Bitmap/Midpoint circle algorithm
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).
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
11l
<lang 11l>T Colour
Byte r, g, b
F (r, g, b)
.r = r
.g = g
.b = b
F ==(other)
R .r == other.r & .g == other.g & .b == other.b
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()</lang>
- Output:
+-------------------------+ | @@@@@@@ | | @@ @@ | | @@ @@ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | |@ @| |@ @| |@ @| |@ @| |@ @| |@ @| |@ @| | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @@ @@ | | @@ @@ | | @@@@@@@ | +-------------------------+
Action!
Part of the task is available in RGBCIRCL.ACT.
<lang Action!>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</lang>
- Output:
Ada
<lang ada>procedure Circle
( Picture : in out Image;
Center : Point;
Radius : Natural;
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;</lang> The following illustrates use: <lang ada> X : Image (1..16, 1..16); begin
Fill (X, White); Circle (X, (8, 8), 5, Black); Print (X);</lang>
- Output:
HHHHH
H H
H H
H H
H H
H H
H H
H H
H H
H H
HHHHH
ALGOL 68
File: prelude/Bitmap/Midpoint_circle_algorithm.a68<lang algol68># -*- coding: utf-8 -*- #
circle OF class image :=
( REF IMAGE picture,
POINT center,
INT radius,
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</lang>File: test/Bitmap/Midpoint_circle_algorithm.a68<lang algol68>#!/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)
)</lang>
- Output:
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffff000000000000000000000000000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffff000000000000000000000000000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
Applesoft BASIC
<lang gwbasic> 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</lang>
bash
<lang bash>#! /bin/bash
function putpixel {
echo -en "\e[$2;$1H#"
}
function drawcircle {
x0=$1 y0=$2 radius=$3
for y in $( seq $((y0-radius)) $((y0+radius)) )
do
echo -en "\e[${y}H"
for x in $( seq $((x0+radius)) )
do echo -n "-" done
done
x=$((radius-1)) y=0 dx=1 dy=1 err=$((dx-(radius<<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))
((err+=dx-(radius<<1)))
fi
done
}
clear drawcircle 13 13 11 echo -en "\e[H" </lang>
- Output:
------#########------ ----##---------##---- ---#-------------#--- --#---------------#-- -#-----------------#- -#-----------------#- #-------------------# #-------------------# #-------------------# #-------------------# #-------------------# #-------------------# #-------------------# #-------------------# #-------------------# -#-----------------#- -#-----------------#- --#---------------#-- ---#-------------#--- ----##---------##---- ------#########------
BASIC256
<lang 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 Function DrawCircle(x0,y0,radius) x=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</lang>
- Output:
Batch File
<lang dos>@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 radius=%3
set x=!radius! 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</lang>
- Output:
█ █
█ █
█ █
█ █
█ █
█ █
█ █
█ █
█ █
█ ███████ █
██ ██ █
██ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ █ █ █
█ ██ █ ██
█ ███ █ ███
█ ███████
█ █
█ █
█ █
██ ██
███████
BBC BASIC
<lang bbcbasic> 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</lang>
C
Interface:
<lang c>void raster_circle(
image img,
unsigned int x0,
unsigned int y0,
unsigned int radius,
color_component r,
color_component g,
color_component b );</lang>
Implementation:
<lang c>#define plot(x, y) put_pixel_clip(img, x, y, r, g, b)
void raster_circle(
image img,
unsigned int x0,
unsigned int y0,
unsigned int radius,
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</lang>
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.
<lang csharp>
/// <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>
/// <param name="radius">
/// 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);
}
</lang>
Clojure
Based upon the Common Lisp version. <lang clojure>(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)))))</lang>
<lang clojure>(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)))))</lang>
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.
<lang lisp>(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)))</lang>
<lang lisp>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)</lang>
;; 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. <lang d>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;
}</lang>
- Output:
.........#######......... .......##.......##....... .....##...........##..... ....#...............#.... ...#.................#... ..#...................#.. ..#...................#.. .#.....................#. .#.....................#. #.......................# #.......................# #.......................# #.......................# #.......................# #.......................# #.......................# .#.....................#. .#.....................#. ..#...................#.. ..#...................#.. ...#.................#... ....#...............#.... .....##...........##..... .......##.......##....... .........#######.........
ERRE
<lang 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 </lang>
FBSL
Using pure FBSL's built-in graphics functions: <lang qbasic>#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</lang>
Ouptut: 
Forth
<lang 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</lang>
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.
<lang fortran>interface draw_circle
module procedure draw_circle_sc, draw_circle_rgb
end interface
private :: plot, draw_circle_toch</lang>
<lang fortran>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 y = radius
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</lang>
FreeBASIC
<lang 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</lang>
Go
This produces identical results to the C code in the WP article, but with more compact code. <lang go>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())
}</lang> Demonstration program: <lang>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)
}
}</lang>
Haskell
The basic algorithm can be implemented generically. <lang haskell>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
</lang> An example using regular 2d arrays of characters to represent a bitmap: <lang haskell>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 </lang> Using the Image type from the Bitmap module defined here: <lang haskell>module CircleBitmapExample where
import Circle import Bitmap import Control.Monad.ST
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
</lang>
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.)
<lang j>NB.*getBresenhamCircle v Returns points for a circle given center and radius
NB. y is: y0 x0 radius
getBresenhamCircle=: monad define
'y0 x0 radius'=. y
x=. 0
y=. radius
f=. -. radius
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 ]</lang>
Example usage: <lang j>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</lang>
Java
<lang 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 - r * 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);
} } </lang>
Julia
<lang julia>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)</lang>
Lua
Uses Bitmap class here, with an ASCII pixel representation, then extending.. <lang lua>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</lang> Demo: <lang lua>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()</lang>
- Output:
· · · · · · · · · · · · | · · · · · · · · · · · · · · · · · · · · · ■ ■ ■ ■ ■ ■ ■ · · · · · · · · · · · · · · · · ■ ■ · · · | · · · ■ ■ · · · · · · · · · · · · ■ ■ · · · · · | · · · · · ■ ■ · · · · · · · · · ■ · · · · · ■ ■ ■ ■ ■ · · · · · ■ · · · · · · · ■ · · · · ■ ■ · · | · · ■ ■ · · · · ■ · · · · · · ■ · · ■ ■ · · · · | · · · · ■ ■ · · ■ · · · · · ■ · · · ■ · · · ■ ■ ■ ■ ■ · · · ■ · · · ■ · · · · ■ · · ■ · · · ■ · · | · · ■ · · · ■ · · ■ · · · ■ · · · ■ · · ■ · · · | · · · ■ · · ■ · · · ■ · · ■ · · ■ · · ■ · · · ■ ■ ■ · · · ■ · · ■ · · ■ · · ■ · · ■ · · ■ · · ■ · | · ■ · · ■ · · ■ · · ■ · - ■ - - ■ - - ■ - - ■ - + - ■ - - ■ - - ■ - - ■ - · ■ · · ■ · · ■ · · ■ · | · ■ · · ■ · · ■ · · ■ · · ■ · · ■ · · ■ · · · ■ ■ ■ · · · ■ · · ■ · · ■ · · ■ · · · ■ · · ■ · · · | · · · ■ · · ■ · · · ■ · · · ■ · · ■ · · · ■ · · | · · ■ · · · ■ · · ■ · · · · ■ · · · ■ · · · ■ ■ ■ ■ ■ · · · ■ · · · ■ · · · · · ■ · · ■ ■ · · · · | · · · · ■ ■ · · ■ · · · · · · ■ · · · · ■ ■ · · | · · ■ ■ · · · · ■ · · · · · · · ■ · · · · · ■ ■ ■ ■ ■ · · · · · ■ · · · · · · · · · ■ ■ · · · · · | · · · · · ■ ■ · · · · · · · · · · · · ■ ■ · · · | · · · ■ ■ · · · · · · · · · · · · · · · · ■ ■ ■ ■ ■ ■ ■ · · · · · · · · · · · · · · · · · · · · · | · · · · · · · · · · · ·
Kotlin
<lang scala>// 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)
}</lang>
Mathematica / Wolfram Language
<lang mathematica>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]]</lang>
Example usage（it will draw a circle on Lena's face.）: <lang mathematica>img = ExampleData[{"TestImage", "Lena"}]; drawcircle[img, {250, 250}, 100]</lang>
Modula-3
<lang modula3>INTERFACE Circle;
IMPORT Bitmap;
PROCEDURE Draw(
img: Bitmap.T; center: Bitmap.Point; radius: CARDINAL; color: Bitmap.Pixel);
END Circle.</lang> <lang modula3>MODULE Circle;
IMPORT Bitmap;
PROCEDURE Draw(
img: Bitmap.T;
center: Bitmap.Point;
radius: CARDINAL;
color: Bitmap.Pixel) =
VAR f := 1 - radius;
ddfx := 0;
ddfy := - 2 * radius;
x := 0;
y := radius;
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.</lang>
Example (outputs a PPM image): <lang modula3>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.</lang>
Nim
<lang 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 y = radius
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()</lang>
- Output:
................ ................ .....HHHHH...... ....H.....H..... ...H.......H.... ..H.........H... ..H.........H... ..H.........H... ..H.........H... ..H.........H... ...H.......H.... ....H.....H..... .....HHHHH...... ................ ................ ................
Perl
<lang 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</lang>
- Output:
#######
## ##
# #
# #
# #
# #
# #
# #
# #
# #
# #
# #
# #
# #
# #
# #
# #
# #
# #
## ##
#######
Phix
Requires new_image() from Bitmap, write_ppm() from Write_a_PPM_file.
Results may be verified with demo\rosetta\viewppm.exw
<lang Phix>-- 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)</lang>
PicoLisp
<lang 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) ) )</lang>
PL/I
<lang 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);
f = 1-radius; ddfx = 1; ddfy = -2*radius; x = 0; y = radius; 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; </lang>
- 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
<lang 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</lang>
Python
Extending the example given here <lang python>def circle(self, x0, y0, radius, colour=black):
f = 1 - radius ddf_x = 1 ddf_y = -2 * radius x = 0 y = radius 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.circle(x0=12, y0=12, radius=12) 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 :
+-------------------------+ | @@@@@@@ | | @@ @@ | | @@ @@ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | |@ @| |@ @| |@ @| |@ @| |@ @| |@ @| |@ @| | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @@ @@ | | @@ @@ | | @@@@@@@ | +-------------------------+ </lang>
Racket
Port of the Pyhton solution.
<lang racket>
- 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 </lang>
Raku
(formerly Perl 6)
We'll augment the Pixel and Bitmap classes from the Bitmap task.
<lang perl6>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 $b.P3;</lang>
OCaml
<lang ocaml>let raster_circle ~img ~color ~c:(x0, y0) ~r =
let plot = put_pixel img color in
let x = 0
and y = r
and m = 5 - 4 * r
in
let rec loop x y m =
plot (x0 + x) (y0 + y);
plot (x0 + y) (y0 + x);
plot (x0 - x) (y0 + y);
plot (x0 - y) (y0 + x);
plot (x0 + x) (y0 - y);
plot (x0 + y) (y0 - x);
plot (x0 - x) (y0 - y);
plot (x0 - y) (y0 - x);
let y, m =
if m > 0
then (y - 1), (m - 8 * y)
else y, m
in
if x <= y then
let x = x + 1 in
let m = m + 8 * x + 4 in
loop x y m
in
loop x y m
- </lang>
REXX
Programming note: because of character output to a terminal screen, a circle appears to be elongated in the
vertical direction because characters are "taller" than they're "wide", so this REXX version attempts to maintain
a good aspect ratio.
The program automatically shows all of the plot's points by finding the minimum and maximum X,Y coördinates. <lang rexx>/*REXX program plots three circles using midpoint/Bresenham's circle algorithm. */ @.= '·' /*fill the array with middle─dots char.*/ minX= 0; maxX= 0; minY= 0; maxY= 0 /*initialize the minimums and maximums.*/ call drawCircle 0, 0, 8, '#' /*plot 1st circle with pound character.*/ call drawCircle 0, 0, 11, '$' /* " 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</lang>
- output when using the default inputs:
·······················│······················· ·······················│······················· ····················@@@@@@@···················· ·················@@@···│···@@@················· ···············@@······│······@@··············· ··············@········│········@·············· ············@@·········│·········@@············ ···········@···········│···········@··········· ··········@············│············@·········· ·········@·············│·············@········· ········@············$$$$$············@········ ········@··········$$··│··$$··········@········ ·······@··········$····│····$··········@······· ······@·········$$····###····$$·········@······ ······@········$····##·│·##····$········@······ ·····@·········$···#···│···#···$·········@····· ·····@········$···#····│····#···$········@····· ·····@·······$···#·····│·····#···$·······@····· ····@········$··#······│······#··$········@···· ····@·······$···#······│······#···$·······@···· ····@·······$··#·······│·······#··$·······@···· ────@───────$──#───────┼───────#──$───────@──── ····@·······$··#·······│·······#··$·······@···· ····@·······$···#······│······#···$·······@···· ····@········$··#······│······#··$········@···· ·····@·······$···#·····│·····#···$·······@····· ·····@········$···#····│····#···$········@····· ·····@·········$···#···│···#···$·········@····· ······@········$····##·│·##····$········@······ ······@·········$$····###····$$·········@······ ·······@··········$····│····$··········@······· ········@··········$$··│··$$··········@········ ········@············$$$$$············@········ ·········@·············│·············@········· ··········@············│············@·········· ···········@···········│···········@··········· ············@@·········│·········@@············ ··············@········│········@·············· ···············@@······│······@@··············· ·················@@@···│···@@@················· ····················@@@@@@@···················· ·······················│······················· ·······················│·······················
Ruby
<lang 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
y = radius
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)</lang>
Scala
Uses the Scala Basic Bitmap Storage class. <lang scala>object BitmapOps {
def midpoint(bm:RgbBitmap, x0:Int, y0:Int, radius:Int, c:Color)={
var f=1-radius
var ddF_x=1
var ddF_y= -2*radius
var x=0
var y=radius
bm.setPixel(x0, y0+radius, c)
bm.setPixel(x0, y0-radius, c)
bm.setPixel(x0+radius, y0, c)
bm.setPixel(x0-radius, y0, c)
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)
}
}
}</lang>
Tcl
ref Basic bitmap storage#Tcl and Assertions#Tcl <lang tcl>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
set y $radius
while {$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</lang>
Vedit macro language
<lang vedit> // 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 </lang>
Wren
<lang ecmascript>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)</lang>
XPL0
<lang XPL0>include c:\cxpl\codes; \include 'code' declarations
proc Circle(X0, Y0, Radius, Color); \Display a circle int X0, Y0, \coordinates of center
Radius, \radius in (pixels)
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; V:= 1 -Radius -Radius; E:= 1 -Radius; 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 ]</lang>
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: <lang zkl> fcn circle(x0,y0,r,rgb){
x:=r; y:=0; radiusError:=1-x;
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; if (radiusError<0) radiusError+=2*y + 1; else{ x-=1; radiusError+=2*(y - x + 1); }
} }</lang>
<lang zkl>ppm:=PPM(200,200,0xFF|FF|FF); ppm.circle(100,100,40,00); // black circle ppm.circle(100,100,80,0xFF|00|00); // red circle
ppm.write(File("foo.ppm","wb"));</lang>