Voronoi diagram
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
![](http://static.miraheze.org/rosettacodewiki/thumb/6/6b/Voronoi-C.png/300px-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
.
<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>
printf.icn provides the printf family graphics.icn provides graphics support strings.icn provides cat
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
- 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 </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
![](http://static.miraheze.org/rosettacodewiki/thumb/6/6d/Voronoi_PureBasic.png/320px-Voronoi_PureBasic.png)
<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$, #PB_ImagePlugin_PNG)
EndIf</lang>
Taxicab
![](http://static.miraheze.org/rosettacodewiki/thumb/5/5d/Voronoi_Diagram_in_PureBasic_%28Taxicab%29.png/320px-Voronoi_Diagram_in_PureBasic_%28Taxicab%29.png)
<lang PureBasic>Structure VCoo
x.i: y.i Colour.i: FillColour.i
EndStructure
Macro RandInt(MAXLIMIT)
Int(MAXLIMIT*(Random(#MAXLONG)/#MAXLONG))
EndMacro
Procedure GenRandomPoints(Array a.VCoo(1), xMax, yMax, cnt)
Protected i, j, k, l cnt-1 Dim a(cnt) For i=0 To cnt a(i)\x = RandInt(xMax): a(i)\y = RandInt(yMax) j = RandInt(255): k = RandInt(255): l = RandInt(255) a(i)\Colour = RGBA(j, k, l, 255) a(i)\FillColour = RGBA(255-j, 255-k, 255-l, 255) Next i ProcedureReturn #True
EndProcedure
Procedure MakeVoronoiDiagram(Array a.VCoo(1),xMax, yMax)
Protected i, x, y, img, dist, dt, dx, dy img = CreateImage(#PB_Any, xMax+1, yMax+1, 32) If StartDrawing(ImageOutput(img)) For y=0 To yMax For x=0 To xMax dist = #MAXLONG For i=0 To ArraySize(a()) dx = x-a(i)\x dy = y-a(i)\y dt = Sign(dx)*dx + Sign(dy)*dy If dt > dist ; no update Continue ElseIf dt < dist ; an new 'owner' is found dist = dt Plot(x,y,a(i)\FillColour) Else ; dt = dist Plot(x,y,RGBA(0,0,0,0)) ; no clear 'owner', make the pixel transparent EndIf Next Next Next For i=0 To ArraySize(a()) Circle(a(i)\x, a(i)\y, 1, a(i)\Colour) Next StopDrawing() EndIf ProcedureReturn img
EndProcedure
- Main code
Define img, x, y, file$ 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$, #PB_ImagePlugin_PNG)
EndIf</lang>
Python
This implementation takes in a list of points, each point being a tuple and returns a dictionary consisting of all the points at a given site. <lang python>from PIL import Image import random import math
def generate_voronoi_diagram(width, height, num_cells): image = Image.new("RGB", (width, height)) putpixel = image.putpixel imgx, imgy = image.size nx = [] ny = [] nr = [] ng = [] nb = [] for i in range(num_cells): nx.append(random.randrange(imgx)) ny.append(random.randrange(imgy)) nr.append(random.randrange(256)) ng.append(random.randrange(256)) nb.append(random.randrange(256)) for y in range(imgy): for x in range(imgx): dmin = math.hypot(imgx-1, imgy-1) j = -1 for i in range(num_cells): d = math.hypot(nx[i]-x, ny[i]-y) if d < dmin: dmin = d j = i putpixel((x, y), (nr[j], ng[j], nb[j])) image.save("VoronoiDiagram.png", "PNG")
image.show()
generate_voronoi_diagram(500, 500, 25)</lang>
Sample Output:
![](http://static.miraheze.org/rosettacodewiki/8/83/Voronoi_python.png)
Tcl
<lang tcl>package require Tk proc r to {expr {int(rand()*$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>