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Voronoi diagram

From Rosetta Code
Task
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[edit]

Voronoi-C.png

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.

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
 
#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;
}
 
#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;
}
 
#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);
}
 
#define for_i for (i = 0; i < size_y; i++)
#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);
}
 
#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;
}

C++[edit]

Voronoi cpp.png

 
#include <windows.h>
#include <vector>
#include <string>
 
using namespace std;
 
//////////////////////////////////////////////////////
struct Point {
int x, y;
};
 
//////////////////////////////////////////////////////
class MyBitmap {
public:
MyBitmap() : pen_(nullptr) {}
~MyBitmap() {
DeleteObject(pen_);
DeleteDC(hdc_);
DeleteObject(bmp_);
}
 
bool Create(int w, int h) {
BITMAPINFO bi;
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;
 
void *bits_ptr = nullptr;
HDC dc = GetDC(GetConsoleWindow());
bmp_ = CreateDIBSection(dc, &bi, DIB_RGB_COLORS, &bits_ptr, nullptr, 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_);
}
 
bool SaveBitmap(const char* path) {
HANDLE file = CreateFile(path, GENERIC_WRITE, 0, nullptr, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, nullptr);
if (file == INVALID_HANDLE_VALUE) {
return false;
}
 
BITMAPFILEHEADER fileheader;
BITMAPINFO infoheader;
BITMAP bitmap;
GetObject(bmp_, sizeof(bitmap), &bitmap);
 
DWORD* dwp_bits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
ZeroMemory(dwp_bits, 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)dwp_bits, &infoheader, DIB_RGB_COLORS);
 
DWORD wb;
WriteFile(file, &fileheader, sizeof(BITMAPFILEHEADER), &wb, nullptr);
WriteFile(file, &infoheader.bmiHeader, sizeof(infoheader.bmiHeader), &wb, nullptr);
WriteFile(file, dwp_bits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, nullptr);
CloseHandle(file);
 
delete[] dwp_bits;
return true;
}
 
HDC hdc() { return hdc_; }
int width() { return width_; }
int height() { return height_; }
 
private:
HBITMAP bmp_;
HDC hdc_;
HPEN pen_;
int width_, height_;
};
 
static int DistanceSqrd(const Point& point, int x, int y) {
int xd = x - point.x;
int yd = y - point.y;
return (xd * xd) + (yd * yd);
}
 
//////////////////////////////////////////////////////
class Voronoi {
public:
void Make(MyBitmap* bmp, int count) {
bmp_ = bmp;
CreatePoints(count);
CreateColors();
CreateSites();
SetSitesPoints();
}
 
private:
void CreateSites() {
int w = bmp_->width(), h = bmp_->height(), d;
for (int hh = 0; hh < h; hh++) {
for (int ww = 0; ww < w; ww++) {
int ind = -1, dist = INT_MAX;
for (size_t it = 0; it < points_.size(); it++) {
const Point& p = points_[it];
d = DistanceSqrd(p, ww, hh);
if (d < dist) {
dist = d;
ind = it;
}
}
 
if (ind > -1)
SetPixel(bmp_->hdc(), ww, hh, colors_[ind]);
else
__asm nop // should never happen!
}
}
}
 
void SetSitesPoints() {
for (const auto& point : points_) {
int x = point.x, y = point.y;
for (int i = -1; i < 2; i++)
for (int j = -1; j < 2; j++)
SetPixel(bmp_->hdc(), x + i, y + j, 0);
}
}
 
void CreatePoints(int count) {
const int w = bmp_->width() - 20, h = bmp_->height() - 20;
for (int i = 0; i < count; i++) {
points_.push_back({ rand() % w + 10, rand() % h + 10 });
}
}
 
void CreateColors() {
for (size_t 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, 512, 512, bmp.hdc(), 0, 0, SRCCOPY);
bmp.SaveBitmap("v.bmp");
 
system("pause");
 
return 0;
}
 

D[edit]

Translation of: Go
import std.random, std.algorithm, std.range, bitmap;
 
struct Point { uint x, y; }
 
enum randomPoints = (in size_t nPoints, in size_t nx, in size_t ny) =>
nPoints.iota
.map!((int) => Point(uniform(0, nx), uniform(0, ny)))
.array;
 
Image!RGB generateVoronoi(in Point[] pts,
in size_t nx, in size_t ny) /*nothrow*/ {
// Generate a random color for each centroid.
immutable rndRBG = (int) => RGB(uniform!"[]"(ubyte.min, ubyte.max),
uniform!"[]"(ubyte.min, ubyte.max),
uniform!"[]"(ubyte.min, ubyte.max));
const colors = pts.length.iota.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) pure nothrow =>
((a.x - x) ^^ 2 + (a.y - y) ^^ 2) <
((b.x - x) ^^ 2 + (b.y - y) ^^ 2);
// img[x, y] = colors[pts.reduce!(min!dCmp)];
img[x, y] = colors[pts.length - pts.minPos!dCmp.length];
}
 
// Mark each centroid with a white dot.
foreach (immutable p; pts)
img[p.tupleof] = RGB.white;
return img;
}
 
void main() {
enum imageWidth = 640,
imageHeight = 480;
randomPoints(150, imageWidth, imageHeight)
.generateVoronoi(imageWidth, imageHeight)
.savePPM6("voronoi.ppm");
}

Go[edit]

Output png
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)
}
}

Haskell[edit]

Uses the repa and repa-io libraries.

 
-- Compile with: ghc -O2 -fllvm -fforce-recomp -threaded --make
{-# LANGUAGE BangPatterns #-}
module Main where
 
import System.Random
 
import Data.Word
import Data.Array.Repa as Repa
import Data.Array.Repa.IO.BMP
 
{-# INLINE sqDistance #-}
sqDistance :: Word32 -> Word32 -> Word32 -> Word32 -> Word32
sqDistance !x1 !y1 !x2 !y2 = ((x1-x2)^2) + ((y1-y2)^2)
 
centers :: Int -> Int -> Array U DIM2 Word32
centers nCenters nCells =
fromListUnboxed (Z :. nCenters :. 2) $ take (2*nCenters) $ randomRs (0, fromIntegral nCells) (mkStdGen 1)
 
applyReduce2 arr f =
traverse arr (\(i :. j) -> i) $ \lookup (Z:.i) ->
f (lookup (Z:.i:.0)) (lookup (Z:.i:.1))
 
minimize1D arr = foldS f h t
where
indexed arr = traverse arr id (\src idx@(Z :. i) -> (src idx, (fromIntegral i)))
(Z :. n) = extent arr
iarr = indexed arr
h = iarr ! (Z :. 0)
t = extract (Z :. 1) (Z :. (n-1)) iarr
 
f min@(!valMin, !iMin ) x@(!val, !i) | val < valMin = x
| otherwise = min
 
voronoi :: Int -> Int -> Array D DIM2 Word32
voronoi nCenters nCells =
let
{-# INLINE cellReducer #-}
cellReducer = applyReduce2 (centers nCenters nCells)
{-# INLINE nearestCenterIndex #-}
nearestCenterIndex = snd . (Repa.! Z) . minimize1D
in
Repa.fromFunction (Z :. nCells :. nCells :: DIM2) $ \ (Z:.i:.j) ->
nearestCenterIndex $ cellReducer (sqDistance (fromIntegral i) (fromIntegral j))
 
genColorTable :: Int -> Array U DIM1 (Word8, Word8, Word8)
genColorTable n = fromListUnboxed (Z :. n) $ zip3 l1 l2 l3
where
randoms = randomRs (0,255) (mkStdGen 1)
(l1, rest1) = splitAt n randoms
(l2, rest2) = splitAt n rest1
l3 = take n rest2
 
colorize :: Array U DIM1 (Word8, Word8, Word8) -> Array D DIM2 Word32 -> Array D DIM2 (Word8, Word8, Word8)
colorize ctable = Repa.map $ \x -> ctable Repa.! (Z:. fromIntegral x)
 
main = do
let nsites = 150
let ctable = genColorTable nsites
voro <- computeP $ colorize ctable (voronoi nsites 512) :: IO (Array U DIM2 (Word8, Word8, Word8))
writeImageToBMP "out.bmp" voro
 
 

Icon and Unicon[edit]

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

Voronoi-normal unicon.PNG
Voronoi-taxi unicon.PNG
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

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


J[edit]

Explicit version[edit]

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.

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
)
 
load'viewmat'
viewmat 25 voronoi 500 500

Another solution generates Voronoi cells from Delaunay triangulation. The page Voronoi diagram/J/Delaunay triangulation also contains a convex hull algorithm. This is a vector based approach instead of a pixel based approach and is about twice as fast for this task's example.

Tacit version[edit]

This a direct reformulation of the explicit version.

Voronoi=. ,"0/&i./@:] (i. <./)@:(+/@:*:@:-"1)"1 _ ] ?@$~ 2 ,~ [
viewmat 25 Voronoi 500 500 [ load'viewmat'

Delphi[edit]

 
procedure TForm1.Voronoi;
const
p = 3;
cells = 100;
size = 1000;
 
var
aCanvas : TCanvas;
px, py: array of integer;
color: array of Tcolor;
Img: TBitmap;
lastColor:Integer;
auxList: TList<TPoint>;
poligonlist : TDictionary<integer,TList<TPoint>>;
pointarray : array of TPoint;
 
n,i,x,y,k,j: Integer;
d1,d2: double;
 
function distance(x1,x2,y1,y2 :Integer) : Double;
begin
result := sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); ///Euclidian
// result := abs(x1 - x2) + abs(y1 - y2); // Manhattan
// result := power(power(abs(x1 - x2), p) + power(abs(y1 - y2), p), (1 / p)); // Minkovski
end;
 
begin
 
poligonlist := TDictionary<integer,TList<Tpoint>>.create;
 
n := 0;
Randomize;
 
img := TBitmap.Create;
img.Width :=1000;
img.Height :=1000;
 
setlength(px,cells);
setlength(py,cells);
setlength(color,cells);
 
for i:= 0 to cells-1 do
begin
px[i] := Random(size);
py[i] := Random(size);
 
color[i] := Random(16777215);
auxList := TList<Tpoint>.Create;
poligonlist.Add(i,auxList);
end;
 
for x := 0 to size - 1 do
begin
lastColor:= 0;
for y := 0 to size - 1 do
begin
n:= 0;
 
for i := 0 to cells - 1 do
begin
d1:= distance(px[i], x, py[i], y);
d2:= distance(px[n], x, py[n], y);
 
if d1 < d2 then
begin
n := i;
end;
end;
if n <> lastColor then
begin
poligonlist[n].Add(Point(x,y));
poligonlist[lastColor].Add(Point(x,y));
lastColor := n;
end;
end;
 
poligonlist[n].Add(Point(x,y));
poligonlist[lastColor].Add(Point(x,y));
lastColor := n;
end;
 
for j := 0 to cells -1 do
begin
 
SetLength(pointarray, poligonlist[j].Count);
for I := 0 to poligonlist[j].Count - 1 do
begin
if Odd(i) then
pointarray[i] := poligonlist[j].Items[i];
end;
for I := 0 to poligonlist[j].Count - 1 do
begin
if not Odd(i) then
pointarray[i] := poligonlist[j].Items[i];
end;
Img.Canvas.Pen.Color := color[j];
Img.Canvas.Brush.Color := color[j];
Img.Canvas.Polygon(pointarray);
 
Img.Canvas.Pen.Color := clBlack;
Img.Canvas.Brush.Color := clBlack;
Img.Canvas.Rectangle(px[j] -2, py[j] -2, px[j] +2, py[j] +2);
end;
Canvas.Draw(0,0, img);
end;
 
 

Java[edit]

Library: Swing
Library: AWT
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.geom.Ellipse2D;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.Random;
 
import javax.imageio.ImageIO;
import javax.swing.JFrame;
 
public class Voronoi extends JFrame {
static double p = 3;
static BufferedImage I;
static int px[], py[], color[], cells = 100, size = 1000;
 
public Voronoi() {
super("Voronoi Diagram");
setBounds(0, 0, size, size);
setDefaultCloseOperation(EXIT_ON_CLOSE);
int n = 0;
Random rand = new Random();
I = new BufferedImage(size, size, BufferedImage.TYPE_INT_RGB);
px = new int[cells];
py = new int[cells];
color = new int[cells];
for (int i = 0; i < cells; i++) {
px[i] = rand.nextInt(size);
py[i] = rand.nextInt(size);
color[i] = rand.nextInt(16777215);
 
}
for (int x = 0; x < size; x++) {
for (int y = 0; y < size; y++) {
n = 0;
for (byte i = 0; i < cells; i++) {
if (distance(px[i], x, py[i], y) < distance(px[n], x, py[n], y)) {
n = i;
 
}
}
I.setRGB(x, y, color[n]);
 
}
}
 
Graphics2D g = I.createGraphics();
g.setColor(Color.BLACK);
for (int i = 0; i < cells; i++) {
g.fill(new Ellipse2D .Double(px[i] - 2.5, py[i] - 2.5, 5, 5));
}
 
try {
ImageIO.write(I, "png", new File("voronoi.png"));
} catch (IOException e) {
 
}
 
}
 
public void paint(Graphics g) {
g.drawImage(I, 0, 0, this);
}
 
static double distance(int x1, int x2, int y1, int y2) {
double d;
d = Math.sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); // Euclidian
// d = Math.abs(x1 - x2) + Math.abs(y1 - y2); // Manhattan
// d = Math.pow(Math.pow(Math.abs(x1 - x2), p) + Math.pow(Math.abs(y1 - y2), p), (1 / p)); // Minkovski
return d;
}
 
public static void main(String[] args) {
new Voronoi().setVisible(true);
}
}
 

JavaScript[edit]

Version #1.[edit]

The obvious route to this in JavaScript would be to use Mike Bostock's D3.js library.

There are various examples of Voronoi tesselations,

some dynamic:

http://bl.ocks.org/mbostock/d1d81455dc21e10f742f

some interactive:

http://bl.ocks.org/mbostock/4060366

and all with source code, at http://bl.ocks.org/mbostock

Version #2.[edit]

I would agree: using D3.js library can be very helpful. But having stable and compact algorithm in Python (Sidef) made it possible to develop looking the same Voronoi diagram in "pure" JavaScript. A few custom helper functions simplified code, and they can be used for any other applications.

Works with: Chrome
File:VDjs1150.png
Output VDjs1150.png
File:VDjs210.png
Output VDjs210.png
File:VDjs310.png
Output VDjs310.png
 
<!-- VoronoiD.html -->
<html>
<head><title>Voronoi diagram</title>
<script>
// HF#1 Like in PARI/GP: return random number 0..max-1
function randgp(max) {return Math.floor(Math.random()*max)}
// HF#2 Random hex color
function randhclr() {
return "#"+
("00"+randgp(256).toString(16)).slice(-2)+
("00"+randgp(256).toString(16)).slice(-2)+
("00"+randgp(256).toString(16)).slice(-2)
}
// HF#3 Metrics: Euclidean, Manhattan and Minkovski 3/20/17
function Metric(x,y,mt) {
if(mt==1) {return Math.sqrt(x*x + y*y)}
if(mt==2) {return Math.abs(x) + Math.abs(y)}
if(mt==3) {return(Math.pow(Math.pow(Math.abs(x),3) + Math.pow(Math.abs(y),3),0.33333))}
}
// Plotting Voronoi diagram. aev 3/10/17
function pVoronoiD() {
var cvs=document.getElementById("cvsId");
var ctx=cvs.getContext("2d");
var w=cvs.width, h=cvs.height;
var x=y=d=dm=j=0, w1=w-2, h1=h-2;
var n=document.getElementById("sites").value;
var mt=document.getElementById("mt").value;
var X=new Array(n), Y=new Array(n), C=new Array(n);
ctx.fillStyle="white"; ctx.fillRect(0,0,w,h);
for(var i=0; i<n; i++) {
X[i]=randgp(w1); Y[i]=randgp(h1); C[i]=randhclr();
}
for(y=0; y<h1; y++) {
for(x=0; x<w1; x++) {
dm=Metric(h1,w1,mt); j=-1;
for(var i=0; i<n; i++) {
d=Metric(X[i]-x,Y[i]-y,mt)
if(d<dm) {dm=d; j=i;}
}//fend i
ctx.fillStyle=C[j]; ctx.fillRect(x,y,1,1);
}//fend x
}//fend y
ctx.fillStyle="black";
for(var i=0; i<n; i++) {
ctx.fillRect(X[i],Y[i],3,3);
}
}
</script></head>
<body style="font-family: arial, helvatica, sans-serif;">
<b>Please input number of sites: </b>
<input id="sites" value=100 type="number" min="10" max="150" size="3">&nbsp;&nbsp;
<b>Metric: </b>
<select id="mt">
<option value=1 selected>Euclidean</option>
<option value=2>Manhattan</option>
<option value=3>Minkovski</option>
</select>&nbsp;
<input type="button" value="Plot it!" onclick="pVoronoiD();">&nbsp;&nbsp;
<h3>Voronoi diagram</h3>
<canvas id="cvsId" width="640" height="640" style="border: 2px inset;"></canvas>
</body>
</html>
 
Output:
Page demonstrating Voronoi diagram for any reasonable number of sites and selected metric.
Right clicking on canvas with image allows you to save it as png-file, for example.

Liberty BASIC[edit]

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..

 
WindowWidth =600
WindowHeight =600
 
sites = 100
xEdge = 400
yEdge = 400
graphicbox #w.gb1, 10, 10, xEdge, yEdge
 
open "Voronoi neighbourhoods" for window as #w
 
#w "trapclose quit"
#w.gb1 "down ; fill black ; size 4"
#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
 
#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
 
#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
 
#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
 

Lua[edit]

Library: LÖVE
Works with: LÖVE version 0.10.1
Translation of: Python
 
function love.load( )
love.math.setRandomSeed( os.time( ) ) --set the random seed
keys = { } --an empty table where we will store key presses
number_cells = 50 --the number of cells we want in our diagram
--draw the voronoi diagram to a canvas
voronoiDiagram = generateVoronoi( love.graphics.getWidth( ), love.graphics.getHeight( ), number_cells )
end
 
function hypot( x, y )
return math.sqrt( x*x + y*y )
end
 
function generateVoronoi( width, height, num_cells )
canvas = love.graphics.newCanvas( width, height )
local imgx = canvas:getWidth( )
local imgy = canvas:getHeight( )
local nx = { }
local ny = { }
local nr = { }
local ng = { }
local nb = { }
for a = 1, num_cells do
table.insert( nx, love.math.random( 0, imgx ) )
table.insert( ny, love.math.random( 0, imgy ) )
table.insert( nr, love.math.random( 0, 255 ) )
table.insert( ng, love.math.random( 0, 255 ) )
table.insert( nb, love.math.random( 0, 255 ) )
end
love.graphics.setColor( { 255, 255, 255 } )
love.graphics.setCanvas( canvas )
for y = 1, imgy do
for x = 1, imgx do
dmin = hypot( imgx-1, imgy-1 )
j = -1
for i = 1, num_cells do
d = hypot( nx[i]-x, ny[i]-y )
if d < dmin then
dmin = d
j = i
end
end
love.graphics.setColor( { nr[j], ng[j], nb[j] } )
love.graphics.points( x, y )
end
end
--reset color
love.graphics.setColor( { 255, 255, 255 } )
--draw points
for b = 1, num_cells do
love.graphics.points( nx[b], ny[b] )
end
love.graphics.setCanvas( )
return canvas
end
 
--RENDER
function love.draw( )
--reset color
love.graphics.setColor( { 255, 255, 255 } )
--draw diagram
love.graphics.draw( voronoiDiagram )
--draw drop shadow text
love.graphics.setColor( { 0, 0, 0 } )
love.graphics.print( "space: regenerate\nesc: quit", 1, 1 )
--draw text
love.graphics.setColor( { 200, 200, 0 } )
love.graphics.print( "space: regenerate\nesc: quit" )
end
 
--CONTROL
function love.keyreleased( key )
if key == 'space' then
voronoiDiagram = generateVoronoi( love.graphics.getWidth( ), love.graphics.getHeight( ), number_cells )
elseif key == 'escape' then
love.event.quit( )
end
end
 

Mathematica[edit]

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}}]

Right

МК-61/52[edit]

0	П4
0 П5
ИП0 1 - x^2 ИП1 1 - x^2 + КвКор П3
9 П6
КИП6 П8 {x} 2 10^x * П9
[x] ИП5 - x^2 ИП9 {x} 2 10^x * ИП4 - x^2 + КвКор П9
ИП3 - x<0 47 ИП9 П3 ИП6 П7
ИП6 ИП2 - 9 - x>=0 17
КИП7 [x] С/П
КИП5 ИП5 ИП1 - x>=0 04
КИП4 ИП4 ИП0 - x>=0 02

Input: Р0 - diagram width; Р1 - diagram height; Р0 - number of the points; РA - РE - coordinates and colors of the points in format C,XXYY (example: 3,0102).

Example of the manually compiled output (graphical output from this class of devices is missing):

· · · · · · · · · ·
· · · · · · · · · ·
· · · · · · · · · ·
· · · · · · · · ·
· · · · · · · · · ·
· · · · · · · · · ·
· · · · · · · · ·
· · · · · · · · · ·
· · · · · · · · ·
· · · · · · · · · ·

Phix[edit]

Translation of: Liberty_BASIC

Lifted the calculation strategy from Liberty Basic. Can resize, double or halve sites (press +/-), and toggle between Euclid, Manhattan, and Minkowski (press e/m/w).

--
-- demo\rosetta\VoronoiDiagram.exw
-- ===============================
--
include pGUI.e
 
Ihandle dlg, canvas, timer
cdCanvas cddbuffer, cdcanvas
 
-- Stop any current drawing process before starting a new one:
-- Without this it /is/ going to crash, if it tries to finish
-- drawing all 100 sites, when there are now only 50, for eg.
integer timer_active = 0
 
integer nsites = 200
integer last_width = -1, last_height
sequence siteX, siteY, siteC
 
enum EUCLID, MANHATTAN, MINKOWSKI
 
constant dmodes = {"Euclid", "Manhattan", "Minkowski"}
 
integer dmode = EUCLID,
drawn = 0 -- (last dmode actually shown)
 
function distance(integer x1,y1, x2,y2)
atom d
x1 -= x2
y1 -= y2
switch dmode do
case EUCLID: d = x1*x1+y1*y1 -- (no need for sqrt)
case MANHATTAN: d = abs(x1)+abs(y1)
case MINKOWSKI: d = power(abs(x1),3)+power(abs(y1),3) -- ("" power(d,1/3))
end switch
return d
end function
 
sequence nearestIndex, dist
 
function checkRow(integer site, integer x, integer height)
bool res = false
atom dxSquared
integer x1 = siteX[site]-x
switch dmode do
case EUCLID: dxSquared = x1*x1
case MANHATTAN: dxSquared = abs(x1)
case MINKOWSKI: dxSquared = power(abs(x1),3)
end switch
for y=1 to height do
-- atom dSquared = distance(siteX[site],siteY[site],x,y) -- (sub-optimal..)
atom dSquared
integer y1 = siteY[site]-y
switch dmode do
case EUCLID: dSquared = dxSquared + y1*y1
case MANHATTAN: dSquared = dxSquared + abs(y1)
case MINKOWSKI: dSquared = dxSquared + power(abs(y1),3)
end switch
if dSquared<=dist[x,y] then
dist[x,y] = dSquared
nearestIndex[x,y] = site
res = true
end if
end for
return res
end function
 
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
integer {width, height} = IupGetIntInt(canvas, "DRAWSIZE")
if width!=last_width
or height!=last_height
or nsites!=length(siteX) then
if nsites<1 then nsites = 1 end if
siteX = sq_rand(repeat(width,nsites))
siteY = sq_rand(repeat(height,nsites))
siteC = sq_rand(repeat(#FFFFFF,nsites))
last_width = width
last_height = height
drawn = 0
end if
if drawn!=dmode -- (prevent double-draw, and)
and not timer_active then -- (drawing when rug moved..)
drawn = dmode
cdCanvasActivate(cddbuffer)
atom t0 = time(), t1
t1 = time()+0.25
nearestIndex = repeat(repeat(1,height),width)
dist = repeat(repeat(0,height),width)
-- fill distance table with distances from the first site
integer x1 = siteX[1], y1 = siteY[1]
for x=1 to width do
for y=1 to height do
dist[x,y] = distance(x1,y1,x,y)
end for
if timer_active then exit end if
end for
--for other towns
for i=2 to nsites do
-- look left
for x=siteX[i] to 1 by -1 do
if not checkRow(i, x, height) then exit end if
end for
-- look right
for x=siteX[i]+1 to width do
if not checkRow(i, x, height) then exit end if
end for
if timer_active then exit end if
if time()>t1 then
IupSetStrAttribute(dlg, "TITLE", "Voronoi diagram (generating - %3.2f%%)",{100*i/nsites})
IupFlush()
t1 = time()+0.25
end if
end for
t1 = time()
for y=1 to height do
integer nearest = nearestIndex[1,y]
integer s = 1
for x=2 to width do
if nearestIndex[x,y]<>nearest then
cdCanvasSetForeground(cddbuffer, siteC[nearest])
cdCanvasLine(cddbuffer, s-1, y-1, x-2, y-1)
nearest = nearestIndex[x,y]
s = x
end if
end for
if timer_active then exit end if
cdCanvasSetForeground(cddbuffer, siteC[nearest])
cdCanvasLine(cddbuffer, s-1, y-1, width-1, y-1)
end for
if not timer_active then
cdCanvasSetForeground(cddbuffer, CD_BLACK)
for i=1 to nsites do
cdCanvasSector(cddbuffer, siteX[i], siteY[i], 2, 2, 0, 360)
end for
cdCanvasFlush(cddbuffer)
IupSetStrAttribute(dlg, "TITLE", "Voronoi diagram - %s, %dx%d, %d sites, %3.2fs",{dmodes[dmode],width,height,nsites,time()-t0})
end if
end if
return IUP_DEFAULT
end function
 
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_WHITE)
cdCanvasSetForeground(cddbuffer, CD_BLACK)
return IUP_DEFAULT
end function
 
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
integer wasdmode = dmode
switch c do
case '+': nsites *= 2
case '-': nsites = max(floor(nsites/2),1)
case 'E','e': dmode = EUCLID
case 'M','m': dmode = MANHATTAN
case 'W','w': dmode = MINKOWSKI
end switch
if dmode!=wasdmode
or nsites!=length(siteX) then
-- give any current drawing process 0.1s to abandon:
timer_active = 1
IupStoreAttribute(timer, "RUN", "YES")
-- IupUpdate(canvas)
end if
return IUP_CONTINUE
end function
 
function timer_cb(Ihandle /*ih*/)
timer_active = 0
IupStoreAttribute(timer, "RUN", "NO")
IupUpdate(canvas)
return IUP_IGNORE
end function
 
procedure main()
IupOpen(join_path({"..","pGUI"},1))
 
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "600x400") -- initial size
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
 
timer = IupTimer(Icallback("timer_cb"), 100, 0) -- (inactive)
 
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Voronoi diagram")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
 
IupMap(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release the minimum limitation
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure
main()

Prolog[edit]

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).


:- 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.
 

Prolog manhattan.png Prolog euclide.png Prolog minkowski.png

PureBasic[edit]

Euclidean[edit]

Voronoi Diagram in 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

Taxicab[edit]

Voronoi Diagram in 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

Python[edit]

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.

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)
Output:
Voronoi Diagram in Python

R[edit]

One of the R's great powers is its unlimited number of packages, virtually thousands of them. For any applications big or small you can find a package. In case of Voronoi diagram there are many of packages, e.g.: deldir, alphahull, dismo, ggplot, ggplot2, tripack, CGAL, etc. Not to mention all linked packages. Do you need random colors? Again, find a few packages more...
So, I've decided to use proven algorithms instead. Result - small compact code and beautiful diagrams with any reasonable amount of sites. A few custom helper functions simplified code, and they can be used for any other applications.
If you have not a super fast computer, you can watch animation of plotting in "R Graphics" sub-window of the "RGui" window.

Translation of: JavaScript v.#2
Works with: R version 3.3.3 and above
File:VDR1150.png
Output VDR1150.png
File:VDR210.png
Output VDR210.png
File:VDR310.png
Output VDR310.png
 
## HF#1 Random Hex color
randHclr <- function() {
m=255;r=g=b=0;
r <- sample(0:m, 1, replace=TRUE);
g <- sample(0:m, 1, replace=TRUE);
b <- sample(0:m, 1, replace=TRUE);
return(rgb(r,g,b,maxColorValue=m));
}
## HF#2 Metrics: Euclidean, Manhattan and Minkovski
Metric <- function(x, y, mt) {
if(mt==1) {return(sqrt(x*x + y*y))}
if(mt==2) {return(abs(x) + abs(y))}
if(mt==3) {return((abs(x)^3 + abs(y)^3)^0.33333)}
}
 
## Plotting Voronoi diagram. aev 3/12/17
## ns - number of sites, fn - file name, ttl - plot title.
## mt - type of metric: 1 - Euclidean, 2 - Manhattan, 3 - Minkovski.
pVoronoiD <- function(ns, fn="", ttl="",mt=1) {
cat(" *** START VD:", date(), "\n");
if(mt<1||mt>3) {mt=1}; mts=""; if(mt>1) {mts=paste0(", mt - ",mt)};
m=640; i=j=k=m1=m-2; x=y=d=dm=0;
if(fn=="") {pf=paste0("VDR", mt, ns, ".png")} else {pf=paste0(fn, ".png")};
if(ttl=="") {ttl=paste0("Voronoi diagram, sites - ", ns, mts)};
cat(" *** Plot file -", pf, "title:", ttl, "\n");
plot(NA, xlim=c(0,m), ylim=c(0,m), xlab="", ylab="", main=ttl);
X=numeric(ns); Y=numeric(ns); C=numeric(ns);
for(i in 1:ns) {
X[i]=sample(0:m1, 1, replace=TRUE);
Y[i]=sample(0:m1, 1, replace=TRUE);
C[i]=randHclr();
}
for(i in 0:m1) {
for(j in 0:m1) {
dm=Metric(m1,m1,mt); k=-1;
for(n in 1:ns) {
d=Metric(X[n]-j,Y[n]-i, mt);
if(d<dm) {dm=d; k=n;}
}
clr=C[k]; segments(j, i, j, i, col=clr);
}
}
points(X, Y, pch = 19, col = "black", bg = "white")
dev.copy(png, filename=pf, width=m, height=m);
dev.off(); graphics.off();
cat(" *** END VD:",date(),"\n");
}
## Executing:
pVoronoiD(150) ## Euclidean metric
pVoronoiD(10,"","",2) ## Manhattan metric
pVoronoiD(10,"","",3) ## Minkovski metric
 
Output:
> pVoronoiD(150)          ## Euclidean metric
 *** START VD: Sun Mar 12 19:04:26 2017
 *** Plot file - VDR1150.png title: Voronoi diagram, sites - 150 
 *** END VD: Sun Mar 12 19:11:03 2017 
> pVoronoiD(10,"","",2)   ## Manhattan metric
 *** START VD: Mon Mar 20 13:57:46 2017 
 *** Plot file - VDR210.png title: Voronoi diagram, sites - 10, mt - 2 
 *** END VD: Mon Mar 20 13:59:42 2017 
 > pVoronoiD(10,"","",3)   ## Minkovski metric
 *** START VD: Mon Mar 20 14:45:15 2017 
 *** Plot file - VDR310.png title: Voronoi diagram, sites - 10, mt - 3 
 *** END VD: Mon Mar 20 14:47:21 2017 

Racket[edit]

Clustering using the nearest neigbour approach.

First approach

 
#lang racket
 
(require plot)
 
;; Performs clustering of points in a grid
;; using the nearest neigbour approach and shows
;; clusters in different colors
(define (plot-Voronoi-diagram point-list)
(define pts
(for*/list ([x (in-range 0 1 0.005)]
[y (in-range 0 1 0.005)])
(vector x y)))
 
(define clusters (clusterize pts point-list))
 
(plot
(append
(for/list ([r (in-list clusters)] [i (in-naturals)])
(points (rest r) #:color i #:sym 'fullcircle1))
(list (points point-list #:sym 'fullcircle5 #:fill-color 'white)))))
 
;; Divides the set of points into clusters
;; using given centroids
(define (clusterize data centroids)
(for*/fold ([res (map list centroids)]) ([x (in-list data)])
(define c (argmin (curryr (metric) x) centroids))
(dict-set res c (cons x (dict-ref res c)))))
 

Different metrics

 
(define (euclidean-distance a b)
(for/sum ([x (in-vector a)] [y (in-vector b)])
(sqr (- x y))))
 
(define (manhattan-distance a b)
(for/sum ([x (in-vector a)] [y (in-vector b)])
(abs (- x y))))
 
(define metric (make-parameter euclidean-distance))
 
The contour plot of the classification function.
Using Manhattan metric.
Voronoi diagram in 3D space.

Alternative approach

 
;; Plots the Voronoi diagram as a contour plot of
;; the classification function built for a set of points
(define (plot-Voronoi-diagram2 point-list)
(define n (length point-list))
(define F (classification-function point-list))
(plot
(list
(contour-intervals (compose F vector) 0 1 0 1
#:samples 300
#:levels n
#:colors (range n)
#:contour-styles '(solid)
#:alphas '(1))
(points point-list #:sym 'fullcircle3))))
 
;; For a set of centroids returns a function
;; which finds the index of the centroid nearest
;; to a given point
(define (classification-function centroids)
(define tbl
(for/hash ([p (in-list centroids)] [i (in-naturals)])
(values p i)))
(λ (x)
(hash-ref tbl (argmin (curry (metric) x) centroids))))
 


Output:
 
(define pts
(for/list ([i 50]) (vector (random) (random))))
 
(display (plot-Voronoi-diagram pts))
 
(display (plot-Voronoi-diagram2 pts))
 
(parameterize ([metric manhattan-distance])
(display (plot-Voronoi-diagram2 pts)))
 
;; Using the classification function it is possible to plot Voronoi diagram in 3D.
(define pts3d (for/list ([i 7]) (vector (random) (random) (random))))
(plot3d (list
(isosurfaces3d (compose (classification-function pts3d) vector)
0 1 0 1 0 1
#:line-styles '(transparent)
#:samples 100
#:colors (range 7)
#:alphas '(1))
(points3d pts3d #:sym 'fullcircle3)))
 

Ruby[edit]

Uses Raster graphics operations/Ruby

Sample output from Ruby program
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")

Run BASIC[edit]

graphic #g, 400,400
#g flush()
spots = 100
leftSide = 400
rightSide = 400
 
dim locX(spots)
dim locY(spots)
dim rgb(spots,3)
dim seal(leftSide, rightSide)
dim reach(leftSide, rightSide)
 
for i =1 to spots
locX(i) = int(leftSide * rnd(1))
locY(i) = int(rightSide * rnd(1))
rgb(i,1) = int(256 * rnd(1))
rgb(i,2) = int(256 * rnd(1))
rgb(i,3) = int(256 * rnd(1))
#g color(rgb(i,1),rgb(i,2),rgb(i,3))
#g set(locX(i),locY(i))
next i
#g size(1)
' find reach to the first site
for x = 0 to leftSide - 1
for y = 0 to rightSide - 1
reach(x, y) = (locX(1) - x) ^ 2 + (locY(1) - y) ^ 2
seal(x, y) = 1
next y
next x
#g color("darkblue")
 
' spots other than 1st spot
for i = 2 to spots
for x = locX(i) to 0 step -1 ' looking left
if not(chkPos(i,x,0, rightSide - 1)) then exit for
next x
for x = locX(i) + 1 to leftSide - 1 ' looking right
if not(chkPos(i, x, 0, rightSide - 1)) then exit for
next x
next i
 
for x = 0 to leftSide - 1
for y = 0 to rightSide - 1
c1 = rgb(seal(x, y),1)
c2 = rgb(seal(x, y),2)
c3 = rgb(seal(x, y),3)
#g color(c1,c2,c3)
startY = y
nearest = seal(x, y)
for y = y + 1 to rightSide
if seal(x, y) <> nearest then y = y - 1 : exit for
next y
#g line(x,startY,x,y + 1)
next y
next x
 
#g color("black")
#g size(4)
for i =1 to spots
#g set(locX(i),locY(i))
next i
render #g
end
 
function chkPos(site, x, startY, endY)
dxSqr = (locX(site) - x) ^ 2
for y = startY to endY
dSqr = (locY(site) - y) ^ 2 + dxSqr
if dSqr <= reach(x, y) then
reach(x,y) = dSqr
seal(x,y) = site
chkPos = 1
end if
next y
end function

Seed7[edit]

Seed7Voronoi.png
$ 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;

Original source: [1]

Sidef[edit]

Translation of: Python
require('Imager')
 
func generate_voronoi_diagram(width, height, num_cells) {
var img = %s<Imager>.new(xsize => width, ysize => height)
var (nx,ny,nr,ng,nb) = 5.of { [] }...
 
for i in ^num_cells {
nx << rand(^width)
ny << rand(^height)
nr << rand(^256)
ng << rand(^256)
nb << rand(^256)
}
 
for y in ^height {
for x in ^width {
var dmin = hypot(width-1, height-1)
var j = -1
for i in ^num_cells {
var d = hypot(nx[i]-x, ny[i]-y)
if (d < dmin) { (dmin, j) = (d, i) }
}
img.setpixel(x => x, y => y, color => [nr[j], ng[j], nb[j]])
}
}
return img
}
 
var img = generate_voronoi_diagram(500, 500, 25)
img.write(file => 'VoronoiDiagram.png')

Tcl[edit]

Library: Tk
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}
}
}
 
# Generate a 600x400 Voronoi diagram with 60 random points
image create photo demo -width 600 -height 400
pack [label .l -image demo]
# To display while generating, uncomment this line and the other one so commented
#update
voronoi demo 60

XPL0[edit]

include c:\cxpl\codes;          \intrinsic 'code' declarations
 
def N = 15; \number of sites
int SiteX(N), SiteY(N), \coordinates of sites
Dist2, MinDist2, MinI, \distance squared, and minimums
X, Y, I;
[SetVid($13); \set 320x200x8 graphics
for I:= 0 to N-1 do \create a number of randomly placed sites
[SiteX(I):= Ran(160); SiteY(I):= Ran(100)];
for Y:= 0 to 100-1 do \generate Voronoi diagram
for X:= 0 to 160-1 do \for all points...
[MinDist2:= -1>>1; \find closest site
for I:= 0 to N-1 do
[Dist2:= sq(X-SiteX(I)) + sq(Y-SiteY(I));
if Dist2 < MinDist2 then
[MinDist2:= Dist2; MinI:= I];
];
if MinDist2 then Point(X, Y, MinI+1); \leave center black
];
I:= ChIn(1); \wait for keystroke
SetVid($03); \restore normal text screen
]

zkl[edit]

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

Translation of: Python
VoronoiDiagram.zkl.jpg
fcn generate_voronoi_diagram(width,height,num_cells){
image,imgx,imgy:=PPM(width,height),width,height;
nx:=num_cells.pump(List,(0).random.fp(imgx));
ny:=num_cells.pump(List,(0).random.fp(imgy));
nr:=num_cells.pump(List,(0).random.fp(256)); // red
ng:=num_cells.pump(List,(0).random.fp(256)); // blue
nb:=num_cells.pump(List,(0).random.fp(256)); // green
 
foreach y,x in (imgy,imgx){
dmin:=(imgx-1).toFloat().hypot(imgy-1);
j:=-1;
foreach i in (num_cells){
d:=(nx[i] - x).toFloat().hypot(ny[i] - y);
if(d<dmin) dmin,j = d,i
}
image[x,y]=(nr[j]*0xff00 + ng[j])*0xff00 + nb[j];
}
image
}
generate_voronoi_diagram(500,500,25).write(File("VoronoiDiagram.ppm","wb"));