) :- foldl(L, compare(Distance, I, J), (65535, nil), (_, S)).

manhattan(X1, Y1, X2, Y2, D) :- D is abs(X2 - X1) + abs(Y2-Y1).

euclide(X1, Y1, X2, Y2, D) :- D is sqrt((X2 - X1)**2 + (Y2-Y1)**2).

minkowski_3(X1, Y1, X2, Y2, D) :- D is (abs(X2 - X1)**3 + abs(Y2-Y1)**3)**0.33. </lang>

PureBasic

Euclidean

Voronoi Diagram in PureBasic

<lang PureBasic>Structure VCoo

 x.i:  y.i
 Colour.i: FillColour.i

EndStructure

Macro RandInt(MAXLIMIT)

 Int(MAXLIMIT*(Random(#MAXLONG)/#MAXLONG))

EndMacro

Macro SQ2(X, Y)

 ((X)*(X) + (Y)*(Y))

EndMacro

Procedure GenRandomPoints(Array a.VCoo(1), xMax, yMax, cnt)

 Protected i, j, k, l
 cnt-1
 Dim a(cnt)
 For i=0 To cnt
   a(i)\x = RandInt(xMax): a(i)\y = RandInt(yMax)
   j = RandInt(255): k = RandInt(255): l = RandInt(255)
   a(i)\Colour = RGBA(j, k, l, 255)
   a(i)\FillColour = RGBA(255-j, 255-k, 255-l, 255)
 Next i
 ProcedureReturn #True

EndProcedure

Procedure MakeVoronoiDiagram(Array a.VCoo(1),xMax, yMax) ; Euclidean

 Protected i, x, y, img, dist.d, dt.d
 img = CreateImage(#PB_Any, xMax+1, yMax+1)
 If StartDrawing(ImageOutput(img))
   For y=0 To yMax
     For x=0 To xMax
       dist = Infinity()
       For i=0 To ArraySize(a())
         dt = SQ2(x-a(i)\x, y-a(i)\y)
         If dt > dist 
           Continue
         ElseIf dt < dist
           dist = dt
           Plot(x,y,a(i)\FillColour)
         Else ; 'Owner ship' is unclear, set pixel to transparent.
           Plot(x,y,RGBA(0, 0, 0, 0))
         EndIf
       Next
     Next
   Next
   For i=0 To ArraySize(a())
     Circle(a(i)\x, a(i)\y, 1, a(i)\Colour)
   Next
   StopDrawing()
 EndIf
 ProcedureReturn img 

EndProcedure

Main code

Define img, x, y, file$ Dim V.VCoo(0) x = 640: y = 480 If Not GenRandomPoints(V(), x, y, 150): End: EndIf img = MakeVoronoiDiagram(V(), x, y) If img And OpenWindow(0, 0, 0, x, y, "Voronoi Diagram in PureBasic", #PB_Window_SystemMenu)

 ImageGadget(0, 0, 0, x, y, ImageID(img))
 Repeat: Until WaitWindowEvent() = #PB_Event_CloseWindow

EndIf

UsePNGImageEncoder() file$ = SaveFileRequester("Save Image?", "Voronoi_Diagram_in_PureBasic.png", "PNG|*.png", 0) If file$ <> ""

 SaveImage(img, file$, #PB_ImagePlugin_PNG)

EndIf</lang>

Taxicab

Voronoi Diagram in PureBasic

<lang PureBasic>Structure VCoo

 x.i:  y.i
 Colour.i: FillColour.i

EndStructure

Macro RandInt(MAXLIMIT)

 Int(MAXLIMIT*(Random(#MAXLONG)/#MAXLONG))

EndMacro

Procedure GenRandomPoints(Array a.VCoo(1), xMax, yMax, cnt)

 Protected i, j, k, l
 cnt-1
 Dim a(cnt)
 For i=0 To cnt
   a(i)\x = RandInt(xMax): a(i)\y = RandInt(yMax)
   j = RandInt(255): k = RandInt(255): l = RandInt(255)
   a(i)\Colour = RGBA(j, k, l, 255)
   a(i)\FillColour = RGBA(255-j, 255-k, 255-l, 255)
 Next i
 ProcedureReturn #True

EndProcedure

Procedure MakeVoronoiDiagram(Array a.VCoo(1),xMax, yMax)

 Protected i, x, y, img, dist, dt, dx, dy
 img = CreateImage(#PB_Any, xMax+1, yMax+1, 32)
 If StartDrawing(ImageOutput(img))
   For y=0 To yMax
     For x=0 To xMax
       dist = #MAXLONG
       For i=0 To ArraySize(a())
         dx = x-a(i)\x
         dy = y-a(i)\y
         dt = Sign(dx)*dx + Sign(dy)*dy
         If dt > dist ; no update
           Continue 
         ElseIf dt < dist  ; an new 'owner' is found
           dist = dt
           Plot(x,y,a(i)\FillColour)
         Else ; dt = dist
           Plot(x,y,RGBA(0,0,0,0)) ; no clear 'owner', make the pixel transparent
         EndIf
       Next
     Next
   Next
   For i=0 To ArraySize(a())
     Circle(a(i)\x, a(i)\y, 1, a(i)\Colour)
   Next
   StopDrawing()
 EndIf
 ProcedureReturn img 

EndProcedure

Main code

Define img, x, y, file$ Dim V.VCoo(0) x = 640: y = 480 If Not GenRandomPoints(V(), x, y, 150): End: EndIf img = MakeVoronoiDiagram(V(), x, y) If img And OpenWindow(0, 0, 0, x, y, "Voronoi Diagram in PureBasic", #PB_Window_SystemMenu)

 ImageGadget(0, 0, 0, x, y, ImageID(img))
 Repeat: Until WaitWindowEvent() = #PB_Event_CloseWindow

EndIf

UsePNGImageEncoder() file$ = SaveFileRequester("Save Image?", "Voronoi_Diagram_in_PureBasic.png", "PNG|*.png", 0) If file$ <> ""

 SaveImage(img, file$, #PB_ImagePlugin_PNG)

EndIf</lang>

Python

This implementation takes in a list of points, each point being a tuple and returns a dictionary consisting of all the points at a given site. <lang python>from PIL import Image import random import math

def generate_voronoi_diagram(width, height, num_cells): image = Image.new("RGB", (width, height)) putpixel = image.putpixel imgx, imgy = image.size nx = [] ny = [] nr = [] ng = [] nb = [] for i in range(num_cells): nx.append(random.randrange(imgx)) ny.append(random.randrange(imgy)) nr.append(random.randrange(256)) ng.append(random.randrange(256)) nb.append(random.randrange(256)) for y in range(imgy): for x in range(imgx): dmin = math.hypot(imgx-1, imgy-1) j = -1 for i in range(num_cells): d = math.hypot(nx[i]-x, ny[i]-y) if d < dmin: dmin = d j = i putpixel((x, y), (nr[j], ng[j], nb[j])) image.save("VoronoiDiagram.png", "PNG")

       image.show()

generate_voronoi_diagram(500, 500, 25)</lang>

Sample Output:

Voronoi Diagram in Python

Ruby

Uses Raster graphics operations/Ruby

Sample output from Ruby program

<lang ruby>load 'raster_graphics.rb'

class ColourPixel < Pixel

 def initialize(x, y, colour)
   @colour = colour
   super x, y
 end
 attr_accessor :colour

 def distance_to(px, py)
   Math::hypot(px - x, py - y)
 end 

end

width, height = 300, 200 npoints = 20 pixmap = Pixmap.new(width,height)

@bases = npoints.times.collect do |i|

 ColourPixel.new(
     3+rand(width-6), 3+rand(height-6),  # provide a margin to draw a circle
     RGBColour.new(rand(256), rand(256), rand(256))
 )

end

pixmap.each_pixel do |x, y|

 nearest = @bases.min_by {|base| base.distance_to(x, y)}
 pixmap[x, y] = nearest.colour

end

@bases.each do |base|

 pixmap[base.x, base.y] = RGBColour::BLACK
 pixmap.draw_circle(base, 2, RGBColour::BLACK)

end

pixmap.save_as_png("voronoi_rb.png")</lang>

Seed7

<lang seed7>$ include "seed7_05.s7i";

 include "draw.s7i";
 include "keybd.s7i";

const type: point is new struct

   var integer: xPos is 0;
   var integer: yPos is 0;
   var color: col is black;
 end struct;

const proc: generateVoronoiDiagram (in integer: width, in integer: height, in integer: numCells) is func

 local
   var array point: points is 0 times point.value;
   var integer: index is 0;
   var integer: x is 0;
   var integer: y is 0;
   var integer: distSquare is 0;
   var integer: minDistSquare is 0;
   var integer: indexOfNearest is 0;
 begin
   screen(width, height);
   points := numCells times point.value;
   for index range 1 to numCells do
     points[index].xPos := rand(0, width);
     points[index].yPos := rand(0, height);
     points[index].col := color(rand(0, 65535), rand(0, 65535), rand(0, 65535));
   end for;
   for y range 0 to height do
     for x range 0 to width do
       minDistSquare := width ** 2 + height ** 2;
       for index range 1 to numCells do
         distSquare := (points[index].xPos - x) ** 2 + (points[index].yPos - y) ** 2;
         if distSquare < minDistSquare then
           minDistSquare := distSquare;
           indexOfNearest := index;
         end if;
       end for;
       point(x, y, points[indexOfNearest].col);
     end for;
   end for;
   for index range 1 to numCells do
     line(points[index].xPos - 2, points[index].yPos, 4, 0, black);
     line(points[index].xPos, points[index].yPos - 2, 0, 4, black);
   end for;
 end func;

const proc: main is func

 begin
   generateVoronoiDiagram(500, 500, 25);
   KEYBOARD := GRAPH_KEYBOARD;
   readln(KEYBOARD);
 end func;</lang>

Original source: [1]

Tcl

Library: Tk

<lang tcl>package require Tk proc r to {expr {int(rand()*$to)}}; # Simple helper

proc voronoi {photo pointCount} {

   for {set i 0} {$i < $pointCount} {incr i} {

lappend points [r [image width $photo]] [r [image height $photo]]

   }
   foreach {x y} $points {

lappend colors [format "#%02x%02x%02x" [r 256] [r 256] [r 256]]

   }
   set initd [expr {[image width $photo] + [image height $photo]}]
   for {set i 0} {$i < [image width $photo]} {incr i} {

for {set j 0} {$j < [image height $photo]} {incr j} { set color black set d $initd foreach {x y} $points c $colors { set h [expr {hypot($x-$i,$y-$j)}] ### Other interesting metrics #set h [expr {abs($x-$i)+abs($y-$j)}] #set h [expr {(abs($x-$i)**3+abs($y-$j)**3)**0.3}] if {$d > $h} {set d $h;set color $c} } $photo put $color -to $i $j } # To display while generating, uncomment this line and the other one so commented #if {$i%4==0} {update idletasks}

   }

}

1. Generate a 600x400 Voronoi diagram with 60 random points

image create photo demo -width 600 -height 400 pack [label .l -image demo]

1. To display while generating, uncomment this line and the other one so commented
2. update

voronoi demo 60</lang>