Task
{{task|Raster graphics operations}}Using the data storage type defined [[Basic_bitmap_storage|on this page]] for raster images,
write an implementation of the '''midpoint circle algorithm'''
(also known as '''Bresenham's circle algorithm''').
([[wp:Midpoint_circle_algorithm|definition on Wikipedia]]).
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;
The following illustrates use:
X : Image (1..16, 1..16);
begin
Fill (X, White);
Circle (X, (8, 8), 5, Black);
Print (X);
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'''
# -*- 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
'''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)
)
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffff000000000000000000000000000000ffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff
ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff
ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffff000000000000000000000000000000ffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
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
[http://s16.postimg.org/ge0ndfs9h/Output.jpg http://s16.postimg.org/ge0ndfs9h/Output.jpg]
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
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"
------#########------
----##---------##----
---#-------------#---
--#---------------#--
-#-----------------#-
-#-----------------#-
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
#-------------------#
-#-----------------#-
-#-----------------#-
--#---------------#--
---#-------------#---
----##---------##----
------#########------
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 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
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BBC BASIC
[[Image:circle_bbc.gif|right]]
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
== {{header|C}} ==
Interface:
void raster_circle(
image img,
unsigned int x0,
unsigned int y0,
unsigned int radius,
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,
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
== {{header|C sharp}} ==
This extension method extends GenericImage which is very similar to [http://rosettacode.org/wiki/Bitmap#C.23 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>
/// <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);
}
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;
}
.........#######.........
.......##.......##.......
.....##...........##.....
....#...............#....
...#.................#...
..#...................#..
..#...................#..
.#.....................#.
.#.....................#.
#.......................#
#.......................#
#.......................#
#.......................#
#.......................#
#.......................#
#.......................#
.#.....................#.
.#.....................#.
..#...................#..
..#...................#..
...#.................#...
....#...............#....
.....##...........##.....
.......##.......##.......
.........#######.........
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
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:''' [[File:FBSLMidpoint.PNG]]
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 [[Bresenham's line algorithm#Fortran|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 ''[[Basic bitmap storage#Fortran|rgb]]'' images and [[Grayscale image#Fortran|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
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
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
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:
// 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) } }
## Haskell
The basic algorithm can be implemented generically.
```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
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 [[Basic_bitmap_storage|here]]:
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
J
'''Solution:'''
Using definitions from [[Basic bitmap storage#J|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
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 ]
'''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
== {{header|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);
}
}
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)
Kotlin
// 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)
}
=={{header|Mathematica}} / {{header|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]
=={{header|Modula-3}}==
INTERFACE Circle;
IMPORT Bitmap;
PROCEDURE Draw(
img: Bitmap.T;
center: Bitmap.Point;
radius: CARDINAL;
color: Bitmap.Pixel);
END Circle.
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.
Example (outputs a [[Write_ppm_file | 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.
Perl 6
We'll augment the Pixel and Bitmap classes from the [[Bitmap#Perl_6|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 = $p.clone xx ($!width*$!height)
}
method pixel(
$i where ^$!width,
$j where ^$!height
--> Pixel
) is rw { @!data[$i + $j * $!width] }
method set-pixel ($i, $j, Pixel $p) {
self.pixel($i, $j) = $p.clone;
}
method get-pixel ($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 $.height" 255»,
do for ^$.height { join ' ', @.data[]»[$_] }
}
method raster-circle ( $x0, $y0, $r, Pixel $value ) {
my $f = 1 - $r;
my $ddF_x = 0;
my $ddF_y = -2 * $r;
my ($x, $y) = 0, $r;
self.set-pixel($x0, $y0 + $r, $value);
self.set-pixel($x0, $y0 - $r, $value);
self.set-pixel($x0 + $r, $y0, $value);
self.set-pixel($x0 - $r, $y0, $value);
while $x < $y {
if $f >= 0 {
$y--;
$ddF_y += 2;
$f += $ddF_y;
}
$x++;
$ddF_x += 2;
$f += $ddF_x + 1;
self.set-pixel($x0 + $x, $y0 + $y, $value);
self.set-pixel($x0 - $x, $y0 + $y, $value);
self.set-pixel($x0 + $x, $y0 - $y, $value);
self.set-pixel($x0 - $x, $y0 - $y, $value);
self.set-pixel($x0 + $y, $y0 + $x, $value);
self.set-pixel($x0 - $y, $y0 + $x, $value);
self.set-pixel($x0 + $y, $y0 - $x, $value);
self.set-pixel($x0 - $y, $y0 - $x, $value);
}
}
}
== {{Header|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
;;
Phix
Requires new_image() from [[Bitmap#Phix|Bitmap]], write_ppm() from [[Bitmap/Write_a_PPM_file#Phix|Write_a_PPM_file]]. Included as demo\rosetta\Bitmap_Circle.exw, results may be verified with demo\rosetta\viewppm.exw
constant red = 0xff2020,
yellow = 0xffdf20
function SetPx(sequence img, atom x, atom 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, atom y, atom 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);
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;
{{out}} 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
Extending the example given [[Basic_bitmap_storage#Alternative_version|here]]
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 :
+-------------------------+
| @@@@@@@ |
| @@ @@ |
| @@ @@ |
| @ @ |
| @ @ |
| @ @ |
| @ @ |
| @ @ |
| @ @ |
|@ @|
|@ @|
|@ @|
|@ @|
|@ @|
|@ @|
|@ @|
| @ @ |
| @ @ |
| @ @ |
| @ @ |
| @ @ |
| @ @ |
| @@ @@ |
| @@ @@ |
| @@@@@@@ |
+-------------------------+
'''
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
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'''
·······················│·······················
·······················│·······················
····················@@@@@@@····················
·················@@@···│···@@@·················
···············@@······│······@@···············
··············@········│········@··············
············@@·········│·········@@············
···········@···········│···········@···········
··········@············│············@··········
·········@·············│·············@·········
········@············$$$$$············@········
········@··········$$··│··$$··········@········
·······@··········$····│····$··········@·······
······@·········$$····###····$$·········@······
······@········$····##·│·##····$········@······
·····@·········$···#···│···#···$·········@·····
·····@········$···#····│····#···$········@·····
·····@·······$···#·····│·····#···$·······@·····
····@········$··#······│······#··$········@····
····@·······$···#······│······#···$·······@····
····@·······$··#·······│·······#··$·······@····
────@───────$──#───────┼───────#──$───────@────
····@·······$··#·······│·······#··$·······@····
····@·······$···#······│······#···$·······@····
····@········$··#······│······#··$········@····
·····@·······$···#·····│·····#···$·······@·····
·····@········$···#····│····#···$········@·····
·····@·········$···#···│···#···$·········@·····
······@········$····##·│·##····$········@······
······@·········$$····###····$$·········@······
·······@··········$····│····$··········@·······
········@··········$$··│··$$··········@········
········@············$$$$$············@········
·········@·············│·············@·········
··········@············│············@··········
···········@···········│···········@···········
············@@·········│·········@@············
··············@········│········@··············
···············@@······│······@@···············
·················@@@···│···@@@·················
····················@@@@@@@····················
·······················│·······················
·······················│·······················
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)
Scala
Uses the [[Basic_bitmap_storage#Scala|Scala Basic Bitmap Storage]] class.
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)
}
}
}
Tcl
ref [[Basic bitmap storage#Tcl]] and [[Assertions#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
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
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
]
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
[[Image:circle_bbc.gif|right]]
This is the code from the PPM class:
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); }
}
}
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"));