Color wheel

From Rosetta Code
Color wheel is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Task

Write a function to draw a HSV color wheel[1] completely with code.

This is strictly for learning purposes only. It's highly recommended that you use an image in an actual application to actually draw the color wheel   (as procedurally drawing is super slow). This does help you understand how color wheels work and this can easily be used to determine a color value based on a position within a circle.

AppleScript[edit]

 
choose color default color {0, 0, 0, 0}
 

Fōrmulæ[edit]

In this page you can see the solution of this task.

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.

The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.

GML[edit]

 
for (var i = 1; i <= 360; i++) {
for (var j = 0; j < 255; j++) {
 
var hue = 255*(i/360);
var saturation = j;
var value = 255;
 
var c = make_colour_hsv(hue,saturation,value);
 
//size of circle determined by how far from the center it is
//if you just draw them too small the circle won't be full.
//it will have patches inside it that didn't get filled in with color
var r = max(1,3*(j/255));
 
//Math for built-in GMS functions
//lengthdir_x(len,dir) = +cos(degtorad(direction))*length;
//lengthdir_y(len,dir) = -sin(degtorad(direction))*length;
draw_circle_colour(x+lengthdir_x(m_radius*(j/255),i),y+lengthdir_y(m_radius*(j/255),i),r,c,c,false);
}
}
 

Go[edit]

Library: Go Graphics
Translation of: Kotlin
package main
 
import (
"github.com/fogleman/gg"
"math"
)
 
const tau = 2 * math.Pi
 
func hsb2rgb(hue, sat, bri float64) (r, g, b int) {
u := int(bri*255 + 0.5)
if sat == 0 {
r, g, b = u, u, u
} else {
h := (hue - math.Floor(hue)) * 6
f := h - math.Floor(h)
p := int(bri*(1-sat)*255 + 0.5)
q := int(bri*(1-sat*f)*255 + 0.5)
t := int(bri*(1-sat*(1-f))*255 + 0.5)
switch int(h) {
case 0:
r, g, b = u, t, p
case 1:
r, g, b = q, u, p
case 2:
r, g, b = p, u, t
case 3:
r, g, b = p, q, u
case 4:
r, g, b = t, p, u
case 5:
r, g, b = u, p, q
}
}
return
}
 
func colorWheel(dc *gg.Context) {
width, height := dc.Width(), dc.Height()
centerX, centerY := width/2, height/2
radius := centerX
if centerY < radius {
radius = centerY
}
for y := 0; y < height; y++ {
dy := float64(y - centerY)
for x := 0; x < width; x++ {
dx := float64(x - centerX)
dist := math.Sqrt(dx*dx + dy*dy)
if dist <= float64(radius) {
theta := math.Atan2(dy, dx)
hue := (theta + math.Pi) / tau
r, g, b := hsb2rgb(hue, 1, 1)
dc.SetRGB255(r, g, b)
dc.SetPixel(x, y)
}
}
}
}
 
func main() {
const width, height = 480, 480
dc := gg.NewContext(width, height)
dc.SetRGB(1, 1, 1) // set background color to white
dc.Clear()
colorWheel(dc)
dc.SavePNG("color_wheel.png")
}
Output:
Image is same as Kotlin entry


Julia[edit]

using Gtk, Graphics, Colors
 
const win = GtkWindow("Color Wheel", 450, 450) |> (const can = @GtkCanvas())
set_gtk_property!(can, :expand, true)
 
@guarded draw(can) do widget
ctx = getgc(can)
h = height(can)
w = width(can)
center = (x = w / 2, y = h / 2)
anglestep = 1/w
for θ in 0:0.1:360
rgb = RGB(HSV(θ, 1, 1))
set_source_rgb(ctx, rgb.r, rgb.g, rgb.b)
line_to(ctx, center...)
arc(ctx, center.x, center.y, w/2.2, 2π * θ / 360, anglestep)
line_to(ctx, center...)
stroke(ctx)
end
end
 
show(can)
const condition = Condition()
endit(w) = notify(condition)
signal_connect(endit, win, :destroy)
wait(condition)
 

Kotlin[edit]

We reuse the class in the Bitmap task for this and add a member function to draw the color wheel. To give a more 'wheel-like' image, a constant 'saturation' of 1.0 has been used rather than one which varies in line with distance from the center.

// Version 1.2.41
 
import java.awt.Color
import java.awt.Graphics
import java.awt.image.BufferedImage
import java.io.File
import javax.imageio.ImageIO
import kotlin.math.*
 
class BasicBitmapStorage(width: Int, height: Int) {
val image = BufferedImage(width, height, BufferedImage.TYPE_3BYTE_BGR)
 
fun fill(c: Color) {
val g = image.graphics
g.color = c
g.fillRect(0, 0, image.width, image.height)
}
 
fun setPixel(x: Int, y: Int, c: Color) = image.setRGB(x, y, c.getRGB())
 
fun getPixel(x: Int, y: Int) = Color(image.getRGB(x, y))
 
fun colorWheel() {
val centerX = image.width / 2
val centerY = image.height / 2
val radius = minOf(centerX, centerY)
for (y in 0 until image.height) {
val dy = (y - centerY).toDouble()
for (x in 0 until image.width) {
val dx = (x - centerX).toDouble()
val dist = sqrt(dx * dx + dy * dy)
if (dist <= radius) {
val theta = atan2(dy, dx)
val hue = (theta + PI) / (2.0 * PI)
val rgb = Color.HSBtoRGB(hue.toFloat(), 1.0f, 1.0f)
setPixel(x, y, Color(rgb))
}
}
}
}
}
 
fun main(args: Array<String>) {
val bbs = BasicBitmapStorage(480, 480)
with (bbs) {
fill(Color.white)
colorWheel()
val cwFile = File("Color_wheel.png")
ImageIO.write(image, "png", cwFile)
}
}
 
Output:
Looks like mirror image of Smart BASIC entry 

M2000 Interpreter[edit]

 
Module Check {
\\ we use an internal object for Math functions (here for Atan2)
Declare Math Math
Const tau=2*Pi, Center=2
\\ change console size, and center it ( using ;) to current monitor
Window 12, 800*twipsX,600*twipsY;
\\ actual size maybe less (so can fit text exactly)
Double ' Double height characters
Report Center, "Color wheel"
Normal ' restore to normal
Atan2=Lambda Math (a, b) ->{
Method Math, "Atan2", a, b As ret
=ret
}
\\ brightness=1 for this program
hsb2rgb=Lambda (hue, sat) ->{
If sat == 0 Then {
= 255, 255, 255
} Else {
h=frac(hue+1)*6
f = frac(h)
p = Int((1-sat)*255 + 0.5)
q = Int((1-sat*f)*255 + 0.5)
t = Int((1-sat*(1-f))*255 + 0.5)
Select Case Int(h)
Case 1
= q, 255, p
Case 2
= p, 255, t
Case 3
= p, q, 255
Case 4
= t, p, 255
Case 5
= 255, p, q
Else Case
= 255, t, p
End Select
}
}
Let OffsetX=X.twips/2-128*TwipsX, OffsetY=Y.twips/2-128*TwipsY
\\ a pixel has a size of TwipsX x TwipsY
OffsetX=(OffsetX div TwipsX)*TwipsX
OffsetY=(OffsetY div TwipsY)*TwipsY
\\ We set hsb2rgb, OffsetX, OffsetY as closures to PrintPixel
\\ We send to stack the R G B values using Stack ! array
\\ hsb2rgb() return an array of values
\\ we pop these values using Number
PrintPixel = Lambda hsb2rgb, OffsetX, OffsetY (x,y, theta, sat) -> {
Stack ! hsb2rgb(theta,sat)
PSet Color(number, number, number), x*TwipsX+offsetX, y*TwipsY+offsetY
}
\\ set Atan2, tau as closures to HueCircle
\\ we can rotate/flip the wheel by changing signs in Atan2() and
\\ by changing order of arguments (dx,dy) or (dy,dx). 8 combinations
HueCircle= Lambda Atan2, tau (PrintPixel) -> {
Let c_width=256, c_height=256
Let cx=c_width/2, cy=c_height/2
Let radius=If(cx<=cy->cx, cy)
c_width--
c_height--
dy=-cy
For y=0 To c_height {
dy++ : dy2=dy*dy : dx=-cx
For x=0 To c_width {
dx++ : dist=Sqrt(dx^2+dy2)
If dist>radius Then continue
Call PrintPixel(x,y, Atan2(dx, -dy)/tau, dist/radius)
}
}
}
Call HueCircle(PrintPixel)
Scr$="" ' we use this string to load an image
Move 0,0
\\ scale.x, scale.y are twips height and width, of current layer
Copy scale.x, scale.y to Scr$
Clipboard Scr$ ' save window to clipboard
}
Check
 
Output:

see this image

Perl[edit]

Translation of: Sidef
use Imager;
use Math::Complex qw(cplx i pi);
 
my ($width, $height) = (300, 300);
my $center = cplx($width/2, $height/2);
 
my $img = Imager->new(xsize => $width,
ysize => $height);
 
foreach my $y (0 .. $height - 1) {
foreach my $x (0 .. $width - 1) {
 
my $vec = $center - $x - $y * i;
my $mag = 2 * abs($vec) / $width;
my $dir = (pi + atan2($vec->Re, $vec->Im)) / (2 * pi);
 
$img->setpixel(x => $x, y => $y,
color => {hsv => [360 * $dir, $mag, $mag < 1 ? 1 : 0]});
}
}
 
$img->write(file => 'color_wheel.png');

Perl 6[edit]

Works with: Rakudo version 2016.08
use Image::PNG::Portable;
 
my ($w, $h) = 300, 300;
 
my $out = Image::PNG::Portable.new: :width($w), :height($h);
 
my $center = $w/2 + $h/2*i;
 
color-wheel($out);
 
$out.write: 'Color-wheel-perl6.png';
 
sub color-wheel ( $png ) {
^$w .race.map: -> $x {
for ^$h -> $y {
my $vector = $center - $x - $y*i;
my $magnitude = $vector.abs * 2 / $w;
my $direction = ( π + atan2( |$vector.reals ) ) / τ;
$png.set: $x, $y, |hsv2rgb( $direction, $magnitude, $magnitude < 1 );
}
}
}
 
sub hsv2rgb ( $h, $s, $v ){
my $c = $v * $s;
my $x = $c * (1 - abs( (($h*6) % 2) - 1 ) );
my $m = $v - $c;
(do given $h {
when 0..^1/6 { $c, $x, 0 }
when 1/6..^1/3 { $x, $c, 0 }
when 1/3..^1/2 { 0, $c, $x }
when 1/2..^2/3 { 0, $x, $c }
when 2/3..^5/6 { $x, 0, $c }
when 5/6..1 { $c, 0, $x }
} ).map: ((*+$m) * 255).Int
}

Until local image uploading is re-enabled, see Color-wheel-perl6.png

Phix[edit]

Library: pGUI
-- demo\rosetta\Colour_wheel.exw
include pGUI.e
 
Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas
 
function hsv_to_rgb(atom h, s, v)
atom r,g,b
if s=0 then
{r,g,b} @= v
else
integer i = floor(h*6)
atom f = h*6-i,
p = v*(1-s),
q = v*(1-s*f),
t = v*(1-s*(1-f))
switch i do
case 0,
6: {r,g,b} = {v, t, p}
case 1: {r,g,b} = {q, v, p}
case 2: {r,g,b} = {p, v, t}
case 3: {r,g,b} = {p, q, v}
case 4: {r,g,b} = {t, p, v}
case 5: {r,g,b} = {v, p, q}
end switch
end if
return cdEncodeColor(r*255, g*255, b*255)
end function
 
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
integer {w, h} = IupGetIntInt(canvas, "DRAWSIZE")
cdCanvasActivate(cddbuffer)
integer radius = floor(min(w,h)/2)
integer cx = floor(w/2),
cy = floor(h/2)
for x=1 to w do
for y=1 to h do
integer rx = x - cx,
ry = y - cy
atom s = sqrt(rx*rx+ry*ry) / radius
if s <= 1.0 then
atom hue = ((atan2(ry, rx) / PI) + 1.0) / 2.0
cdCanvasPixel(cddbuffer, x, h-y, hsv_to_rgb(hue, s, 1))
end if
end for
end for
cdCanvasFlush(cddbuffer)
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_MAGENTA)
return IUP_DEFAULT
end function
 
procedure main()
IupOpen()
 
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "400x400") -- initial size
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
 
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Colour wheel")
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupCloseOnEscape(dlg)
 
IupMap(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure
 
main()

Python[edit]

from PIL import Image
import colorsys
import math
 
if __name__ == "__main__":
 
im = Image.new("RGB", (300,300))
radius = min(im.size)/2.0
centre = im.size[0]/2, im.size[1]/2
pix = im.load()
 
for x in range(im.width):
for y in range(im.height):
rx = x - centre[0]
ry = y - centre[1]
s = ((x - centre[0])**2.0 + (y - centre[1])**2.0)**0.5 / radius
if s <= 1.0:
h = ((math.atan2(ry, rx) / math.pi) + 1.0) / 2.0
rgb = colorsys.hsv_to_rgb(h, s, 1.0)
pix[x,y] = tuple([int(round(c*255.0)) for c in rgb])
 
im.show()

Racket[edit]

With the colors package

#lang racket
 
(require racket/draw
colors)
 
(define DIM 500)
(define target (make-bitmap DIM DIM))
(define dc (new bitmap-dc% [bitmap target]))
(define radius 200)
(define center (/ DIM 2))
 
(define (atan2 y x) (if (= 0 y x) 0 (atan y x)))
 
(for* ([x (in-range DIM)]
[y (in-range DIM)]
[rx (in-value (- x center))]
[ry (in-value (- y center))]
[s (in-value (/ (sqrt (+ (sqr rx) (sqr ry))) radius))]
#:when (<= s 1))
(define h (* 0.5 (+ 1 (/ (atan2 ry rx) pi))))
(send dc set-pen (hsv->color (hsv (if (= 1 h) 0 h) s 1)) 1 'solid)
(send dc draw-point x y))
 
target

Run BASIC[edit]

' -----------------------------------
' color wheel
' -----------------------------------
global pi
pi = 22 / 7
steps = 1
 
graphic #g, 525, 525
 
 
for x =0 to 525 step steps
for y =0 to 525 step steps
angle = atan2(y - 250, x - 250) * 360 / 2 / pi ' full degrees....
sector = int(angle / 60) ' 60 degree sectors (0 to 5)
slope = (angle mod 60) /60 * 255 ' 1 degree sectors.
 
if sector = 0 then col$ = "255 "; str$( int( slope)); " 0"
if sector = 1 then col$ = str$(int(256 - slope)); " 255 0"
if sector = 2 then col$ = "0 255 "; str$( int( slope))
if sector = 3 then col$ = "0 "; str$( int( 256 -slope)); " 255"
if sector = 4 then col$ = str$(int(slope)); " 0 255"
if sector = 5 then col$ = "255 0 "; str$( int( 256 -slope))
 
red = val( word$( col$, 1))
grn = val( word$( col$, 2))
blu = val( word$( col$, 3))
p = ((x -270)^2 +(y -270)^2)^0.5 / 250
r = min(255,p * red)
g = min(255,p * grn)
b = min(255,p * blu)
if p > 1 then #g "color white" else #g color(r,g,b)
#g "set "; x; " "; y
next y
next x
render #g
end
 
function atan2(y,x)
if (x = 0) and (y <> 0) then
r$ = "Y"
if y > 0 then atan2 = pi /2
if y < 0 then atan2 = 3 * pi /2
end if
 
if y = 0 and (x <> 0) then
r$ = "Y"
if x > 0 then atan2 = 0
if x < 0 then atan2 = pi
end if
 
If r$ <> "Y" then
if x = 0 and y = 0 then
atan2 = 0
else
baseAngle = atn(abs(y) / abs(x))
if x > 0 then
if y > 0 then atan2 = baseAngle
If y < 0 then atan2 = 2 * pi - baseAngle
end if
if x < 0 then
If y > 0 then atan2 = pi - baseAngle
If y < 0 then atan2 = pi + baseAngle
end if
end if
end if
end function

Sidef[edit]

Translation of: Perl 6
require('Imager')
 
var (width, height) = (300, 300)
var center = Complex(width/2 , height/2)
 
var img = %O<Imager>.new(xsize => width, ysize => height)
 
for y=(^height), x=(^width) {
var vector = (center - x - y.i)
var magnitude = (vector.abs * 2 / width)
var direction = ((Num.pi + atan2(vector.real, vector.imag)) / Num.tau)
img.setpixel(x => x, y => y,
color => Hash(hsv => [360*direction, magnitude, magnitude < 1 ? 1 : 0])
)
}
 
img.write(file => 'color_wheel.png')

Output image: Color wheel

Smart BASIC[edit]

' Runs on iOS
GET SCREEN SIZE sw,sh
xmax=0.45*3/7*(sw+sh)
x0=sw/2!y0=sh/2
twopi=2*3.1415926
GRAPHICS
GRAPHICS CLEAR
DIM triX(1000), triY(1000)
triX(0)=x0 ! triY(0)=y0
steps=INT(1^2*360)+1
dAngle=twopi/steps
dAngle2=dAngle/2
REFRESH OFF
FOR i=0 TO steps-1
pal(i/steps+TintOffset)
ANGLE=i*dAngle
FILL COLOR pal.r,pal.g,pal.b
DRAW COLOR pal.r,pal.g,pal.b
x=x0+(xmax-radius)*COS(ANGLE)
y=y0-(xmax-radius)*SIN(ANGLE)
k=0
FOR j=-dAngle2 TO dAngle2 STEP 0.02
k+=1
triX(k)=x0+xmax*COS(ANGLE+j)
triY(k)=y0-xmax*SIN(ANGLE+j)
NEXT j
k+=1
triX(k)=x0+xmax*COS(ANGLE+dAngle2)
triY(k)=y0-xmax*SIN(ANGLE+dAngle2)
DRAW POLY triX,triY COUNT k+1
FILL POLY triX,triY COUNT k+1
NEXT i
REFRESH ON
END
 
DEF pal(tint)
tint=tint*360
h=(tint%360)/60 ! f=FRACT(h) ! z=1-f ! ic=FLOOR(h)+1
ON ic GOTO s1,s2,s3,s4,s5,s6
s1: r=1 ! g=f ! b=0 ! GOTO done
s2: r=z ! g=1 ! b=0 ! GOTO done
s3: r=0 ! g=1 ! b=f ! GOTO done
s4: r=0 ! g=z ! b=1 ! GOTO done
s5: r=f ! g=0 ! b=1 ! GOTO done
s6: r=1 ! g=0 ! b=z ! done:
END DEF

View the output on Dropbox https://www.dropbox.com/s/g3l5rbywo34bnp6/IMG_4600.PNG?dl=0

zkl[edit]

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

var w=300,h=300,out=PPM(w,h);
colorWheel(out);
out.writeJPGFile("colorWheel.zkl.jpg");
 
fcn colorWheel(ppm){
zero,R:=ppm.w/2, zero;
foreach x,y in (w,h){
v,hue:=(x - zero).toFloat().toPolar(y - zero);
if(v<=R){ // only render in the circle
if((hue = hue.toDeg())<0) hue+=360; // (-pi..pi] to [0..2pi)
s:=v/R; // scale saturation zero at center to 1 at edge
ppm[x,y]=hsv2rgb(hue,1.0,s);
}
}
}
 
fcn hsv2rgb(hue,v,s){ // 0<=H<360, 0<=v(brightness)<=1, 0<=saturation<=1
// --> 24 bit RGB each R,G,B in [0..255]
to24bit:=fcn(r,g,b,m){
r,g,b=((r+m)*255).toInt(),((g+m)*255).toInt(),((b+m)*255).toInt();
r*0x10000 + g*0x100 + b
};
c:=v*s;
x:=c*(1.0 - (hue.toFloat()/60%2 - 1).abs());
m:=v - c;
if (0 <=hue< 60) return(to24bit(c, x, 0.0,m));
else if(60 <=hue<120) return(to24bit(x, c, 0.0,m));
else if(120<=hue<180) return(to24bit(0.0,c, x, m));
else if(180<=hue<240) return(to24bit(0.0,x, c, m));
else if(240<=hue<300) return(to24bit(x, 0.0,c, m));
else return(to24bit(c, 0.0,x, m));
}
Output:

See this image

References[edit]

  1. [1]