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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.

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>

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; }</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

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)),

forall(between(0,399, I), forall(between(0,399, J), ( get_nearest_site(V, Distance, I, J, 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).

get_nearest_site(V, Distance, I, J, S) :- get_nearest_site(V, Distance, I, J, 0, 65535, S).

get_nearest_site(0, _Distance, _I, _J, S, _D, S).

get_nearest_site(V, Distance, I, J, S, D, SF) :- pt(V, XV, YV, _, _, _), call(Distance, I, J, XV, YV, DT), ( DT < D -> S1 = V, D1 = DT; S1 = S, D1 = D), V1 is V - 1, get_nearest_site(V1, Distance, I, J, S1, D1, SF).

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

<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

<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.randint(0, imgx-1)) ny.append(random.randint(0, imgy-1)) nr.append(random.randint(0, 255)) ng.append(random.randint(0, 255)) nb.append(random.randint(0, 255)) 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:

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}

}

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</lang>

@@ Line 266: / Line 266: @@
 	D is (abs(X2 - X1)**3 + abs(Y2-Y1)**3)**0.33.
 </lang>
+[[File:prolog_manhattan.png]]
+[[File:prolog_euclide.png‎]]
+[[File:prolog_minkowski.png‎]]
 =={{header|PureBasic}}==