# Bitmap/Midpoint circle algorithm

(Redirected from Midpoint circle algorithm)
Bitmap/Midpoint circle algorithm
You are encouraged to solve this task according to the task description, using any language you may know.

Using the data storage type defined on this page for raster images, write an implementation of the midpoint circle algorithm   (also known as Bresenham's circle algorithm).

## 11l

Translation of: Python
```T Colour = BVec3

V black = Colour(0, 0, 0)
V white = Colour(255, 255, 255)

T Bitmap
Int width, height
Colour background
[[Colour]] map

F (width = 40, height = 40, background = white)
assert(width > 0 & height > 0)
.width = width
.height = height
.background = background
.map = (0 .< height).map(h -> (0 .< @width).map(w -> @@background))

F fillrect(x, y, width, height, colour = black)
assert(x >= 0 & y >= 0 & width > 0 & height > 0)
L(h) 0 .< height
L(w) 0 .< width
.map[y + h][x + w] = colour

F chardisplay()
V txt = .map.map(row -> row.map(bit -> (I bit == @@.background {‘ ’} E ‘@’)).join(‘’))
txt = txt.map(row -> ‘|’row‘|’)
txt.insert(0, ‘+’(‘-’ * .width)‘+’)
txt.append(‘+’(‘-’ * .width)‘+’)
print(reversed(txt).join("\n"))

F set(x, y, colour = black)
.map[y][x] = colour

F get(x, y)
R .map[y][x]

F circle(x0, y0, radius, colour = black)
V f = 1 - radius
V ddf_x = 1
V ddf_y = -2 * radius
V x = 0
V y = radius
.set(x0, y0 + radius, colour)
.set(x0, y0 - radius, colour)
.set(x0 + radius, y0, colour)
.set(x0 - radius, y0, colour)

L x < y
I f >= 0
y--
ddf_y += 2
f += ddf_y
x++
ddf_x += 2
f += ddf_x
.set(x0 + x, y0 + y, colour)
.set(x0 - x, y0 + y, colour)
.set(x0 + x, y0 - y, colour)
.set(x0 - x, y0 - y, colour)
.set(x0 + y, y0 + x, colour)
.set(x0 - y, y0 + x, colour)
.set(x0 + y, y0 - x, colour)
.set(x0 - y, y0 - x, colour)

V bitmap = Bitmap(25, 25)
bitmap.circle(x0' 12, y0' 12, radius' 12)
bitmap.chardisplay()```
Output:
```+-------------------------+
|         @@@@@@@         |
|       @@       @@       |
|     @@           @@     |
|    @               @    |
|   @                 @   |
|  @                   @  |
|  @                   @  |
| @                     @ |
| @                     @ |
|@                       @|
|@                       @|
|@                       @|
|@                       @|
|@                       @|
|@                       @|
|@                       @|
| @                     @ |
| @                     @ |
|  @                   @  |
|  @                   @  |
|   @                 @   |
|    @               @    |
|     @@           @@     |
|       @@       @@       |
|         @@@@@@@         |
+-------------------------+
```

## Action!

Part of the task is available in RGBCIRCL.ACT.

```INCLUDE "H6:RGBCIRCL.ACT" ;from task Midpoint circle algorithm

RGB black,yellow,violet,blue

PROC DrawImage(RgbImage POINTER img BYTE x,y)
RGB POINTER ptr
BYTE i,j

ptr=img.data
FOR j=0 TO img.h-1
DO
FOR i=0 TO img.w-1
DO
IF RgbEqual(ptr,yellow) THEN
Color=1
ELSEIF RgbEqual(ptr,violet) THEN
Color=2
ELSEIF RgbEqual(ptr,blue) THEN
Color=3
ELSE
Color=0
FI
Plot(x+i,y+j)
ptr==+RGBSIZE
OD
OD
RETURN

PROC Main()
RgbImage img
BYTE CH=\$02FC,width=[81],height=[51],st=[3]
BYTE ARRAY ptr(12393)
BYTE n
INT x,y
RGB POINTER col

Graphics(7+16)
SetColor(0,13,12) ;yellow
SetColor(1,4,8)   ;violet
SetColor(2,8,6)   ;blue
SetColor(4,0,0)   ;black

RgbBlack(black)
RgbYellow(yellow)
RgbViolet(violet)
RgbBlue(blue)

InitRgbImage(img,width,height,ptr)
FillRgbImage(img,black)

FOR n=0 TO height/st
DO
IF n MOD 3=0 THEN col=yellow
ELSEIF n MOD 3=1 THEN col=violet
ELSE col=blue FI
RgbCircle(img,width/2,height/2,st*n,col)
OD

DrawImage(img,(160-width)/2,(96-height)/2)

DO UNTIL CH#\$FF OD
CH=\$FF
RETURN```
Output:

```procedure Circle
(  Picture : in out Image;
Center  : Point;
Color   : Pixel
)  is
F     : Integer := 1 - Radius;
ddF_X : Integer := 0;
ddF_Y : Integer := -2 * Radius;
X     : Integer := 0;
Y     : Integer := Radius;
begin
Picture (Center.X, Center.Y + Radius) := Color;
Picture (Center.X, Center.Y - Radius) := Color;
Picture (Center.X + Radius, Center.Y) := Color;
Picture (Center.X - Radius, Center.Y) := Color;
while X < Y loop
if F >= 0 then
Y := Y - 1;
ddF_Y := ddF_Y + 2;
F := F + ddF_Y;
end if;
X := X + 1;
ddF_X := ddF_X + 2;
F := F + ddF_X + 1;
Picture (Center.X + X, Center.Y + Y) := Color;
Picture (Center.X - X, Center.Y + Y) := Color;
Picture (Center.X + X, Center.Y - Y) := Color;
Picture (Center.X - X, Center.Y - Y) := Color;
Picture (Center.X + Y, Center.Y + X) := Color;
Picture (Center.X - Y, Center.Y + X) := Color;
Picture (Center.X + Y, Center.Y - X) := Color;
Picture (Center.X - Y, Center.Y - X) := Color;
end loop;
end Circle;
```

The following illustrates use:

```   X : Image (1..16, 1..16);
begin
Fill (X, White);
Circle (X, (8, 8), 5, Black);
Print (X);
```
Output:
```

HHHHH
H     H
H       H
H         H
H         H
H         H
H         H
H         H
H       H
H     H
HHHHH

```

## ALGOL 68

Works with: ALGOL 68 version Revision 1 - one minor extension to language used - PRAGMA READ, similar to C's #include directive.
Works with: ALGOL 68G version Any - tested with release algol68g-2.6.

File: prelude/Bitmap/Midpoint_circle_algorithm.a68

```# -*- coding: utf-8 -*- #

circle OF class image :=
(  REF IMAGE picture,
POINT center,
PIXEL color
)VOID:
BEGIN
INT f     := 1 - radius,
POINT ddf := (0, -2 * radius),
df := (0, radius);
picture [x OF center, y OF center + radius] :=
picture [x OF center, y OF center - radius] :=
picture [x OF center + radius, y OF center] :=
picture [x OF center - radius, y OF center] := color;
WHILE x OF df < y OF df DO
IF f >= 0 THEN
y OF df -:= 1;
y OF ddf +:= 2;
f +:= y OF ddf
FI;
x OF df +:= 1;
x OF ddf +:= 2;
f +:= x OF ddf + 1;
picture [x OF center + x OF df, y OF center + y OF df] :=
picture [x OF center - x OF df, y OF center + y OF df] :=
picture [x OF center + x OF df, y OF center - y OF df] :=
picture [x OF center - x OF df, y OF center - y OF df] :=
picture [x OF center + y OF df, y OF center + x OF df] :=
picture [x OF center - y OF df, y OF center + x OF df] :=
picture [x OF center + y OF df, y OF center - x OF df] :=
picture [x OF center - y OF df, y OF center - x OF df] := color
OD
END # circle #;

SKIP```

File: test/Bitmap/Midpoint_circle_algorithm.a68

```#!/usr/bin/a68g --script #
# -*- coding: utf-8 -*- #

PR READ "prelude/Bitmap.a68" PR; # c.f. [[rc:Bitmap]] #
PR READ "prelude/Bitmap/Bresenhams_line_algorithm.a68" PR; # c.f. [[rc:Bitmap/Bresenhams_line_algorithm]] #
PR READ "prelude/Bitmap/Midpoint_circle_algorithm.a68" PR;

# The following illustrates use: #

test:(
REF IMAGE x = INIT LOC [1:16, 1:16] PIXEL;
(fill OF class image)(x, (white OF class image));
(circle OF class image)(x, (8, 8), 5, (black OF class image));
(print OF class image)(x)
)```
Output:
```ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffff000000000000000000000000000000ffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff
ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff
ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffff000000000000000000000000000000ffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
```

## Applesoft BASIC

``` 10  GR : GOSUB 330: END
330  COLOR= 15:CX = 20:CY = 20:R = 18: GOSUB 350"CIRCLE"
340  COLOR= 0:CX = 15:CY = 15:R = 6
350 F = 1 - R:X = 0:Y = R:DX = 0:DY =  - 2 * R: PLOT CX,CY + R: PLOT CX,CY - R: HLIN CX - R,CX + R AT CY: IF X >  = Y THEN  RETURN
360  FOR I = 0 TO 1: IF F >  = 0 THEN Y = Y - 1:DY = DY + 2:F = F + DY
370 X = X + 1:DX = DX + 2:F = F + DX + 1: HLIN CX - X,CX + X AT CY + Y: HLIN CX - X,CX + X AT CY - Y: HLIN CX - Y,CX + Y AT CY + X: HLIN CX - Y,CX + Y AT CY - X:I = X >  = Y: NEXT I: RETURN
```

## bash

```#! /bin/bash
# Based on https://en.wikipedia.org/wiki/Midpoint_circle_algorithm

function putpixel {
echo -en "\e[\$2;\$1H#"
}

function drawcircle {
x0=\$1
y0=\$2

for y in \$( seq \$((y0-radius)) \$((y0+radius)) )
do
echo -en "\e[\${y}H"
for x in \$( seq \$((x0+radius)) )
do
echo -n "-"
done
done

y=0
dx=1
dy=1

while [ \$x -ge \$y ]
do
putpixel \$(( x0 + x )) \$(( y0 + y ))
putpixel \$(( x0 + y )) \$(( y0 + x ))
putpixel \$(( x0 - y )) \$(( y0 + x ))
putpixel \$(( x0 - x )) \$(( y0 + y ))
putpixel \$(( x0 - x )) \$(( y0 - y ))
putpixel \$(( x0 - y )) \$(( y0 - x ))
putpixel \$(( x0 + y )) \$(( y0 - x ))
putpixel \$(( x0 + x )) \$(( y0 - y ))

if [ \$err -le 0 ]
then
((++y))
((err+=dy))
((dy+=2))
fi
if [ \$err -gt 0 ]
then
((--x))
((dx+=2))
fi
done
}

clear
drawcircle 13 13 11
echo -en "\e[H"
```
Output:
```------#########------
----##---------##----
---#-------------#---
--#---------------#--
-#-----------------#-
-#-----------------#-
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
-#-----------------#-
-#-----------------#-
--#---------------#--
---#-------------#---
----##---------##----
------#########------```

## BASIC

### BASIC256

```fastgraphics
clg
color red
call DrawCircle(150,100,100)
refresh
color blue
call DrawCircle(200,200,50)
refresh

#Function DrawCircle
#1st param = X-coord of center
#2nd param = Y-coord of center
#3rd param = radius
y=0
decisionOver2=1-x

while x>=y
plot( x + x0,  y + y0)
plot( y + x0,  x + y0)
plot(-x + x0,  y + y0)
plot(-y + x0,  x + y0)
plot(-x + x0, -y + y0)
plot(-y + x0, -x + y0)
plot( x + x0, -y + y0)
plot( y + x0, -x + y0)

y++

if decisionOver2<=0 then
decisionOver2+=2*y+1
else
x--
decisionOver2+=2*(y-x)+1
end if
end while
return 0
End Function```
Output:

## Batch File

```@echo off
setlocal enabledelayedexpansion

%== Initializations ==%
set width=50
set height=30

set /a allowance=height+2
mode %width%,%allowance%
echo Rendering...

set "outp="
for /l %%i in (1,1,%height%) do (
for /l %%j in (1,1,%width%) do (
set "c[%%i][%%j]= "
)
)

%== Set the parameters for making circle ==%
call :DrawCircle 20 20 10
call :DrawCircle 10 30 15

%== Output result ==%
for /l %%i in (1,1,%height%) do (
for /l %%j in (1,1,%width%) do (
set "outp=!outp!!c[%%i][%%j]!"
)
)
cls
echo !outp!
pause>nul
exit /b

%== The main function ==%
:DrawCircle
set x0=%1
set y0=%2

set y=0
set /a decisionOver2 = 1 - !x!

:circle_loop
if !x! geq !y! (
set /a "hor=x + x0","ver=y + y0"
set "c[!hor!][!ver!]=Û"
set /a "hor=y + x0","ver=x + y0"
set "c[!hor!][!ver!]=Û"
set /a "hor=-x + x0","ver=y + y0"
set "c[!hor!][!ver!]=Û"
set /a "hor=-y + x0","ver=x + y0"
set "c[!hor!][!ver!]=Û"
set /a "hor=-x + x0","ver=-y + y0"
set "c[!hor!][!ver!]=Û"
set /a "hor=-y + x0","ver=-x + y0"
set "c[!hor!][!ver!]=Û"
set /a "hor=x + x0","ver=-y + y0"
set "c[!hor!][!ver!]=Û"
set /a "hor=y + x0","ver=-x + y0"
set "c[!hor!][!ver!]=Û"

set /a y+=1
if !decisionOver2! leq 0 (
set /a "decisionOver2 = !decisionOver2! + (2 * y^) + 1"
) else (
set /a x-=1
set /a "decisionOver2 = !decisionOver2! + 2 * (y - x^) + 1"
)
goto circle_loop
)
goto :EOF
```
Output:
```                 █                       █
█                         █
█                         █
█                           █
█                           █
█                           █
█                             █
█                             █
█                             █
█ ███████                     █
██       ██                   █
██          █                  █
█ █           █                 █
█   █           █               █
█    █            █              █
█    █            █              █
█      █            █            █
█      █            █            █
█       █           █           █
█        █          █          █
█         █         █         █
█          █        █        █
█           ██      █      ██
█            ███  █    ███
█               ███████
█               █
█             █
█           █
██       ██
███████
```

## BBC BASIC

```      Width% = 200
Height% = 200

REM Set window size:
VDU 23,22,Width%;Height%;8,16,16,128

REM Draw circles:
PROCcircle(100,100,40, 0,0,0)
PROCcircle(100,100,80, 255,0,0)
END

DEF PROCcircle(cx%,cy%,r%,R%,G%,B%)
LOCAL f%, x%, y%, ddx%, ddy%
f% = 1 - r% : y% = r% : ddy% = - 2*r%
PROCsetpixel(cx%, cy%+r%, R%,G%,B%)
PROCsetpixel(cx%, cy%-r%, R%,G%,B%)
PROCsetpixel(cx%+r%, cy%, R%,G%,B%)
PROCsetpixel(cx%-r%, cy%, R%,G%,B%)
WHILE x% < y%
IF f% >= 0 THEN
y% -= 1
ddy% += 2
f% += ddy%
ENDIF
x% += 1
ddx% += 2
f% += ddx% + 1
PROCsetpixel(cx%+x%, cy%+y%, R%,G%,B%)
PROCsetpixel(cx%-x%, cy%+y%, R%,G%,B%)
PROCsetpixel(cx%+x%, cy%-y%, R%,G%,B%)
PROCsetpixel(cx%-x%, cy%-y%, R%,G%,B%)
PROCsetpixel(cx%+y%, cy%+x%, R%,G%,B%)
PROCsetpixel(cx%-y%, cy%+x%, R%,G%,B%)
PROCsetpixel(cx%+y%, cy%-x%, R%,G%,B%)
PROCsetpixel(cx%-y%, cy%-x%, R%,G%,B%)
ENDWHILE
ENDPROC

DEF PROCsetpixel(x%,y%,r%,g%,b%)
COLOUR 1,r%,g%,b%
GCOL 1
LINE x%*2,y%*2,x%*2,y%*2
ENDPROC
```

## C

Interface:

```void raster_circle(
image img,
unsigned int x0,
unsigned int y0,
color_component r,
color_component g,
color_component b );
```

Implementation:

```#define plot(x, y) put_pixel_clip(img, x, y, r, g, b)

void raster_circle(
image img,
unsigned int x0,
unsigned int y0,
color_component r,
color_component g,
color_component b )
{
int f = 1 - radius;
int ddF_x = 0;
int ddF_y = -2 * radius;
int x = 0;
int y = radius;

plot(x0, y0 + radius);
plot(x0, y0 - radius);
plot(x0 + radius, y0);
plot(x0 - radius, y0);

while(x < y)
{
if(f >= 0)
{
y--;
ddF_y += 2;
f += ddF_y;
}
x++;
ddF_x += 2;
f += ddF_x + 1;
plot(x0 + x, y0 + y);
plot(x0 - x, y0 + y);
plot(x0 + x, y0 - y);
plot(x0 - x, y0 - y);
plot(x0 + y, y0 + x);
plot(x0 - y, y0 + x);
plot(x0 + y, y0 - x);
plot(x0 - y, y0 - x);
}
}
#undef plot
```

## C#

This extension method extends GenericImage which is very similar to Bitmap but instead of using a SetPixel method it uses a "Color this[int x, int y] { get; set; }" property to get and set pixels.

```        /// <summary>
/// Draws a circle.
/// </summary>
/// <param name="image">
/// The destination image.
/// </param>
/// <param name="centerX">
/// The x center position of the circle.
/// </param>
/// <param name="centerY">
/// The y center position of the circle.
/// </param>
/// The radius of the circle.
/// </param>
/// <param name="color">
/// The color to use.
/// </param>
public static void DrawCircle(this GenericImage image, int centerX, int centerY, int radius, Color color)
{
int d = (5 - radius * 4) / 4;
int x = 0;
int y = radius;

do
{
// ensure index is in range before setting (depends on your image implementation)
// in this case we check if the pixel location is within the bounds of the image before setting the pixel
if (centerX + x >= 0 && centerX + x <= image.Width - 1 && centerY + y >= 0 && centerY + y <= image.Height - 1) image[centerX + x, centerY + y] = color;
if (centerX + x >= 0 && centerX + x <= image.Width - 1 && centerY - y >= 0 && centerY - y <= image.Height - 1) image[centerX + x, centerY - y] = color;
if (centerX - x >= 0 && centerX - x <= image.Width - 1 && centerY + y >= 0 && centerY + y <= image.Height - 1) image[centerX - x, centerY + y] = color;
if (centerX - x >= 0 && centerX - x <= image.Width - 1 && centerY - y >= 0 && centerY - y <= image.Height - 1) image[centerX - x, centerY - y] = color;
if (centerX + y >= 0 && centerX + y <= image.Width - 1 && centerY + x >= 0 && centerY + x <= image.Height - 1) image[centerX + y, centerY + x] = color;
if (centerX + y >= 0 && centerX + y <= image.Width - 1 && centerY - x >= 0 && centerY - x <= image.Height - 1) image[centerX + y, centerY - x] = color;
if (centerX - y >= 0 && centerX - y <= image.Width - 1 && centerY + x >= 0 && centerY + x <= image.Height - 1) image[centerX - y, centerY + x] = color;
if (centerX - y >= 0 && centerX - y <= image.Width - 1 && centerY - x >= 0 && centerY - x <= image.Height - 1) image[centerX - y, centerY - x] = color;
if (d < 0)
{
d += 2 * x + 1;
}
else
{
d += 2 * (x - y) + 1;
y--;
}
x++;
} while (x <= y);
}
```

## Clojure

Based upon the Common Lisp version.

```(defn draw-circle [draw-function x0 y0 radius]
(letfn [(put [x y m]
(let [x+ (+ x0 x)
x- (- x0 x)
y+ (+ y0 y)
y- (- y0 y)
x0y+ (+ x0 y)
x0y- (- x0 y)
xy0+ (+ y0 x)
xy0- (- y0 x)]
(draw-function x+ y+)
(draw-function x+ y-)
(draw-function x- y+)
(draw-function x- y-)
(draw-function x0y+ xy0+)
(draw-function x0y+ xy0-)
(draw-function x0y- xy0+)
(draw-function x0y- xy0-)
(let [[y m] (if (pos? m)
[(dec y) (- m (* 8 y))]
[y m])]
(when (<= x y)
(put (inc x)
y
(+ m 4 (* 8 x)))))))]
(put 0 radius (- 5 (* 4 radius)))))
```
```(let [circle-points (atom [])]
(letfn [(draw-fn [x y]
(swap! circle-points #(conj % [x y])))]
(draw-circle draw-fn 10 10 7))
(let [empty-grid (vec (repeat 20 (vec (repeat 20 " "))))
grid       (reduce (fn [grid xy] (assoc-in grid xy "x"))
empty-grid
@circle-points)]
(doseq [line grid]
(println (clojure.string/join line)))))
```
```

xxxxxxx
xx       xx
x           x
x           x
x             x
x             x
x             x
x             x
x             x
x             x
x             x
x           x
x           x
xx       xx
xxxxxxx

nil
```

## Common Lisp

Based upon the OCaml version.

```(defun draw-circle (draw-function x0 y0 radius)
(labels ((foo (x y)
(funcall draw-function x y))
(put (x y m)
(let ((x+ (+ x0 x))
(x- (- x0 x))
(y+ (+ y0 y))
(y- (- y0 y))
(x0y+ (+ x0 y))
(x0y- (- x0 y))
(xy0+ (+ y0 x))
(xy0- (- y0 x)))
(foo x+ y+)
(foo x+ y-)
(foo x- y+)
(foo x- y-)
(foo x0y+ xy0+)
(foo x0y+ xy0-)
(foo x0y- xy0+)
(foo x0y- xy0-)
(multiple-value-bind (y m) (if (plusp m)
(values (1- y) (- m (* 8 y)))
(values y m))
(when (<= x y)
(put (1+ x)
y
(+ m 4 (* 8 x))))))))
(put 0 radius (- 5 (* 4 radius)))
(values)))
```
```CL-USER> (let ((buffer (make-array '(30 30)
:element-type 'bit)))
(draw-circle (lambda (x y)
(setf (bit buffer x y) 1)) 15 15 10)
buffer)
```
```;; edited for your convenience
((                                                           )
(                        1 1 1 1 1 1 1                      )
(                  1 1 1               1 1 1                )
(                1                           1              )
(              1                               1            )
(            1                                   1          )
(            1                                   1          )
(            1                                   1          )
(          1                                       1        )
(          1                                       1        )
(          1                                       1        )
(          1                                       1        )
(          1                                       1        )
(          1                                       1        )
(          1                                       1        )
(            1                                   1          )
(            1                                   1          )
(            1                                   1          )
(              1                               1            )
(                1                           1              )
(                  1 1 1               1 1 1                )
(                        1 1 1 1 1 1 1                      )
(                                                           ))
```

## D

Uses the bitmap module from the Bitmap Task.

```import bitmap: Image, RGB;

void circle(Color)(Image!Color img, in int x0, in int y0,
in int radius, in Color color)
pure nothrow @nogc @safe {
int f = 1 - radius;
int ddfX = 1;
int ddfY = -2 * radius;
int x = 0;
int y = radius;
img[x0, y0 + radius] = color;
img[x0, y0 - radius] = color;
img[x0 + radius, y0] = color;
img[x0 - radius, y0] = color;

while (x < y) {
if (f >= 0) {
y--;
ddfY += 2;
f += ddfY;
}
x++;
ddfX += 2;
f += ddfX;
img[x0 + x, y0 + y] = color;
img[x0 - x, y0 + y] = color;
img[x0 + x, y0 - y] = color;
img[x0 - x, y0 - y] = color;
img[x0 + y, y0 + x] = color;
img[x0 - y, y0 + x] = color;
img[x0 + y, y0 - x] = color;
img[x0 - y, y0 - x] = color;
}
}

void main() @safe {
auto img = new Image!RGB(25, 25);
img.clear(RGB.white);
circle(img, 12, 12, 12, RGB.black);
img.textualShow;
}
```
Output:
```.........#######.........
.......##.......##.......
.....##...........##.....
....#...............#....
...#.................#...
..#...................#..
..#...................#..
.#.....................#.
.#.....................#.
#.......................#
#.......................#
#.......................#
#.......................#
#.......................#
#.......................#
#.......................#
.#.....................#.
.#.....................#.
..#...................#..
..#...................#..
...#.................#...
....#...............#....
.....##...........##.....
.......##.......##.......
.........#######.........```

## Delphi

Works with: Delphi version 6.0

```procedure DrawCircle(Image: TImage; Radius: integer; Center: TPoint);
var T1,T2: integer;
var X,Y: integer;
var Cnt: integer;

procedure DrawPixels(X,Y: integer);
{Draw pixel into all 8 octents}
begin
Image.Canvas.Pixels[Center.X + x, Center.Y + y]:=clRed;
Image.Canvas.Pixels[Center.X - X, Center.Y + Y]:=clRed;
Image.Canvas.Pixels[Center.X + X, Center.Y - Y]:=clRed;
Image.Canvas.Pixels[Center.X - X, Center.Y - Y]:=clRed;
Image.Canvas.Pixels[Center.X + Y, Center.Y + X]:=clRed;
Image.Canvas.Pixels[Center.X - Y, Center.Y + X]:=clRed;
Image.Canvas.Pixels[Center.X + y, Center.Y - X]:=clRed;
Image.Canvas.Pixels[Center.X - Y, Center.Y - X]:=clRed;
end;

begin
Cnt:=0;
T1:= Radius div 32;
{Start on X-axis}
X:= Radius; Y:= 0;
repeat
begin
DrawPixels(X, Y);
Y:=Y + 1;
T1:=T1 + Y;
T2:=T1 - X;
if T2 >= 0 then
begin
T1:=T2;
X:=X - 1;
end;
Inc(Cnt);
end
until x < y;
Form1.Caption:=IntToStr(Cnt);
end;

procedure ShowBrezCircle(Image: TImage);
begin
{Draw three times to make line thicker}
DrawCircle(Image,100,Point(200,200));
DrawCircle(Image,99,Point(200,200));
DrawCircle(Image,98,Point(200,200));
Image.Invalidate;
end;
```
Output:
```Elapsed Time: 7.341 ms.
```

## ERRE

```PROGRAM BCircle

!\$INCLUDE="PC.LIB"

PROCEDURE BCircle(cx%,cy%,r%)
local f%,x%,y%,ddx%,ddy%
f%=1-r%  y%=r%  ddy%=-2*r%
PSET(cx%,cy%+r%,1)
PSET(cx%,cy%-r%,1)
PSET(cx%+r%,cy%,1)
PSET(cx%-r%,cy%,1)
WHILE x%<y% DO
IF f%>=0 THEN
y%=y%-1
ddy%=ddy%+2
f%=f%+ddy%
END IF
x%=x%+1
ddx%=ddx%+2
f%=f%+ddx%+1
PSET(cx%+x%,cy%+y%,1)
PSET(cx%-x%,cy%+y%,1)
PSET(cx%+x%,cy%-y%,1)
PSET(cx%-x%,cy%-y%,1)
PSET(cx%+y%,cy%+x%,1)
PSET(cx%-y%,cy%+x%,1)
PSET(cx%+y%,cy%-x%,1)
PSET(cx%-y%,cy%-x%,1)
END WHILE
END PROCEDURE

BEGIN
SCREEN(1)
! Draw circles
BCircle(100,100,40)
BCircle(100,100,80)
END PROGRAM```

## Evaldraw

Gives slightly faster (in some cases), but more importantly prettier circles than the builtin drawsph(x,y,-rad) function.

```()
{
cls(0);
setcol(0xffffff);
srand(1234);
for(i=0; i<1000; i++) {
rad = int( abs(nrnd*10) );
x=rnd*xres;
y=rnd*yres;
}
}

drawcircle(cx,cy,r) {
if (cx+r < 0 || cy+r < 0) return;
if (cx-r > xres || cy-r > yres) return;
r = int(r);
if (r<=0) return;
r2 = r+r;
x = r; y = 0;
dy = -2; dx = r2+r2 - 4;
d = r2-1;
while(y<=x) {
setpix(cx-x, cy-y);
setpix(cx+x, cy-y);
setpix(cx-x, cy+y);
setpix(cx+x, cy+y);
setpix(cx-y, cy-x);
setpix(cx+y, cy-x);
setpix(cx-y, cy+x);
setpix(cx+y, cy+x);
d += dy;
dy -= 4;
++y;
if (d<0) {
d += dx;
dx -= 4;
--x;
}
}
}
```

## FBSL

Using pure FBSL's built-in graphics functions:

```#DEFINE WM_LBUTTONDOWN 513
#DEFINE WM_CLOSE 16

FBSLSETTEXT(ME, "Bresenham Circle") ' Set form caption
FBSLSETFORMCOLOR(ME, RGB(0, 255, 255)) ' Cyan: persistent background color
FBSL.GETDC(ME) ' Use volatile FBSL.GETDC below to avoid extra assignments

RESIZE(ME, 0, 0, 220, 220)
CENTER(ME)
SHOW(ME)

DIM Breadth AS INTEGER, Height AS INTEGER
FBSL.GETCLIENTRECT(ME, 0, 0, Breadth, Height)

BEGIN EVENTS ' Main message loop
SELECT CASE CBMSG
CASE WM_LBUTTONDOWN: MidpointCircle() ' Draw
CASE WM_CLOSE: FBSL.RELEASEDC(ME, FBSL.GETDC) ' Clean up
END SELECT
END EVENTS

SUB MidpointCircle()
BresenhamCircle(Breadth \ 2, Height \ 2, 80, &HFF) ' Red: Windows stores colors in BGR order
BresenhamCircle(Breadth \ 2, Height \ 2, 40, 0) ' Black

SUB BresenhamCircle(cx, cy, radius, colour)
DIM x = 0, y = radius, f = 1 - radius, dx = 0, dy = -2 * radius

PSET(FBSL.GETDC, cx, cy + radius, colour)(FBSL.GETDC, cx, cy - radius, colour)
PSET(FBSL.GETDC, cx + radius, cy, colour)(FBSL.GETDC, cx - radius, cy, colour)

WHILE x < y
IF f >= 0 THEN: DECR(y): INCR(dy, 2)(f, dy): END IF ' Try also "IF f THEN" :)
INCR(x)(dx, 2)(f, dx + 1)
PSET(FBSL.GETDC, cx + x, cy + y, colour)(FBSL.GETDC, cx - x, cy + y, colour)
PSET(FBSL.GETDC, cx + x, cy - y, colour)(FBSL.GETDC, cx - x, cy - y, colour)
PSET(FBSL.GETDC, cx + y, cy + x, colour)(FBSL.GETDC, cx - y, cy + x, colour)
PSET(FBSL.GETDC, cx + y, cy - x, colour)(FBSL.GETDC, cx - y, cy - x, colour)
WEND
END SUB
END SUB
```

Ouptut:

## Forth

```: circle { x y r color bmp -- }
1 r -  0 r 2* negate  0 r  { f ddx ddy dx dy }
color x     y r + bmp b!
color x     y r - bmp b!
color x r + y     bmp b!
color x r - y     bmp b!
begin dx dy < while
f 0< 0= if
dy  1-      to dy
ddy 2 + dup to ddy
f +         to f
then
dx 1+       to dx
ddx 2 + dup to ddx
f 1+ +      to f
color x dx + y dy + bmp b!
color x dx - y dy + bmp b!
color x dx + y dy - bmp b!
color x dx - y dy - bmp b!
color x dy + y dx + bmp b!
color x dy - y dx + bmp b!
color x dy + y dx - bmp b!
color x dy - y dx - bmp b!
repeat ;

12 12 bitmap value test
0 test bfill
6 6 5 blue test circle
test bshow cr
```

## Fortran

This code should be inside RCImagePrimitive (see here). The private subroutine `draw_circle_toch`, which writes to a channel, is used by both `draw_circle_rgb` and `draw_circle_sc` and the interface allows to use `draw_circle` with rgb images and grayscale images.

```interface draw_circle
module procedure draw_circle_sc, draw_circle_rgb
end interface

private :: plot, draw_circle_toch
```
```subroutine plot(ch, p, v)
integer, dimension(:,:), intent(out) :: ch
type(point), intent(in) :: p
integer, intent(in) :: v

integer :: cx, cy
! I've kept the default 1-based array, but top-left corner pixel
! is labelled as (0,0).
cx = p%x + 1
cy = p%y + 1

if ( (cx > 0) .and. (cx <= ubound(ch,1)) .and. &
(cy > 0) .and. (cy <= ubound(ch,2)) ) then
ch(cx,cy) = v
end if
end subroutine plot

subroutine draw_circle_toch(ch, c, radius, v)
integer, dimension(:,:), intent(out) :: ch
type(point), intent(in) :: c
integer, intent(in) :: radius, v

integer :: f, ddf_x, ddf_y, x, y

f = 1 - radius
ddf_x = 0
ddf_y = -2 * radius
x = 0

call plot(ch, point(c%x, c%y + radius), v)
call plot(ch, point(c%x, c%y - radius), v)
call plot(ch, point(c%x + radius, c%y), v)
call plot(ch, point(c%x - radius, c%y), v)

do while ( x < y )
if ( f >= 0 ) then
y = y - 1
ddf_y = ddf_y + 2
f = f + ddf_y
end if
x = x + 1
ddf_x = ddf_x + 2
f = f + ddf_x + 1
call plot(ch, point(c%x + x, c%y + y), v)
call plot(ch, point(c%x - x, c%y + y), v)
call plot(ch, point(c%x + x, c%y - y), v)
call plot(ch, point(c%x - x, c%y - y), v)
call plot(ch, point(c%x + y, c%y + x), v)
call plot(ch, point(c%x - y, c%y + x), v)
call plot(ch, point(c%x + y, c%y - x), v)
call plot(ch, point(c%x - y, c%y - x), v)
end do

end subroutine draw_circle_toch

subroutine draw_circle_rgb(img, c, radius, color)
type(rgbimage), intent(out) :: img
type(point), intent(in) :: c
integer, intent(in) :: radius
type(rgb), intent(in) :: color

call draw_circle_toch(img%red, c, radius, color%red)
call draw_circle_toch(img%green, c, radius, color%green)
call draw_circle_toch(img%blue, c, radius, color%blue)
end subroutine draw_circle_rgb

subroutine draw_circle_sc(img, c, radius, lum)
type(scimage), intent(out) :: img
type(point), intent(in) :: c
integer, intent(in) :: radius, lum

call draw_circle_toch(img%channel, c, radius, lum)
end subroutine draw_circle_sc
```

## FreeBASIC

```' version 15-10-2016
' compile with: fbc -s gui

' Variant with Integer-Based Arithmetic from Wikipedia page:
' Midpoint circle algorithm
Sub circle_(x0 As Integer, y0 As Integer , radius As Integer, Col As Integer)

Dim As Integer x = radius
Dim As Integer y
' Decision criterion divided by 2 evaluated at x=r, y=0
Dim As Integer decisionOver2 = 1 - x

While(x >= y)
PSet(x0 + x, y0 + y), col
PSet(x0 - x, y0 + y), col
PSet(x0 + x, y0 - y), col
PSet(x0 - x, y0 - y), col
PSet(x0 + y, y0 + x), col
PSet(x0 - y, y0 + x), col
PSet(x0 + y, y0 - x), col
PSet(x0 - y, y0 - x), col
y = y +1
If decisionOver2 <= 0 Then
decisionOver2 += y * 2 +1 ' Change in decision criterion for y -> y +1
Else
x = x -1
decisionOver2 += (y - x) * 2 +1  '  Change for y -> y +1, x -> x -1
End If
Wend

End Sub

' ------=< MAIN >=------

ScreenRes 600, 600, 32
Dim As Integer w, h, depth
Randomize Timer

ScreenInfo w, h

For i As Integer = 1 To 10
circle_(Rnd * w,  Rnd * h , Rnd * 200 , Int(Rnd *&hFFFFFF))
Next

'save screen to BMP file
BSave "Name.BMP", 0

' empty keyboard buffer
While Inkey <> "" : Wend
WindowTitle "hit any key to end program"
Sleep
End
```

## FutureBasic

FB has native functions that handle bitmap calculations. This compiles as a stand-alone Macintosh app that allows the user to adjust the screen-centered bitmap width from a single pixel to a large circle.

```_wndW = 600
_wndH = 600

_window = 1
begin enum 1
_sliderBtn
_sliderValue
_cWell
_pixelView
_quitBtn
end enum

void local fn ViewDrawRect
CGRect   viewRect, dotRect

CGContextRef ctx = fn GraphicsContextCurrentCGContext
viewRect = fn ViewBounds( _pixelView )

long sliderValue = fn ControlIntegerValue( _sliderBtn )

CGContextSaveGState( ctx )

CGContextSetLineWidth(ctx, 1.0)
CGContextSetRGBStrokeColor( ctx, 0.0, 0.0, 0.0, 1.0  )
CGContextStrokeRect( ctx, viewRect )

dotRect.origin.x = viewRect.size.width/2 - sliderValue
dotRect.origin.y = viewRect.size.height/2 - sliderValue
dotRect.size.width = 2 *  sliderValue
dotRect.size.height = 2 *  sliderValue

ColorRef col = fn ColorWellColor(_cWell)
CGColorRef myColor = fn ColorCGColor( col )

CGContextSetStrokeColorWithColor( ctx, myColor )
CGContextStrokeEllipseInRect(  ctx, dotRect )
CGContextRestoreGState( ctx )
end fn

void local fn BuildWindow
window 1, @"DotView", ( 0, 0, _wndW, _wndH )

view subclass _pixelView, ( 0, 0, _wndH, _wndW)

ColorRef myColor = fn ColorWithRGB( 1.0, 0.0, 0.0, 1.0 )
colorwell _cWell,, myColor, ( 30, 30, 50, 30 )
ViewAddSubview( _pixelView, _cWell )

slider _sliderBtn,, 75, ( 170, 30, 250, 20 ), 1, 240
ControlSetContinuous( _sliderBtn, YES )

ViewAddSubview( _pixelView, _sliderBtn )
textlabel _sliderValue, @"75", ( 430, 35, 36, 17 )
ControlSetAlignment( _sliderValue, NSTextAlignmentCenter )
ViewAddSubview( _pixelView, _sliderValue )

button _quitBtn, , , @"Q", (_wndW - 50, 10, 40, 40),, NSBezelStyleCircular
ControlSetAction( _quitBtn, @"terminate:" )
end fn

void local fn DoDialog( ev as long, tag as long )
select ( ev )
case _btnClick
select (tag)
case _cWell : ViewSetNeedsDisplay( _pixelView )
case _sliderBtn
ControlTakeIntegerValueFrom( _sliderValue, _sliderBtn )
ViewSetNeedsDisplay( _pixelView )
end select
case _viewDrawRect
select ( tag )
case _pixelView : fn ViewDrawRect
end select
end select
end fn

on dialog fn DoDialog
fn BuildWindow

HandleEvents```

## Go

This produces identical results to the C code in the WP article, but with more compact code.

```package raster

// Circle plots a circle with center x, y and radius r.
// Limiting behavior:
// r < 0 plots no pixels.
// r = 0 plots a single pixel at x, y.
// r = 1 plots four pixels in a diamond shape around the center pixel at x, y.
func (b *Bitmap) Circle(x, y, r int, p Pixel) {
if r < 0 {
return
}
// Bresenham algorithm
x1, y1, err := -r, 0, 2-2*r
for {
b.SetPx(x-x1, y+y1, p)
b.SetPx(x-y1, y-x1, p)
b.SetPx(x+x1, y-y1, p)
b.SetPx(x+y1, y+x1, p)
r = err
if r > x1 {
x1++
err += x1*2 + 1
}
if r <= y1 {
y1++
err += y1*2 + 1
}
if x1 >= 0 {
break
}
}
}

func (b *Bitmap) CircleRgb(x, y, r int, c Rgb) {
b.Circle(x, y, r, c.Pixel())
}
```

Demonstration program:

```package main

// Files required to build supporting package raster are found in:
// * This task (immediately above)
// * Bitmap
// * Write a PPM file

import (
"raster"
"fmt"
)

func main() {
b := raster.NewBitmap(400, 300)
b.FillRgb(0xffdf20) // yellow
// large circle, demonstrating clipping to image boundaries
b.CircleRgb(300, 249, 200, 0xff2020) // red
if err := b.WritePpmFile("circle.ppm"); err != nil {
fmt.Println(err)
}
}
```

The basic algorithm can be implemented generically.

```module Circle where

import Data.List

type Point = (Int, Int)

-- Takes the center of the circle and radius, and returns the circle points
generateCirclePoints :: Point -> Int -> [Point]
generateCirclePoints (x0, y0) radius
-- Four initial points, plus the generated points
= (x0, y0 + radius) : (x0, y0 - radius) : (x0 + radius, y0) : (x0 - radius, y0) : points
where
-- Creates the (x, y) octet offsets, then maps them to absolute points in all octets.
points = concatMap generatePoints \$ unfoldr step initialValues
generatePoints (x, y)
= [(xop x0 x', yop y0 y') | (x', y') <- [(x, y), (y, x)], xop <- [(+), (-)], yop <- [(+), (-)]]

-- The initial values for the loop
initialValues = (1 - radius, 1, (-2) * radius, 0, radius)

-- One step of the loop. The loop itself stops at Nothing.
step (f, ddf_x, ddf_y, x, y) | x >= y = Nothing
| otherwise = Just ((x', y'), (f', ddf_x', ddf_y', x', y'))
where
(f', ddf_y', y') | f >= 0 = (f + ddf_y' + ddf_x', ddf_y + 2, y - 1)
| otherwise = (f + ddf_x, ddf_y, y)
ddf_x' = ddf_x + 2
x' = x + 1
```

An example using regular 2d arrays of characters to represent a bitmap:

```module CircleArrayExample where

import Circle

-- A surface is just a 2d array of characters for the purposes of this example
type Colour = Char
type Surface = Array (Int, Int) Colour

-- Returns a surface of the given width and height filled with the colour
blankSurface :: Int -> Int -> Colour -> Surface
blankSurface width height filler = listArray bounds (repeat filler)
where
bounds = ((0, 0), (width - 1, height - 1))

-- Generic plotting function. Plots points onto a surface with the given colour.
plotPoints :: Surface -> Colour -> [Point] -> Surface
plotPoints surface colour points = surface // zip points (repeat colour)

-- Draws a circle of the given colour on the surface given a center and radius
drawCircle :: Surface -> Colour -> Point -> Int -> Surface
drawCircle surface colour center radius
= plotPoints surface colour (generateCirclePoints center radius)

-- Converts a surface to a string
showSurface image = unlines [[image ! (x, y) | x <- xRange] | y <- yRange]
where
((xLow, yLow), (xHigh, yHigh)) = bounds image
(xRange, yRange) = ([xLow..xHigh], [yLow..yHigh])

-- Converts a surface to a string and prints it
printSurface = putStrLn . showSurface
```

Using the Image type from the Bitmap module defined here:

```module CircleBitmapExample where

import Circle
import Bitmap

drawCircle :: (Color c) => Image s c -> c -> Point -> Int -> ST s (Image s c)
drawCircle image colour center radius = do
let pixels = map Pixel (generateCirclePoints center radius)
forM_ pixels \$ \pixel -> setPix image pixel colour
return image
```

## J

Solution:
Using definitions from Basic bitmap storage. (Note that viewRGB is at the bottom of the entry - separate from the rest of the definitions.)

```NB.*getBresenhamCircle v Returns points for a circle given center and radius
NB. y is: y0 x0 radius
'y0 x0 radius'=. y
x=. 0
pts=. 0 2\$0
while. x <: y do.
pts=. pts , y , x
if. f >: 0 do.
y=. <:y
f=. f + _2 * y
end.
x=. >:x
f =. f + >: 2 * x
end.
offsets=. (,|."1) (1 _1 {~ #: i.4) *"1"1 _ pts
~.,/ (y0,x0) +"1 offsets
)

NB.*drawCircles v Draws circle(s) (x) on image (y)
NB. x is: 2-item list of boxed (y0 x0 radius) ; (color)
drawCircles=: (1&{:: ;~ [: ; [: <@getBresenhamCircle"1 (0&{::))@[ setPixels ]
```

Example usage:

```myimg=: 0 255 0 makeRGB 25 25                              NB. 25 by 25 green image
myimg=: (12 12 12 ; 255 0 0) drawCircles myimg              NB. draw red circle with radius 12
viewRGB ((12 12 9 ,: 12 12 6) ; 0 0 255) drawCircles myimg  NB. draw two more concentric circles
```

## Java

```import java.awt.Color;

public class MidPointCircle {
private BasicBitmapStorage image;

public MidPointCircle(final int imageWidth, final int imageHeight) {
this.image = new BasicBitmapStorage(imageWidth, imageHeight);
}

private void drawCircle(final int centerX, final int centerY, final int radius) {
int d = (5 - radius * 4)/4;
int x = 0;
int y = radius;
Color circleColor = Color.white;

do {
image.setPixel(centerX + x, centerY + y, circleColor);
image.setPixel(centerX + x, centerY - y, circleColor);
image.setPixel(centerX - x, centerY + y, circleColor);
image.setPixel(centerX - x, centerY - y, circleColor);
image.setPixel(centerX + y, centerY + x, circleColor);
image.setPixel(centerX + y, centerY - x, circleColor);
image.setPixel(centerX - y, centerY + x, circleColor);
image.setPixel(centerX - y, centerY - x, circleColor);
if (d < 0) {
d += 2 * x + 1;
} else {
d += 2 * (x - y) + 1;
y--;
}
x++;
} while (x <= y);

}
}
```

## Julia

Works with: Julia version 0.6
```function drawcircle!(img::Matrix{T}, col::T, x0::Int, y0::Int, radius::Int) where T
x = radius - 1
y = 0
δx = δy = 1
er = δx - (radius << 1)

s = x + y
while x ≥ y
for opx in (+, -), opy in (+, -), el in (x, y)
@inbounds img[opx(x0, el) + 1, opy(y0, s - el) + 1] = col
end
if er ≤ 0
y  += 1
er += δy
δy += 2
end
if er > 0
x  -= 1
δx += 2
er += (-radius << 1) + δx
end
s = x + y
end
return img
end

# Test
using Images

img = fill(Gray(255.0), 25, 25);
drawcircle!(img, Gray(0.0), 12, 12, 12)
```

## Kotlin

Translation of: Java
```// version 1.1.4-3

import java.awt.Color
import java.awt.Graphics
import java.awt.image.BufferedImage
import javax.swing.JOptionPane
import javax.swing.JLabel
import javax.swing.ImageIcon

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 drawCircle(bbs: BasicBitmapStorage, centerX: Int, centerY: Int, radius: Int, circleColor: Color) {
var d = (5 - radius * 4) / 4
var x = 0
var y = radius

do {
with(bbs) {
setPixel(centerX + x, centerY + y, circleColor)
setPixel(centerX + x, centerY - y, circleColor)
setPixel(centerX - x, centerY + y, circleColor)
setPixel(centerX - x, centerY - y, circleColor)
setPixel(centerX + y, centerY + x, circleColor)
setPixel(centerX + y, centerY - x, circleColor)
setPixel(centerX - y, centerY + x, circleColor)
setPixel(centerX - y, centerY - x, circleColor)
}
if (d < 0) {
d += 2 * x + 1
}
else {
d += 2 * (x - y) + 1
y--
}
x++
}
while (x <= y)
}

fun main(args: Array<String>) {
val bbs = BasicBitmapStorage(400, 400)
bbs.fill(Color.pink)
drawCircle(bbs, 200, 200, 100, Color.black)
drawCircle(bbs, 200, 200,  50, Color.white)
val label = JLabel(ImageIcon(bbs.image))
val title = "Bresenham's circle algorithm"
JOptionPane.showMessageDialog(null, label, title, JOptionPane.PLAIN_MESSAGE)
}
```

## Lua

Uses Bitmap class here, with an ASCII pixel representation, then extending..

```function Bitmap:circle(x, y, r, c)
local dx, dy, err = r, 0, 1-r
while dx >= dy do
self:set(x+dx, y+dy, c)
self:set(x-dx, y+dy, c)
self:set(x+dx, y-dy, c)
self:set(x-dx, y-dy, c)
self:set(x+dy, y+dx, c)
self:set(x-dy, y+dx, c)
self:set(x+dy, y-dx, c)
self:set(x-dy, y-dx, c)
dy = dy + 1
if err < 0 then
err = err + 2 * dy + 1
else
dx, err = dx-1, err + 2 * (dy - dx) + 1
end
end
end
```

Demo:

```function Bitmap:axes()
local hw, hh = math.floor(self.width/2), math.floor(self.height/2)
for i = 0, self.width-1 do self:set(i,hh,"-") end
for i = 0, self.height-1 do self:set(hw,i,"|") end
self:set(hw,hh,"+")
end

function Bitmap:render()
for y = 1, self.height do
print(table.concat(self.pixels[y]," "))
end
end

bitmap = Bitmap(25, 25)
bitmap:clear("·")
bitmap:axes()
bitmap:circle(12, 12, 11, "■")
bitmap:circle(12, 12, 8, "■")
bitmap:circle(12, 12, 5, "■")
bitmap:circle(12, 12, 2, "■")
bitmap:render()
```
Output:
```· · · · · · · · · · · · | · · · · · · · · · · · ·
· · · · · · · · · ■ ■ ■ ■ ■ ■ ■ · · · · · · · · ·
· · · · · · · ■ ■ · · · | · · · ■ ■ · · · · · · ·
· · · · · ■ ■ · · · · · | · · · · · ■ ■ · · · · ·
· · · · ■ · · · · · ■ ■ ■ ■ ■ · · · · · ■ · · · ·
· · · ■ · · · · ■ ■ · · | · · ■ ■ · · · · ■ · · ·
· · · ■ · · ■ ■ · · · · | · · · · ■ ■ · · ■ · · ·
· · ■ · · · ■ · · · ■ ■ ■ ■ ■ · · · ■ · · · ■ · ·
· · ■ · · ■ · · · ■ · · | · · ■ · · · ■ · · ■ · ·
· ■ · · · ■ · · ■ · · · | · · · ■ · · ■ · · · ■ ·
· ■ · · ■ · · ■ · · · ■ ■ ■ · · · ■ · · ■ · · ■ ·
· ■ · · ■ · · ■ · · ■ · | · ■ · · ■ · · ■ · · ■ ·
- ■ - - ■ - - ■ - - ■ - + - ■ - - ■ - - ■ - - ■ -
· ■ · · ■ · · ■ · · ■ · | · ■ · · ■ · · ■ · · ■ ·
· ■ · · ■ · · ■ · · · ■ ■ ■ · · · ■ · · ■ · · ■ ·
· ■ · · · ■ · · ■ · · · | · · · ■ · · ■ · · · ■ ·
· · ■ · · ■ · · · ■ · · | · · ■ · · · ■ · · ■ · ·
· · ■ · · · ■ · · · ■ ■ ■ ■ ■ · · · ■ · · · ■ · ·
· · · ■ · · ■ ■ · · · · | · · · · ■ ■ · · ■ · · ·
· · · ■ · · · · ■ ■ · · | · · ■ ■ · · · · ■ · · ·
· · · · ■ · · · · · ■ ■ ■ ■ ■ · · · · · ■ · · · ·
· · · · · ■ ■ · · · · · | · · · · · ■ ■ · · · · ·
· · · · · · · ■ ■ · · · | · · · ■ ■ · · · · · · ·
· · · · · · · · · ■ ■ ■ ■ ■ ■ ■ · · · · · · · · ·
· · · · · · · · · · · · | · · · · · · · · · · · ·```

## Mathematica / Wolfram Language

```SetAttributes[drawcircle, HoldFirst];
drawcircle[img_, {x0_, y0_}, r_, color_: White] :=
Module[{f = 1 - r, ddfx = 1, ddfy = -2 r, x = 0, y = r,
pixels = {{0, r}, {0, -r}, {r, 0}, {-r, 0}}},
While[x < y,
If[f >= 0, y--; ddfy += 2; f += ddfy];
x++; ddfx += 2; f += ddfx;
pixels = Join[pixels, {{x, y}, {x, -y}, {-x, y}, {-x, -y},
{y, x}, {y, -x}, {-y, x}, {-y, -x}}]];
img = ReplacePixelValue[img, {x0, y0} + # -> color & /@ pixels]]
```

Example usage（it will draw a circle on Lena's face.）:

```img = ExampleData[{"TestImage", "Lena"}];
drawcircle[img, {250, 250}, 100]
```

## Modula-3

```INTERFACE Circle;

IMPORT Bitmap;

PROCEDURE Draw(
img: Bitmap.T;
center: Bitmap.Point;
color: Bitmap.Pixel);

END Circle.
```
```MODULE Circle;

IMPORT Bitmap;

PROCEDURE Draw(
img: Bitmap.T;
center: Bitmap.Point;
color: Bitmap.Pixel) =
VAR f := 1 - radius;
ddfx := 0;
ddfy := - 2 * radius;
x := 0;
BEGIN
Bitmap.SetPixel(img, Bitmap.Point{center.x, center.y + radius}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x, center.y - radius}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x + radius, center.y}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x - radius, center.y}, color);
WHILE x < y DO
IF f >= 0 THEN
y := y - 1;
ddfy := ddfy + 2;
f := f + ddfy;
END;
x := x + 1;
ddfx := ddfx + 2;
f := f + ddfx + 1;
Bitmap.SetPixel(img, Bitmap.Point{center.x + x, center.y + y}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x - x, center.y + y}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x + x, center.y - y}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x - x, center.y - y}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x + y, center.y + x}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x - y, center.y + x}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x + y, center.y - x}, color);
Bitmap.SetPixel(img, Bitmap.Point{center.x - y, center.y - x}, color);
END;
END Draw;

BEGIN
END Circle.
```

Example (outputs a PPM image):

```MODULE Main;

IMPORT Circle, Bitmap, PPM;

VAR testpic: Bitmap.T;

BEGIN
testpic := Bitmap.NewImage(32, 32);
Bitmap.Fill(testpic, Bitmap.White);
Circle.Draw(testpic, Bitmap.Point{16, 16}, 10, Bitmap.Black);
PPM.Create("testpic.ppm", testpic);
END Main.
```

## Nim

```import bitmap

proc setPixel(img: Image; x, y: int; color: Color) {.inline.} =
# Set a pixel at a given color.
# Ignore if the point is outside of the image.
if x in 0..<img.w and y in 0..<img.h:
img[x, y] = color

proc drawCircle(img: Image; center: Point; radius: Natural; color: Color) =
## Draw a circle using midpoint circle algorithm.

var
f = 1 - radius
ddFX = 0
ddFY = -2 * radius
x = 0

img.setPixel(center.x, center.y + radius, color)
img.setPixel(center.x, center.y - radius, color)
img.setPixel(center.x + radius, center.y, color)
img.setPixel(center.x - radius, center.y, color)

while x < y:
if f >= 0:
dec y
inc ddFY, 2
inc f, ddFY
inc x
inc ddFX, 2
inc f, ddFX + 1

img.setPixel(center.x + x, center.y + y, color)
img.setPixel(center.x - x, center.y + y, color)
img.setPixel(center.x + x, center.y - y, color)
img.setPixel(center.x - x, center.y - y, color)
img.setPixel(center.x + y, center.y + x, color)
img.setPixel(center.x - y, center.y + x, color)
img.setPixel(center.x + y, center.y - x, color)
img.setPixel(center.x - y, center.y - x, color)

#———————————————————————————————————————————————————————————————————————————————————————————————————

when isMainModule:
var img = newImage(16, 16)
img.fill(White)
img.drawCircle((7, 7), 5, Black)
img.print()
```
Output:
```................
................
.....HHHHH......
....H.....H.....
...H.......H....
..H.........H...
..H.........H...
..H.........H...
..H.........H...
..H.........H...
...H.......H....
....H.....H.....
.....HHHHH......
................
................
................```

## OCaml

```let raster_circle ~img ~color ~c:(x0, y0) ~r =
let plot = put_pixel img color in
let x = 0
and y = r
and m = 5 - 4 * r
in
let rec loop x y m =
plot (x0 + x) (y0 + y);
plot (x0 + y) (y0 + x);
plot (x0 - x) (y0 + y);
plot (x0 - y) (y0 + x);
plot (x0 + x) (y0 - y);
plot (x0 + y) (y0 - x);
plot (x0 - x) (y0 - y);
plot (x0 - y) (y0 - x);
let y, m =
if m > 0
then (y - 1), (m - 8 * y)
else y, m
in
if x <= y then
let x = x + 1 in
let m = m + 8 * x + 4 in
loop x y m
in
loop x y m
;;
```

## Perl

```# 20220301 Perl programming solution

use strict;
use warnings;

use Algorithm::Line::Bresenham 'circle';

my @points;
my @circle = circle((10) x 3);

for (@circle) { \$points[\$_->[0]][\$_->[1]] = '#' }

print join "\n", map { join '', map { \$_ || ' ' } @\$_ } @points
```
Output:
```       #######
##       ##
#           #
#             #
#               #
#                 #
#                 #
#                   #
#                   #
#                   #
#                   #
#                   #
#                   #
#                   #
#                 #
#                 #
#               #
#             #
#           #
##       ##
#######
```

## Phix

Translation of: Go

Requires new_image() from Bitmap, write_ppm() from Write_a_PPM_file.
Results may be verified with demo\rosetta\viewppm.exw

```-- demo\rosetta\Bitmap_Circle.exw  (runnable version)
include ppm.e -- red, yellow, new_image(), write_ppm()  -- (covers above requirements)

function SetPx(sequence img, atom x, y, integer colour)
if  x>=1 and x<=length(img)
and y>=1 and y<=length(img[x]) then
img[x][y] = colour
end if
return img
end function

function Circle(sequence img, atom x, y, r, integer colour)
atom x1 = -r,
y1 = 0,
err = 2-2*r
if r>=0 then
-- Bresenham algorithm
while 1 do
img = SetPx(img, x-x1, y+y1, colour)
img = SetPx(img, x-y1, y-x1, colour)
img = SetPx(img, x+x1, y-y1, colour)
img = SetPx(img, x+y1, y+x1, colour)
r = err
if r>x1 then
x1 += 1
err += x1*2 + 1
end if
if r<=y1 then
y1 += 1
err += y1*2 + 1
end if
if x1>=0 then exit end if
end while
end if
return img
end function

sequence img = new_image(400,300,yellow)
img = Circle(img, 200, 150, 100, red)
write_ppm("Circle.ppm",img)
```

## PicoLisp

```(de midPtCircle (Img CX CY Rad)
(let (F (- 1 Rad)  DdFx 0  DdFy (* -2 Rad)  X 0  Y Rad)
(set (nth Img (+ CY Rad) CX) 1)
(set (nth Img (- CY Rad) CX) 1)
(set (nth Img CY (+ CX Rad)) 1)
(set (nth Img CY (- CX Rad)) 1)
(while (> Y X)
(when (ge0 F)
(dec 'Y)
(inc 'F (inc 'DdFy 2)) )
(inc 'X)
(inc 'F (inc (inc 'DdFx 2)))
(set (nth Img (+ CY Y) (+ CX X)) 1)
(set (nth Img (+ CY Y) (- CX X)) 1)
(set (nth Img (- CY Y) (+ CX X)) 1)
(set (nth Img (- CY Y) (- CX X)) 1)
(set (nth Img (+ CY X) (+ CX Y)) 1)
(set (nth Img (+ CY X) (- CX Y)) 1)
(set (nth Img (- CY X) (+ CX Y)) 1)
(set (nth Img (- CY X) (- CX Y)) 1) ) ) )

(let Img (make (do 120 (link (need 120 0))))       # Create image 120 x 120
(midPtCircle Img 60 60 50)                      # Draw circle
(out "img.pbm"                                  # Write to bitmap file
(prinl "P1")
(prinl 120 " " 120)
(mapc prinl Img) ) )```

## PL/I

```/* Plot three circles. */

CIRCLE: PROCEDURE OPTIONS (MAIN);
declare image (-20:20, -20:20) character (1);
declare j fixed binary;

image = '.';
image(0,*) = '-';
image(*,0) = '|';
image(0,0) = '+';

CALL DRAW_CIRCLE (0, 0, 11);
CALL DRAW_CIRCLE (0, 0, 8);
CALL DRAW_CIRCLE (0, 0, 19);

do j = hbound(image,1) to lbound(image,1) by -1;
put skip edit (image(j,*)) (a(1));
end;

draw_circle: procedure (x0, y0, radius);       /* 14 May 2010. */
declare ( x0, y0, radius ) fixed binary;
declare ( ddfx, ddfy, x, y, f ) fixed binary;
declare debug bit (1) aligned static initial ('0'b);

ddfx = 1;
x = 0;
image(x0, y0+radius) = '*';  /* Octet 0. */
image(x0+radius, y0) = '*';  /* Octet 1. */
image(x0, y0-radius) = '*';  /* Octet 2. */
image(x0-radius, y0) = '*';  /* Octet 3. */

do while (x < y);
if f >= 0 then
do; y = y - 1; ddfy = ddfy +2; f = f + ddfy; end;
x = x + 1;
ddfx = ddfx + 2;
f = f + ddfx;
image(x0+x, y0+y) = '0';  /* Draws octant 0. */
image(x0+y, y0+x) = '1';  /* Draws octant 1. */
image(x0+y, y0-x) = '2';  /* Draws octant 2. */
image(x0+x, y0-y) = '3';  /* Draws octant 3. */
image(x0-x, y0-y) = '4';  /* Draws octant 4. */
image(x0-y, y0-x) = '5';  /* Draws octant 5. */
image(x0-y, y0+x) = '6';  /* Draws octant 6. */
image(x0-x, y0+y) = '7';  /* Draws octant 7. */
end;
end draw_circle;

END CIRCLE;```
Output:

for three circles centered at the origin.

```....................|....................
................2222*1111................
.............222....|....111.............
...........22.......|.......11...........
..........2.........|.........1..........
........22..........|..........11........
.......3............|............0.......
......2.............|.............1......
.....3..............|..............0.....
.....3...........222*111...........0.....
....3..........22...|...11..........0....
...3..........2.....|.....1..........0...
...3........32....22*11....11........0...
..3.........3...22..|..11...0.........0..
..3........3...3....|....0...0........0..
..3.......3...2.....|.....1...0.......0..
.3........3..3......|......0..0........0.
.3.......3...3......|......0...0.......0.
.3.......3..3.......|.......0..0.......0.
.3.......3..3.......|.......0..0.......0.
-*-------*--*-------+-------*--*-------*-
.4.......4..4.......|.......7..7.......7.
.4.......4..4.......|.......7..7.......7.
.4.......4...4......|......7...7.......7.
.4........4..4......|......7..7........7.
..4.......4...5.....|.....6...7.......7..
..4........4...4....|....7...7........7..
..4.........4...55..|..66...7.........7..
...4........55....55*66....67........7...
...4..........5.....|.....6..........7...
....4..........55...|...66..........7....
.....4...........555*666...........7.....
.....4..............|..............7.....
......5.............|.............6......
.......4............|............7.......
........55..........|..........66........
..........5.........|.........6..........
...........55.......|.......66...........
.............555....|....666.............
................5555*6666................
....................|....................
```

## PureBasic

```Procedure rasterCircle(cx, cy, r, Color)
;circle must lie completely within the image boundaries
Protected f= 1 - r
Protected ddF_X, ddF_Y = -2 * r
Protected x, y = r

Plot(cx, cy + r, Color)
Plot(cx, cy - r, Color)
Plot(cx + r, cy, Color)
Plot(cx - r, cy, Color)
While x < y
If f >= 0
y - 1
ddF_Y + 2
f + ddF_Y
EndIf
x + 1
ddF_X + 2
f + ddF_X + 1
Plot(cx + x, cy + y, Color)
Plot(cx - x, cy + y, Color)
Plot(cx + x, cy - y, Color)
Plot(cx - x, cy - y, Color)
Plot(cx + y, cy + x, Color)
Plot(cx - y, cy + x, Color)
Plot(cx + y, cy - x, Color)
Plot(cx - y, cy - x, Color)
Wend
EndProcedure

OpenWindow(0, 0, 0, 100, 100, "MidPoint Circle Algorithm", #PB_Window_SystemMenu)
CreateImage(0, 100, 100, 32)
StartDrawing(ImageOutput(0))
Box(0, 0, 100, 100, RGB(0, 0, 0))
rasterCircle(25, 25, 20, RGB(255, 255, 255))
rasterCircle(50, 50, 40, RGB(255, 0, 0))
StopDrawing()
ImageGadget(0, 0, 0, 0, 0, ImageID(0))

Repeat: Until WaitWindowEvent() = #PB_Event_CloseWindow
```

## Python

Works with: Python version 3.1

Extending the example given here

```def circle(self, x0, y0, radius, colour=black):
f = 1 - radius
ddf_x = 1
ddf_y = -2 * radius
x = 0
self.set(x0, y0 + radius, colour)
self.set(x0, y0 - radius, colour)
self.set(x0 + radius, y0, colour)
self.set(x0 - radius, y0, colour)

while x < y:
if f >= 0:
y -= 1
ddf_y += 2
f += ddf_y
x += 1
ddf_x += 2
f += ddf_x
self.set(x0 + x, y0 + y, colour)
self.set(x0 - x, y0 + y, colour)
self.set(x0 + x, y0 - y, colour)
self.set(x0 - x, y0 - y, colour)
self.set(x0 + y, y0 + x, colour)
self.set(x0 - y, y0 + x, colour)
self.set(x0 + y, y0 - x, colour)
self.set(x0 - y, y0 - x, colour)
Bitmap.circle = circle

bitmap = Bitmap(25,25)
bitmap.chardisplay()

'''
The origin, 0,0; is the lower left, with x increasing to the right,
and Y increasing upwards.

The program above produces the following display :

+-------------------------+
|         @@@@@@@         |
|       @@       @@       |
|     @@           @@     |
|    @               @    |
|   @                 @   |
|  @                   @  |
|  @                   @  |
| @                     @ |
| @                     @ |
|@                       @|
|@                       @|
|@                       @|
|@                       @|
|@                       @|
|@                       @|
|@                       @|
| @                     @ |
| @                     @ |
|  @                   @  |
|  @                   @  |
|   @                 @   |
|    @               @    |
|     @@           @@     |
|       @@       @@       |
|         @@@@@@@         |
+-------------------------+
'''
```

## Racket

Port of the Pyhton solution.

```#lang racket
(require racket/draw)

(define-syntax ⊕ (syntax-rules () [(_ id e) (set! id (+ id e))]))

(define (draw-point dc x y)
(send dc draw-point x y))

(define (draw-circle dc x0 y0 r)
(define f (- 1 r))
(define ddf_x 1)
(define ddf_y (* -2 r))
(define x 0)
(define y r)
(draw-point dc    x0    (+ y0 r))
(draw-point dc    x0    (- y0 r))
(draw-point dc (+ x0 r)    y0)
(draw-point dc (- x0 r)    y0)
(let loop ()
(when (< x y)
(when (>= f 0)
(⊕ y -1)
(⊕ ddf_y 2)
(⊕ f ddf_y))
(⊕ x 1)
(⊕ ddf_x 2)
(⊕ f ddf_x)
(draw-point dc (+ x0 x) (+ y0 y))
(draw-point dc (- x0 x) (+ y0 y))
(draw-point dc (+ x0 x) (- y0 y))
(draw-point dc (- x0 x) (- y0 y))
(draw-point dc (+ x0 y) (+ y0 x))
(draw-point dc (- x0 y) (+ y0 x))
(draw-point dc (+ x0 y) (- y0 x))
(draw-point dc (- x0 y) (- y0 x))
(loop))))

(define bm (make-object bitmap% 25 25))
(define dc (new bitmap-dc% [bitmap bm]))
(send dc set-smoothing 'unsmoothed)
(send dc set-pen "red" 1 'solid)
(draw-circle dc 12 12 12)
bm
```

## Raku

(formerly Perl 6)

Translation of: C

We'll augment the Pixel and Bitmap classes from the Bitmap task.

```use MONKEY-TYPING;

class Pixel { has UInt (\$.R, \$.G, \$.B) }
class Bitmap {
has UInt (\$.width, \$.height);
has Pixel @!data;

method fill(Pixel \p) {
@!data = p xx (\$!width × \$!height)
}

method pixel( \i where ^\$!width, \j where ^\$!height --> Pixel) is rw {
@!data[i × \$!width + j]
}

method set-pixel (\i, \j, Pixel \p) {
self.pixel(i, j) = p;
}

method get-pixel (\i, \j) returns Pixel {
self.pixel(i, j);
}
}

augment class Pixel  { method Str { "\$.R \$.G \$.B" } }
augment class Bitmap {
method P3 {
join "\n", «P3 "\$.width \$.height" 255»,
do for ^(\$.width × \$.height) { join ' ', @!data[\$_] }
}

method raster-circle ( \x0, \y0, \r, Pixel \value ) {
my \$ddF_x   =  0;
my \$ddF_y   = -2 × r;
my \$f       =  1 - r;
my (\$x, \$y) =  0,  r;
for flat (0 X 1,-1),(1,-1 X 0) -> \i, \j {
self.set-pixel(x0 + i×r, y0 + j×r, value)
}

while \$x < \$y {
(\$y--; \$f +=     (\$ddF_y += 2)) if \$f ≥ 0;
\$x++; \$f += 1 + (\$ddF_x += 2);
for flat (1,-1) X (1,-1) -> \i, \j {
self.set-pixel(x0 + i×\$x, y0 + j×\$y, value);
self.set-pixel(x0 + i×\$y, y0 + j×\$x, value);
}
}
}
}

my Bitmap \$b = Bitmap.new( width => 32, height => 32);
\$b.fill( Pixel.new( R => 0, G => 0, B => 0) );
\$b.raster-circle(16, 16, 15, Pixel.new(R=>0, G=>0, B=>100));
say \$b.P3;
```

## REXX

Programming note:   because of character output to a terminal screen, a circle appears to be elongated in the
vertical direction because characters are "taller" than they're "wide", so this REXX version attempts to maintain
a good aspect ratio.

The program automatically shows all of the plot's points by finding the minimum and maximum   X,Y   coördinates.

```/*REXX program  plots  three circles  using  midpoint/Bresenham's circle algorithm.     */
@.= '·'                                          /*fill the array with middle─dots char.*/
minX= 0;    maxX= 0;     minY= 0;     maxY= 0    /*initialize the minimums and maximums.*/
call drawCircle   0,   0,   8,   '#'             /*plot 1st circle with pound character.*/
call drawCircle   0,   0,  11,   '\$'             /*  "  2nd    "     "  dollar    "     */
call drawCircle   0,   0,  19,   '@'             /*  "  3rd    "     "  commercial at.  */
border= 2                                        /*BORDER:  shows  N  extra grid points.*/
minX= minX - border*2;    maxX= maxX + border*2  /*adjust min and max  X  to show border*/
minY= minY - border  ;    maxY= maxY + border    /*   "    "   "   "   Y   "   "     "  */
if @.0.0==@.  then @.0.0= '┼'                    /*maybe define the plot's axis origin. */
/*define the plot's horizontal grid──┐ */
do h=minX  to maxX;  if @.h.0==@.  then @.h.0= '─';  end             /* ◄───────────┘ */
do v=minY  to maxY;  if @.0.v==@.  then @.0.v= '│';  end             /* ◄──────────┐  */
/*define the plot's vertical grid───┘  */
do y=maxY  by -1  to minY;   _=             /* [↓]  draw grid from  top ──► bottom.*/
do x=minX  to maxX;  _= _ || @.x.y  /* ◄───   "    "    "  left ──► right. */
end   /*x*/                         /* [↑]  a grid row should be finished. */
say _                                       /*display a single row of the grid.    */
end           /*y*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
drawCircle: procedure expose @. minX maxX minY maxY
parse arg xx,yy,r 1 y,plotChar;     fx= 1;    fy= -2*r /*get X,Y coördinates*/
f= 1 - r
do x=0  while  x<y  /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/
if f>=0  then  do;  y= y - 1;   fy= fy + 2;   f= f + fy;   end  /*▒*/
fx= fx + 2;   f= f + fx         /*▒*/
call plotPoint  xx+x,  yy+y                                     /*▒*/
call plotPoint  xx+y,  yy+x                                     /*▒*/
call plotPoint  xx+y,  yy-x                                     /*▒*/
call plotPoint  xx+x,  yy-y                                     /*▒*/
call plotPoint  xx-y,  yy+x                                     /*▒*/
call plotPoint  xx-x,  yy+y                                     /*▒*/
call plotPoint  xx-x,  yy-y                                     /*▒*/
call plotPoint  xx-y,  yy-x                                     /*▒*/
end   /*x*/         /* [↑]  place plot points ══► plot.▒▒▒▒▒▒▒▒▒▒▒▒*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
plotPoint: parse arg c,r;      @.c.r= plotChar   /*assign a character to be plotted.    */
minX= min(minX,c);  maxX= max(maxX,c) /*determine the minimum and maximum  X.*/
minY= min(minY,r);  maxY= max(maxY,r) /*    "      "     "     "     "     Y.*/
return
```
output   when using the default inputs:
```·······················│·······················
·······················│·······················
····················@@@@@@@····················
·················@@@···│···@@@·················
···············@@······│······@@···············
··············@········│········@··············
············@@·········│·········@@············
···········@···········│···········@···········
··········@············│············@··········
·········@·············│·············@·········
········@············\$\$\$\$\$············@········
········@··········\$\$··│··\$\$··········@········
·······@··········\$····│····\$··········@·······
······@·········\$\$····###····\$\$·········@······
······@········\$····##·│·##····\$········@······
·····@·········\$···#···│···#···\$·········@·····
·····@········\$···#····│····#···\$········@·····
·····@·······\$···#·····│·····#···\$·······@·····
····@········\$··#······│······#··\$········@····
····@·······\$···#······│······#···\$·······@····
····@·······\$··#·······│·······#··\$·······@····
────@───────\$──#───────┼───────#──\$───────@────
····@·······\$··#·······│·······#··\$·······@····
····@·······\$···#······│······#···\$·······@····
····@········\$··#······│······#··\$········@····
·····@·······\$···#·····│·····#···\$·······@·····
·····@········\$···#····│····#···\$········@·····
·····@·········\$···#···│···#···\$·········@·····
······@········\$····##·│·##····\$········@······
······@·········\$\$····###····\$\$·········@······
·······@··········\$····│····\$··········@·······
········@··········\$\$··│··\$\$··········@········
········@············\$\$\$\$\$············@········
·········@·············│·············@·········
··········@············│············@··········
···········@···········│···········@···········
············@@·········│·········@@············
··············@········│········@··············
···············@@······│······@@···············
·················@@@···│···@@@·················
····················@@@@@@@····················
·······················│·······················
·······················│·······················
```

## Ruby

```Pixel = Struct.new(:x, :y)

class Pixmap
def draw_circle(pixel, radius, colour)
validate_pixel(pixel.x, pixel.y)

self[pixel.x, pixel.y + radius] = colour
self[pixel.x, pixel.y - radius] = colour
self[pixel.x + radius, pixel.y] = colour
self[pixel.x - radius, pixel.y] = colour

f = 1 - radius
ddF_x = 1
ddF_y = -2 * radius
x = 0
while x < y
if f >= 0
y -= 1
ddF_y += 2
f += ddF_y
end
x += 1
ddF_x += 2
f += ddF_x
self[pixel.x + x, pixel.y + y] = colour
self[pixel.x + x, pixel.y - y] = colour
self[pixel.x - x, pixel.y + y] = colour
self[pixel.x - x, pixel.y - y] = colour
self[pixel.x + y, pixel.y + x] = colour
self[pixel.x + y, pixel.y - x] = colour
self[pixel.x - y, pixel.y + x] = colour
self[pixel.x - y, pixel.y - x] = colour
end
end
end

bitmap = Pixmap.new(30, 30)
bitmap.draw_circle(Pixel[14,14], 12, RGBColour::BLACK)
```

## Scala

Uses the Scala Basic Bitmap Storage class.

```object BitmapOps {
def midpoint(bm:RgbBitmap, x0:Int, y0:Int, radius:Int, c:Color)={
var ddF_x=1
var x=0

while(x < y)
{
if(f >= 0)
{
y-=1
ddF_y+=2
f+=ddF_y
}
x+=1
ddF_x+=2
f+=ddF_x

bm.setPixel(x0+x, y0+y, c)
bm.setPixel(x0-x, y0+y, c)
bm.setPixel(x0+x, y0-y, c)
bm.setPixel(x0-x, y0-y, c)
bm.setPixel(x0+y, y0+x, c)
bm.setPixel(x0-y, y0+x, c)
bm.setPixel(x0+y, y0-x, c)
bm.setPixel(x0-y, y0-x, c)
}
}
}
```

## Tcl

Library: Tk
```package require Tcl 8.5
package require Tk

proc drawCircle {image colour point radius} {
lassign \$point x0 y0

setPixel \$image \$colour [list \$x0 [expr {\$y0 + \$radius}]]
setPixel \$image \$colour [list \$x0 [expr {\$y0 - \$radius}]]
setPixel \$image \$colour [list [expr {\$x0 + \$radius}] \$y0]
setPixel \$image \$colour [list [expr {\$x0 - \$radius}] \$y0]

set f [expr {1 - \$radius}]
set ddF_x 1
set ddF_y [expr {-2 * \$radius}]
set x 0

while {\$x < \$y} {
assert {\$ddF_x == 2 * \$x + 1}
assert {\$ddF_y == -2 * \$y}
assert {\$f == \$x*\$x + \$y*\$y - \$radius*\$radius + 2*\$x - \$y + 1}
if {\$f >= 0} {
incr y -1
incr ddF_y 2
incr f \$ddF_y
}
incr x
incr ddF_x 2
incr f \$ddF_x
setPixel \$image \$colour [list [expr {\$x0 + \$x}] [expr {\$y0 + \$y}]]
setPixel \$image \$colour [list [expr {\$x0 - \$x}] [expr {\$y0 + \$y}]]
setPixel \$image \$colour [list [expr {\$x0 + \$x}] [expr {\$y0 - \$y}]]
setPixel \$image \$colour [list [expr {\$x0 - \$x}] [expr {\$y0 - \$y}]]
setPixel \$image \$colour [list [expr {\$x0 + \$y}] [expr {\$y0 + \$x}]]
setPixel \$image \$colour [list [expr {\$x0 - \$y}] [expr {\$y0 + \$x}]]
setPixel \$image \$colour [list [expr {\$x0 + \$y}] [expr {\$y0 - \$x}]]
setPixel \$image \$colour [list [expr {\$x0 - \$y}] [expr {\$y0 - \$x}]]

}
}

# create the image and display it
set img [newImage 200 100]
label .l -image \$img
pack .l

fill \$img black
drawCircle \$img blue {100 50} 49
```

## Vedit macro language

```//  Draw a circle using Bresenham's circle algorithm.
//  #21 = center x, #22 = center y; #23 = radius

:DRAW_CIRCLE:
#30 = 1 - #23		// f
#31 = 0			// ddF_x
#32 = -2 * #23		// ddF_y
#41 = 0			// x
#42 = #23		// y

while (#41 <= #42) {
#1 = #21+#41; #2 = #22+#42; Call("DRAW_PIXEL")
#1 = #21-#41; #2 = #22+#42; Call("DRAW_PIXEL")
#1 = #21+#41; #2 = #22-#42; Call("DRAW_PIXEL")
#1 = #21-#41; #2 = #22-#42; Call("DRAW_PIXEL")
#1 = #21+#42; #2 = #22+#41; Call("DRAW_PIXEL")
#1 = #21-#42; #2 = #22+#41; Call("DRAW_PIXEL")
#1 = #21+#42; #2 = #22-#41; Call("DRAW_PIXEL")
#1 = #21-#42; #2 = #22-#41; Call("DRAW_PIXEL")
if (#30 >= 0) {
#42--
#32 += 2
#30 += #32
}
#41++
#31 += 2
#30 += #31 + 1
}

return```

## Wren

Translation of: Kotlin
Library: DOME
```import "graphics" for Canvas, Color, ImageData
import "dome" for Window

class MidpointCircle {
construct new(width, height) {
Window.title = "Midpoint Circle"
Window.resize(width, height)
Canvas.resize(width, height)
_w = width
_h = height
_bmp = ImageData.create("midpoint circle", width, height)
}

init() {
fill(Color.pink)
drawCircle(200, 200, 100, Color.black)
drawCircle(200, 200,  50, Color.white)
_bmp.draw(0, 0)
}

fill(col) {
for (x in 0..._w) {
for (y in 0..._h) pset(x, y, col)
}
}

drawCircle(centerX, centerY, radius, circleColor) {
var d = ((5 - radius * 4)/4).truncate
var x = 0
var y = radius
while (true) {
pset(centerX + x, centerY + y, circleColor)
pset(centerX + x, centerY - y, circleColor)
pset(centerX - x, centerY + y, circleColor)
pset(centerX - x, centerY - y, circleColor)
pset(centerX + y, centerY + x, circleColor)
pset(centerX + y, centerY - x, circleColor)
pset(centerX - y, centerY + x, circleColor)
pset(centerX - y, centerY - x, circleColor)
if (d < 0) {
d = d + 2 * x + 1
} else {
d = d + 2 * (x - y) + 1
y = y - 1
}
x = x + 1
if (x > y) break
}
}

pset(x, y, col) { _bmp.pset(x, y, col) }

pget(x, y) { _bmp.pget(x, y) }

update() {}

draw(alpha) {}
}

var Game = MidpointCircle.new(400, 400)
```

## XPL0

```include c:\cxpl\codes;          \include 'code' declarations

proc Circle(X0, Y0, Radius, Color);     \Display a circle
int  X0, Y0,    \coordinates of center
Color;     \line color
int  X, Y, E, U, V;

proc PlotOctants;               \Segment
[Point(X0+Y, Y0+X, Color);      \ 0
Point(X0+X, Y0+Y, Color);       \ 1
Point(X0-X, Y0+Y, Color);       \ 2
Point(X0-Y, Y0+X, Color);       \ 3
Point(X0-Y, Y0-X, Color);       \ 4
Point(X0-X, Y0-Y, Color);       \ 5
Point(X0+X, Y0-Y, Color);       \ 6
Point(X0+Y, Y0-X, Color);       \ 7
]; \PlotOctants

[X:= 0;  Y:= Radius;
U:= 1;
while X < Y do
[PlotOctants;
if E < 0 then
[U:= U+2;  V:= V+2;  E:= E+U]
else    [U:= U+2;  V:= V+4;  E:= E+V;  Y:= Y-1];
X:= X+1;
];
if X = Y then PlotOctants;
]; \Circle

[SetVid(\$112);          \640x480 in 24-bit RGB color
Circle(110, 110, 50, \$FFFF00);
if ChIn(1) then [];     \wait for keystroke
SetVid(3);              \restore normal text mode
]```

## zkl

Image cribbed from the BBC BASIC entry. Algorithm from Wikipedia article.
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

This is the code from the PPM class:

```   fcn circle(x0,y0,r,rgb){
while(x >= y){
__sSet(rgb, x + x0,  y + y0);
__sSet(rgb, y + x0,  x + y0);
__sSet(rgb,-x + x0,  y + y0);
__sSet(rgb,-y + x0,  x + y0);
self[-x + x0, -y + y0]=rgb;	// or do it this way, __sSet gets called as above
self[-y + x0, -x + y0]=rgb;
self[ x + x0, -y + y0]=rgb;
self[ y + x0, -x + y0]=rgb;
y+=1;
```ppm:=PPM(200,200,0xFF|FF|FF);