Bitmap/Bresenham's line algorithm: Difference between revisions
(Added code for Metal compute shader) |
(→{{header|zkl}}: added flood) |
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=={{header|zkl}}== |
=={{header|zkl}}== |
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[[File:Line.zkl.jpg|200px|thumb]] |
[[File:Line.zkl.jpg|200px|thumb]] |
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Algorithm from Wikipedia. |
Algorithm from Wikipedia plus other functions so I can reference this code in other examples. |
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<lang zkl>ppm:=PPM(200,200,0xFF|FF|FF); |
<lang zkl>ppm:=PPM(200,200,0xFF|FF|FF); |
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ppm.line(50,100, 100,190, 0); |
ppm.line(50,100, 100,190, 0); |
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if(e2 > -dy){ err=err - dy; x0=x0 + sx; } |
if(e2 > -dy){ err=err - dy; x0=x0 + sx; } |
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if(e2 < dx) { err=err + dx; y0=y0 + sy; } |
if(e2 < dx) { err=err + dx; y0=y0 + sy; } |
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} |
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} |
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fcn flood(x,y, repl){ // slow! |
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targ:=self[x,y]; |
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(stack:=List.createLong(10000)).append(T(x,y)); |
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while(stack){ |
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x,y:=stack.pop(); |
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if((0<=y<h) and (0<=x<w)){ |
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p:=self[x,y]; |
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if(p==targ){ |
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self[x,y]=repl; |
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stack.append( T(x-1,y), T(x+1,y), T(x, y-1), T(x, y+1) ); |
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} |
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} |
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} |
} |
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} |
} |
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Revision as of 21:22, 23 April 2016
You are encouraged to solve this task according to the task description, using any language you may know.
Using the data storage type defined on this page for raster graphics images, draw a line given 2 points with the Bresenham's line algorithm.
Ada
<lang ada>procedure Line (Picture : in out Image; Start, Stop : Point; Color : Pixel) is
DX : constant Float := abs Float (Stop.X - Start.X); DY : constant Float := abs Float (Stop.Y - Start.Y); Err : Float; X : Positive := Start.X; Y : Positive := Start.Y; Step_X : Integer := 1; Step_Y : Integer := 1;
begin
if Start.X > Stop.X then
Step_X := -1;
end if;
if Start.Y > Stop.Y then
Step_Y := -1;
end if;
if DX > DY then
Err := DX / 2.0;
while X /= Stop.X loop
Picture (X, Y) := Color;
Err := Err - DY;
if Err < 0.0 then
Y := Y + Step_Y;
Err := Err + DX;
end if;
X := X + Step_X;
end loop;
else
Err := DY / 2.0;
while Y /= Stop.Y loop
Picture (X, Y) := Color;
Err := Err - DX;
if Err < 0.0 then
X := X + Step_X;
Err := Err + DY;
end if;
Y := Y + Step_Y;
end loop;
end if;
Picture (X, Y) := Color; -- Ensure dots to be drawn
end Line;</lang> The test program's <lang ada> X : Image (1..16, 1..16); begin
Fill (X, White); Line (X, ( 1, 8), ( 8,16), Black); Line (X, ( 8,16), (16, 8), Black); Line (X, (16, 8), ( 8, 1), Black); Line (X, ( 8, 1), ( 1, 8), Black); Print (X);</lang>
sample output
H
H H
H H
H HH
H H
H H
H H
H H
H H
H H
H H
H H
H H
H H
H H
H
ALGOL 68
File: prelude/Bitmap/Bresenhams_line_algorithm.a68<lang algol68># -*- coding: utf-8 -*- #
line OF class image := (REF IMAGE picture, POINT start, stop, PIXEL color)VOID: BEGIN
REAL dx = ABS (x OF stop - x OF start),
dy = ABS (y OF stop - y OF start);
REAL err;
POINT here := start,
step := (1, 1);
IF x OF start > x OF stop THEN
x OF step := -1
FI;
IF y OF start > y OF stop THEN
y OF step := -1
FI;
IF dx > dy THEN
err := dx / 2;
WHILE x OF here /= x OF stop DO
picture[x OF here, y OF here] := color;
err -:= dy;
IF err < 0 THEN
y OF here +:= y OF step;
err +:= dx
FI;
x OF here +:= x OF step
OD
ELSE
err := dy / 2;
WHILE y OF here /= y OF stop DO
picture[x OF here, y OF here] := color;
err -:= dx;
IF err < 0 THEN
x OF here +:= x OF step;
err +:= dy
FI;
y OF here +:= y OF step
OD
FI;
picture[x OF here, y OF here] := color # ensure dots to be drawn #
END # line #;
SKIP</lang>File: test/Bitmap/Bresenhams_line_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;
- The test program: ###
test:(
REF IMAGE x = INIT LOC[1:16, 1:16]PIXEL; (fill OF class image)(x, white OF class image); (line OF class image)(x, ( 1, 8), ( 8,16), black OF class image); (line OF class image)(x, ( 8,16), (16, 8), black OF class image); (line OF class image)(x, (16, 8), ( 8, 1), black OF class image); (line OF class image)(x, ( 8, 1), ( 1, 8), black OF class image); (print OF class image)(x)
)</lang>Output:
ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffff000000ffffff000000ffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffff000000ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000000000ffffffffffffffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffff ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffff 000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000 ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffff000000ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffff000000ffffff000000ffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff
Assembly
16 bit Intel 8086\80486 Assembly for dos, see x86 assembly language. To run this code you will need to use Dos emulator.
.486
IDEAL
;---------------------------------------------
; case: DeltaY is bigger than DeltaX
; input: p1X p1Y,
; p2X p2Y,
; Color -> variable
; output: line on the screen
;---------------------------------------------
Macro DrawLine2DDY p1X, p1Y, p2X, p2Y
local l1, lp, nxt
mov dx, 1
mov ax, [p1X]
cmp ax, [p2X]
jbe l1
neg dx ; turn delta to -1
l1:
mov ax, [p2Y]
shr ax, 1 ; div by 2
mov [TempW], ax
mov ax, [p1X]
mov [pointX], ax
mov ax, [p1Y]
mov [pointY], ax
mov bx, [p2Y]
sub bx, [p1Y]
absolute bx
mov cx, [p2X]
sub cx, [p1X]
absolute cx
mov ax, [p2Y]
lp:
pusha
call PIXEL
popa
inc [pointY]
cmp [TempW], 0
jge nxt
add [TempW], bx ; bx = (p2Y - p1Y) = deltay
add [pointX], dx ; dx = delta
nxt:
sub [TempW], cx ; cx = abs(p2X - p1X) = daltax
cmp [pointY], ax ; ax = p2Y
jne lp
call PIXEL
ENDM DrawLine2DDY
;---------------------------------------------
; case: DeltaX is bigger than DeltaY
; input: p1X p1Y,
; p2X p2Y,
; Color -> variable
; output: line on the screen
;---------------------------------------------
Macro DrawLine2DDX p1X, p1Y, p2X, p2Y
local l1, lp, nxt
mov dx, 1
mov ax, [p1Y]
cmp ax, [p2Y]
jbe l1
neg dx ; turn delta to -1
l1:
mov ax, [p2X]
shr ax, 1 ; div by 2
mov [TempW], ax
mov ax, [p1X]
mov [pointX], ax
mov ax, [p1Y]
mov [pointY], ax
mov bx, [p2X]
sub bx, [p1X]
absolute bx
mov cx, [p2Y]
sub cx, [p1Y]
absolute cx
mov ax, [p2X]
lp:
pusha
call PIXEL
popa
inc [pointX]
cmp [TempW], 0
jge nxt
add [TempW], bx ; bx = abs(p2X - p1X) = deltax
add [pointY], dx ; dx = delta
nxt:
sub [TempW], cx ; cx = abs(p2Y - p1Y) = deltay
cmp [pointX], ax ; ax = p2X
jne lp
call PIXEL
ENDM DrawLine2DDX
Macro absolute a
local l1
cmp a, 0
jge l1
neg a
l1:
Endm
MODEL small
STACK 256
DATASEG
TempW dw ?
pointX dw ?
pointY dw ?
point1X dw ?
point1Y dw ?
point2X dw ?
point2Y dw ?
Color db ?
CODESEG
start:
mov ax, @data
mov ds, ax
mov ax, 13h
int 10h ; set graphic mode
mov [Color], 61
mov [point1X], 300
mov [point2X], 6
mov [point1Y], 122
mov [point2Y], 88
call DrawLine2D
mov ah, 00h
int 16h
exit:
mov ax,03h
int 10h ; set text mode
mov ax, 4C00h
int 21h
; procedures
;---------------------------------------------
; input: point1X point1Y,
; point2X point2Y,
; Color
; output: line on the screen
;---------------------------------------------
PROC DrawLine2D
mov cx, [point1X]
sub cx, [point2X]
absolute cx
mov bx, [point1Y]
sub bx, [point2Y]
absolute bx
cmp cx, bx
jae DrawLine2Dp1 ; deltaX > deltaY
mov ax, [point1X]
mov bx, [point2X]
mov cx, [point1Y]
mov dx, [point2Y]
cmp cx, dx
jbe DrawLine2DpNxt1 ; point1Y <= point2Y
xchg ax, bx
xchg cx, dx
DrawLine2DpNxt1:
mov [point1X], ax
mov [point2X], bx
mov [point1Y], cx
mov [point2Y], dx
DrawLine2DDY point1X, point1Y, point2X, point2Y
ret
DrawLine2Dp1:
mov ax, [point1X]
mov bx, [point2X]
mov cx, [point1Y]
mov dx, [point2Y]
cmp ax, bx
jbe DrawLine2DpNxt2 ; point1X <= point2X
xchg ax, bx
xchg cx, dx
DrawLine2DpNxt2:
mov [point1X], ax
mov [point2X], bx
mov [point1Y], cx
mov [point2Y], dx
DrawLine2DDX point1X, point1Y, point2X, point2Y
ret
ENDP DrawLine2D
;-----------------------------------------------
; input: pointX pointY,
; Color
; output: point on the screen
;-----------------------------------------------
PROC PIXEL
mov bh,0h
mov cx,[pointX]
mov dx,[pointY]
mov al,[Color]
mov ah,0Ch
int 10h
ret
ENDP PIXEL
END start
AutoHotkey
<lang AutoHotkey>Blue := Color(0,0,255) White := Color(255,255,255) Bitmap := Bitmap(100,100,Blue) ;create a 100*100 blue bitmap Line(Bitmap,White,5,10,60,80) ;draw a white line from (5,10) to (60,80) Bitmap.Write("Line.ppm") ;write the bitmap to file
Line(ByRef Bitmap,ByRef Color,PosX1,PosY1,PosX2,PosY2) {
DeltaX := Abs(PosX2 - PosX1), DeltaY := -Abs(PosY2 - PosY1) ;calculate deltas
StepX := ((PosX1 < PosX2) ? 1 : -1), StepY := ((PosY1 < PosY2) ? 1 : -1) ;calculate steps
ErrorValue := DeltaX + DeltaY ;calculate error value
Loop ;loop over the pixel values
{
Bitmap[PosX1,PosX2] := Color
If (PosX1 = PosX2 && PosY1 = PosY2)
Break
Temp1 := ErrorValue << 1, ((Temp1 > DeltaY) ? (ErrorValue += DeltaY, PosX1 += StepX) : ""), ((Temp1 < DeltaX) ? (ErrorValue += DeltaX, PosY1 += StepY) : "") ;move forward
}
}</lang>
AutoIt
<lang AutoHotkey>Local $var = drawBresenhamLine(2, 3, 2, 6)
Func drawBresenhamLine($iX0, $iY0, $iX1, $iY1) Local $iDx = Abs($iX1 - $iX0) Local $iSx = $iX0 < $iX1 ? 1 : -1 Local $iDy = Abs($iY1 - $iY0) Local $iSy = $iY0 < $iY1 ? 1 : -1 Local $iErr = ($iDx > $iDy ? $iDx : -$iDy) / 2, $e2
While $iX0 <= $iX1 ConsoleWrite("plot( $x=" & $iX0 & ", $y=" & $iY0 & " )" & @LF) If ($iX0 = $iX1) And ($iY0 = $iY1) Then Return $e2 = $iErr If ($e2 > -$iDx) Then $iErr -= $iDy $iX0 += $iSx EndIf If ($e2 < $iDy) Then $iErr += $iDx $iY0 += $iSy EndIf WEnd EndFunc ;==>drawBresenhamLine</lang>
BASIC
<lang qbasic> 1500 REM === Draw a line. Ported from C version
1510 REM Inputs are X1, Y1, X2, Y2: Destroys value of X1, Y1 1520 DX = ABS(X2 - X1):SX = -1:IF X1 < X2 THEN SX = 1 1530 DY = ABS(Y2 - Y1):SY = -1:IF Y1 < Y2 THEN SY = 1 1540 ER = -DY:IF DX > DY THEN ER = DX 1550 ER = INT(ER / 2) 1560 PLOT X1,Y1:REM This command may differ depending on BASIC dialect 1570 IF X1 = X2 AND Y1 = Y2 THEN RETURN 1580 E2 = ER 1590 IF E2 > -DX THEN ER = ER - DY:X1 = X1 + SX 1600 IF E2 < DY THEN ER = ER + DX:Y1 = Y1 + SY 1610 GOTO 1560</lang>
BBC BASIC
<lang bbcbasic> Width% = 200
Height% = 200
REM Set window size:
VDU 23,22,Width%;Height%;8,16,16,128
REM Draw lines:
PROCbresenham(50,100,100,190,0,0,0)
PROCbresenham(100,190,150,100,0,0,0)
PROCbresenham(150,100,100,10,0,0,0)
PROCbresenham(100,10,50,100,0,0,0)
END
DEF PROCbresenham(x1%,y1%,x2%,y2%,r%,g%,b%)
LOCAL dx%, dy%, sx%, sy%, e
dx% = ABS(x2% - x1%) : sx% = SGN(x2% - x1%)
dy% = ABS(y2% - y1%) : sy% = SGN(y2% - y1%)
IF dx% < dy% e = dx% / 2 ELSE e = dy% / 2
REPEAT
PROCsetpixel(x1%,y1%,r%,g%,b%)
IF x1% = x2% IF y1% = y2% EXIT REPEAT
IF dx% > dy% THEN
x1% += sx% : e -= dy% : IF e < 0 e += dx% : y1% += sy%
ELSE
y1% += sy% : e -= dx% : IF e < 0 e += dy% : x1% += sx%
ENDIF
UNTIL FALSE
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>
Batch File
<lang dos>@echo off setlocal enabledelayedexpansion
set width=87 set height=51
mode %width%,%height%
set "grid=" set /a resolution=height*width for /l %%i in (1,1,%resolution%) do ( set "grid=!grid! " ) call :line 1 1 5 5 call :line 9 30 60 7 call :line 9 30 60 50 call :line 52 50 32 1 echo:%grid% pause>nul exit
- line
set x1=%1 set y1=%2 set x2=%3 set y2=%4
set /a dx=x2-x1 set /a dy=y2-y1
::Clipping done to avoid overflow
if %dx% neq 0 set /a o=y1 - ( x1 * dy / dx ) if %x1% leq %x2% ( if %x1% geq %width% goto :eof if %x2% lss 0 goto :eof
if %x1% lss 0 ( if %dx% neq 0 set y1=%o% set x1=0 ) if %x2% geq %width% ( set /a x2= width - 1 if %dx% neq 0 set /a "y2= x2 * dy / dx + o" ) ) else ( if %x2% geq %width% goto :eof if %x1% lss 0 goto :eof
if %x2% lss 0 ( if %dx% neq 0 set y2=%o% set x2=0 ) if %x1% geq %width% ( set /a x1=width - 1 if %dx% neq 0 set /a "y1= x1 * dy / dx + o" ) ) if %y1% leq %y2% ( if %y1% geq %height% goto :eof if %y2% lss 0 goto :eof
if %y1% lss 0 ( set y1=0 if %dx% neq 0 set /a x1= - o * dx /dy ) if %y2% geq %height% ( set /a y2=height-1 if %dx% neq 0 set /a "x2= (y2 - o) * dx /dy" ) ) else ( if %y2% geq %height% goto :eof if %y1% lss 0 goto :eof
if %y2% lss 0 ( set y2=0 if %dx% neq 0 set /a "x2= - o * dx /dy" ) if %y1% geq %height% ( set /a y1=height-1 if %dx% neq 0 set /a "x1= (y1 - o) * dx /dy" ) )
:: Start of Bresenham's algorithm
set stepy=1 set stepx=1
set /a dx=x2-x1 set /a dy=y2-y1
if %dy% lss 0 set /a "dy=-dy","stepy=-1" if %dx% lss 0 set /a "dx=-dx","stepx=-1"
set /a "dy <<= 1" set /a "dx <<= 1"
if %dx% gtr %dy% ( set /a "fraction=dy-(dx>>1)" set /a "cursor=y1*width + x1" for /l %%x in (%x1%,%stepx%,%x2%) do ( set /a cursorP=cursor+1 for /f "tokens=1-2" %%g in ("!cursor! !cursorP!") do set "grid=!grid:~0,%%g!Û!grid:~%%h!" if !fraction! geq 0 ( set /a y1+=stepy set /a cursor+=stepy*width set /a fraction-=dx ) set /a fraction+=dy set /a cursor+=stepx ) ) else ( set /a "fraction=dx-(dy>>1)" set /a "cursor=y1*width + x1" for /l %%y in (%y1%,%stepy%,%y2%) do ( set /a cursorP=cursor+1 for /f "tokens=1-2" %%g in ("!cursor! !cursorP!") do set "grid=!grid:~0,%%g!Û!grid:~%%h!" if !fraction! geq 0 ( set /a x1+=stepx set /a cursor+=stepx set /a fraction-=dy ) set /a fraction+=dx set /a cursor+=width*stepy ) ) goto :eof</lang>
C
Instead of swaps in the initialisation use error calculation for both directions x and y simultaneously: <lang C>void line(int x0, int y0, int x1, int y1) {
int dx = abs(x1-x0), sx = x0<x1 ? 1 : -1; int dy = abs(y1-y0), sy = y0<y1 ? 1 : -1; int err = (dx>dy ? dx : -dy)/2, e2;
for(;;){
setPixel(x0,y0);
if (x0==x1 && y0==y1) break;
e2 = err;
if (e2 >-dx) { err -= dy; x0 += sx; }
if (e2 < dy) { err += dx; y0 += sy; }
}
}</lang>
C++
<lang cpp> void Line( const float x1, const float y1, const float x2, const float y2, const Color& color ) {
// Bresenham's line algorithm
const bool steep = (fabs(y2 - y1) > fabs(x2 - x1));
if(steep)
{
std::swap(x1, y1);
std::swap(x2, y2);
}
if(x1 > x2)
{
std::swap(x1, x2);
std::swap(y1, y2);
}
const float dx = x2 - x1; const float dy = fabs(y2 - y1); float error = dx / 2.0f; const int ystep = (y1 < y2) ? 1 : -1; int y = (int)y1;
const int maxX = (int)x2;
for(int x=(int)x1; x<maxX; x++)
{
if(steep)
{
SetPixel(y,x, color);
}
else
{
SetPixel(x,y, color);
}
error -= dy;
if(error < 0)
{
y += ystep;
error += dx;
}
}
} </lang>
Clojure
<lang clojure>
(defn draw-line
"Draw a line from x1,y1 to x2,y2 using Bresenham's, to a java BufferedImage in the colour of pixel."
[buffer x1 y1 x2 y2 pixel]
(let [dist-x (Math/abs (- x1 x2))
dist-y (Math/abs (- y1 y2))
steep (> dist-y dist-x)]
(let [[x1 y1 x2 y2] (if steep [y1 x1 y2 x2] [x1 y1 x2 y2])]
(let [[x1 y1 x2 y2] (if (> x1 x2) [x2 y2 x1 y1] [x1 y1 x2 y2])]
(let [delta-x (- x2 x1)
delta-y (Math/abs (- y1 y2))
y-step (if (< y1 y2) 1 -1)]
(let [plot (if steep
#(.setRGB buffer (int %1) (int %2) pixel)
#(.setRGB buffer (int %2) (int %1) pixel))]
(loop [x x1 y y1 error (Math/floor (/ delta-x 2)) ]
(plot x y)
(if (< x x2)
; Rather then rebind error, test that it is less than delta-y rather than zero
(if (< error delta-y)
(recur (inc x) (+ y y-step) (+ error (- delta-x delta-y)))
(recur (inc x) y (- error delta-y)))))))))))
</lang>
CoffeeScript
<lang coffeescript> drawBresenhamLine = (x0, y0, x1, y1) ->
dx = Math.abs(x1 - x0) sx = if x0 < x1 then 1 else -1 dy = Math.abs(y1 - y0) sy = if y0 < y1 then 1 else -1 err = (if dx>dy then dx else -dy) / 2
loop
setPixel(x0, y0)
break if x0 == x1 && y0 == y1
e2 = err
if e2 > -dx
err -= dy
x0 += sx
if e2 < dy
err += dx
y0 += sy
null
</lang>
Common Lisp
<lang lisp>(defun draw-line (buffer x1 y1 x2 y2 pixel)
(declare (type rgb-pixel-buffer buffer))
(declare (type integer x1 y1 x2 y2))
(declare (type rgb-pixel pixel))
(let* ((dist-x (abs (- x1 x2)))
(dist-y (abs (- y1 y2)))
(steep (> dist-y dist-x)))
(when steep
(psetf x1 y1 y1 x1
x2 y2 y2 x2))
(when (> x1 x2)
(psetf x1 x2 x2 x1
y1 y2 y2 y1))
(let* ((delta-x (- x2 x1))
(delta-y (abs (- y1 y2)))
(error (floor delta-x 2))
(y-step (if (< y1 y2) 1 -1))
(y y1))
(loop
:for x :upfrom x1 :to x2
:do (if steep
(setf (rgb-pixel buffer x y) pixel)
(setf (rgb-pixel buffer y x) pixel))
(setf error (- error delta-y))
(when (< error 0)
(incf y y-step)
(incf error delta-x))))
buffer))</lang>
D
This code uses the Image defined in Bitmap Task.
<lang d>module bitmap_bresenhams_line_algorithm;
import std.algorithm, std.math, bitmap;
void drawLine(Color)(Image!Color img,
size_t x1, size_t y1,
in size_t x2, in size_t y2,
in Color color)
pure nothrow @nogc {
immutable int dx = x2 - x1; immutable int ix = (dx > 0) - (dx < 0); immutable size_t dx2 = abs(dx) * 2; int dy = y2 - y1; immutable int iy = (dy > 0) - (dy < 0); immutable size_t dy2 = abs(dy) * 2; img[x1, y1] = color;
if (dx2 >= dy2) {
int error = dy2 - (dx2 / 2);
while (x1 != x2) {
if (error >= 0 && (error || (ix > 0))) {
error -= dx2;
y1 += iy;
}
error += dy2;
x1 += ix;
img[x1, y1] = color;
}
} else {
int error = dx2 - (dy2 / 2);
while (y1 != y2) {
if (error >= 0 && (error || (iy > 0))) {
error -= dy2;
x1 += ix;
}
error += dx2;
y1 += iy;
img[x1, y1] = color;
}
}
}
version (bitmap_bresenhams_line_algorithm_main) {
void main() {
auto img = new Image!RGB(25, 22);
img.drawLine(5, 5, 15, 20, RGB.white);
img.drawLine(3, 20, 10, 12, RGB.white);
img.textualShow();
}
}</lang>
To run the demo code compile with -version=bitmap_bresenhams_line_algorithm_main.
- Output:
######################### ######################### ######################### ######################### ######################### #####.################### ######.################## ######.################## #######.################# ########.################ ########.################ #########.############### ##########.############## #########..############## ########.##.############# #######.####.############ ######.#####.############ ######.######.########### #####.########.########## ####.#########.########## ###.###########.######### #########################
Delphi
<lang delphi> procedure drawLine (bitmap : TBitmap; xStart, yStart, xEnd, yEnd : integer; color : TAlphaColor); // Bresenham's Line Algorithm. Byte, March 1988, pp. 249-253. // Modified from http://www.efg2.com/Lab/Library/Delphi/Graphics/Bresenham.txt and tested. var
a, b : integer; // displacements in x and y
d : integer; // decision variable
diag_inc : integer; // d's increment for diagonal steps
dx_diag : integer; // diagonal x step for next pixel
dx_nondiag : integer; // nondiagonal x step for next pixel
dy_diag : integer; // diagonal y step for next pixel
dy_nondiag : integer; // nondiagonal y step for next pixel
i : integer; // loop index
nondiag_inc: integer; // d's increment for nondiagonal steps
swap : integer; // temporary variable for swap
x,y : integer; // current x and y coordinates
begin
x := xStart; // line starting point}
y := yStart;
// Determine drawing direction and step to the next pixel.
a := xEnd - xStart; // difference in x dimension
b := yEnd - yStart; // difference in y dimension
// Determine whether end point lies to right or left of start point.
if a < 0 then // drawing towards smaller x values?
begin
a := -a; // make 'a' positive
dx_diag := -1
end
else
dx_diag := 1;
// Determine whether end point lies above or below start point.
if b < 0 then // drawing towards smaller x values?
begin
b := -b; // make 'a' positive
dy_diag := -1
end
else
dy_diag := 1;
// Identify octant containing end point.
if a < b then
begin
swap := a;
a := b;
b := swap;
dx_nondiag := 0;
dy_nondiag := dy_diag
end
else
begin
dx_nondiag := dx_diag;
dy_nondiag := 0
end;
d := b + b - a; // initial value for d is 2*b - a
nondiag_inc := b + b; // set initial d increment values
diag_inc := b + b - a - a;
for i := 0 to a do
begin /// draw the a+1 pixels
drawPixel (bitmap, x, y, color);
if d < 0 then // is midpoint above the line?
begin // step nondiagonally
x := x + dx_nondiag;
y := y + dy_nondiag;
d := d + nondiag_inc // update decision variable
end
else
begin // midpoint is above the line; step diagonally}
x := x + dx_diag;
y := y + dy_diag;
d := d + diag_inc
end;
end;
end; </lang>
E
<lang e>def swap(&left, &right) { # From Generic swap
def t := left left := right right := t
}
def drawLine(image, var x0, var y0, var x1, var y1, color) {
def steep := (y1 - y0).abs() > (x1 - x0).abs()
if (steep) {
swap(&x0, &y0)
swap(&x1, &y1)
}
if (x0 > x1) {
swap(&x0, &x1)
swap(&y0, &y1)
}
def deltax := x1 - x0
def deltay := (y1 - y0).abs()
def ystep := if (y0 < y1) { 1 } else { -1 }
var error := deltax // 2
var y := y0
for x in x0..x1 {
if (steep) { image[y, x] := color } else { image[x, y] := color }
error -= deltay
if (error < 0) {
y += ystep
error += deltax
}
}
}</lang>
<lang e>def i := makeImage(5, 20) drawLine(i, 1, 1, 3, 18, makeColor.fromFloat(0,1,1)) i.writePPM(<import:java.io.makeFileOutputStream>(<file:~/Desktop/Bresenham.ppm>))</lang>
Erlang
<lang erlang> build_path({Sx, Sy}, {Tx, Ty}) ->
if
Tx < Sx -> StepX = -1;
true -> StepX = 1
end,
if
Ty < Sy -> StepY = -1;
true -> StepY = 1
end,
Dx = abs((Tx-Sx)*2),
Dy = abs((Ty-Sy)*2),
if
Dy > Dx -> Path = through_y({Sx, Sy}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, Dx*2-Dy, []);
true -> Path = through_x({Sx, Sy}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, Dy*2-Dx, [])
end,
lists:reverse(Path).
through_x({Tx, _}, {Tx, _}, _, _, _, P) -> P; through_x({Sx, Sy}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, F0, P) when F0 >= 0 ->
Ny = Sy + StepY,
F1 = F0 - Dx,
Nx = Sx + StepX,
F2 = F1 + Dy,
through_x({Nx, Ny}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, F2, [{Nx, Ny}|P]);
through_x({Sx, Sy}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, F0, P) when F0 < 0 ->
Ny = Sy,
Nx = Sx + StepX,
F2 = F0 + Dy,
through_x({Nx, Ny}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, F2, [{Nx, Ny}|P]).
through_y({_, Ty}, {_, Ty}, _, _, _, P) -> P; through_y({Sx, Sy}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, F0, P) when F0 >= 0 ->
Nx = Sx + StepX,
F1 = F0 - Dy,
Ny = Sy + StepY,
F2 = F1 + Dx,
through_y({Nx, Ny}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, F2, [{Nx, Ny}|P]);
through_y({Sx, Sy}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, F0, P) when F0 < 0 ->
Nx = Sx,
Ny = Sy + StepY,
F2 = F0 + Dx,
through_y({Nx, Ny}, {Tx, Ty}, {StepX, StepY}, {Dx, Dy}, F2, [{Nx, Ny}|P]).
</lang> OR <lang erlang> line({X0, Y0}, {X1, Y1}) ->
SX = step(X0, X1),
SY = step(Y0, Y1),
DX = abs(X1 - X0),
DY = abs(Y1 - Y0),
Err = DX - DY,
line({X0, Y0}, {X1, Y1}, {SX, SY}, {DX, DY}, Err, []).
line({X1, Y1}, {X1, Y1}, _, _, _, Acc) ->
lists:reverse([{X1, Y1} | Acc]);
line({X, Y}, {X1, Y1}, {SX, SY}, {DX, DY}, Err, Acc) ->
DE = 2 * Err,
{X0, Err0} = next_x(X, SX, DY, Err, DE),
{Y0, Err1} = next_y(Y, SY, DX, Err0, DE),
line({X0, Y0}, {X1, Y1}, {SX, SY}, {DX, DY}, Err1, [{X, Y} | Acc]).
step(P0, P1) when P0 < P1 ->
1;
step(_, _) ->
-1.
next_x(X, SX, DY, E, DE) when DE > -DY ->
{X + SX, E - DY};
next_x(X, _SX, _DY, E, _DE) ->
{X, E}.
next_y(Y, SY, DX, E, DE) when DE < DX ->
{Y + SY, E + DX};
next_y(Y, _SY, _DX, E, _DE) ->
{Y, E}.
</lang>
ERRE
<lang ERRE> PROGRAM BRESENHAM
!$INCLUDE="PC.LIB"
PROCEDURE BRESENHAM ! === Draw a line using graphic coordinates ! Inputs are X1, Y1, X2, Y2: Destroys value of X1, Y1 dx=ABS(x2-x1) sx=-1 IF x1<x2 THEN sx=1 dy=ABS(y2-y1) sy=-1 IF y1<y2 THEN sy=1 er=-dy IF dx>dy THEN er=dx er=INT(er/2) LOOP
PSET(x1,y1,1) EXIT IF x1=x2 AND y1=y2 e2=er IF e2>-dx THEN er=er-dy x1=x1+sx IF e2<dy THEN er=er+dx y1=y1+sy
END LOOP END PROCEDURE
BEGIN
SCREEN(2) INPUT(x1,y1,x2,y2) BRESENHAM GET(A$) SCREEN(0)
END PROGRAM </lang>
Euphoria
<lang euphoria>include std/console.e include std/graphics.e include std/math.e
-- the new_image function and related code in the 25 or so -- lines below are from http://rosettacode.org/wiki/Basic_bitmap_storage#Euphoria -- as of friday, march 2, 2012
-- Some color constants: constant
black = #000000, white = #FFFFFF, red = #FF0000, green = #00FF00, blue = #0000FF
-- Create new image filled with some color function new_image(integer width, integer height, atom fill_color)
return repeat(repeat(fill_color,height),width)
end function
--grid used for drawing lines in this program sequence screenData = new_image(16,16,black)
--the line algorithm function bresLine(sequence screenData, integer x0, integer y0, integer x1, integer y1, integer color)
integer deltaX = abs(x1 - x0), deltaY = abs(y1 - y0)
integer stepX, stepY, lineError, error2
if x0 < x1 then
stepX = 1
else
stepX = -1
end if
if y0 < y1 then
stepY = 1
else
stepY = -1
end if
if deltaX > deltaY then
lineError = deltaX
else
lineError = -deltaY
end if
lineError = round(lineError / 2, 1)
while 1 do
screenData[x0][y0] = color
if (x0 = x1 and y0 = y1) then
exit
end if
error2 = lineError
if error2 > -deltaX then
lineError -= deltaY
x0 += stepX
end if
if error2 < deltaY then
lineError += deltaX
y0 += stepY
end if
end while
return screenData -- return modified version of the screenData sequence
end function
--prevents console output wrapping to next line if it is too big for the screen wrap(0) --outer diamond screenData = bresLine(screenData,8,1,16,8,white) screenData = bresLine(screenData,16,8,8,16,white) screenData = bresLine(screenData,8,16,1,8,white) screenData = bresLine(screenData,1,8,8,1,white) --inner diamond screenData = bresLine(screenData,8,4,12,8,white) screenData = bresLine(screenData,12,8,8,12,white) screenData = bresLine(screenData,8,12,4,8,white) screenData = bresLine(screenData,4,8,8,4,white) -- center lines drawing from left to right, and the next from right to left. screenData = bresLine(screenData,7,7,9,7,white) screenData = bresLine(screenData,9,9,7,9,white) --center dot screenData = bresLine(screenData,8,8,8,8,white)
--print to the standard console output for i = 1 to 16 do
puts(1,"\n")
for j = 1 to 16 do
if screenData[j][i] = black then
printf(1, "%s", ".")
else
printf(1, "%s", "#")
end if
end for
end for
puts(1,"\n\n") any_key()
--/* --output was edited to replace the color's hex digits for clearer output graphics. --to output all the hex digits, use printf(1,"%06x", screenData[j][i]) --to output 'shortened' hex digits, use : --printf(1, "%x", ( abs( ( (screenData[j][i] / #FFFFF) - 1 ) ) - 1 ) ) --and --printf(1,"%x", abs( ( (screenData[j][i] / #FFFFF) - 1 ) ) ) -- --,respectively in the last if check. --*/</lang> Output:
.......#........ ......#.#....... .....#...#...... ....#..#..##.... ...#..#.#...#... ..#..#...#...#.. .#..#.###.#...#. #..#...#...#...# .#..#.###.#...#. ..#..#...#...#.. ...#..#.#...#... ....#..#...#.... ....#.....#..... .....#...#...... ......#.#....... .......#........ Press Any Key to continue...
F#
<lang fsharp>let inline bresenham fill (x0, y0) (x1, y1) =
let steep = abs(y1 - y0) > abs(x1 - x0)
let x0, y0, x1, y1 =
if steep then y0, x0, y1, x1 else x0, y0, x1, y1
let x0, y0, x1, y1 =
if x0 > x1 then x1, y1, x0, y0 else x0, y0, x1, y1
let dx, dy = x1 - x0, abs(y1 - y0)
let s = if y0 < y1 then 1 else -1
let rec loop e x y =
if x <= x1 then
if steep then fill y x else fill x y
if e < dy then
loop (e-dy+dx) (x+1) (y+s)
else
loop (e-dy) (x+1) y
loop (dx/2) x0 y0</lang>
The following program tests the above bresenham function by drawing 100 lines into an image and visualizing the result using
:
<lang fsharp>open System.Windows open System.Windows.Media.Imaging
[<System.STAThread>] do
let rand = System.Random() let n = 256 let pixel = Array.create (n*n) 0uy let rand = System.Random().Next for _ in 1..100 do bresenham (fun x y -> pixel.[x+y*n] <- 255uy) (rand n, rand n) (rand n, rand n) let image = Controls.Image(Stretch=Media.Stretch.Uniform) let format = Media.PixelFormats.Gray8 image.Source <- BitmapSource.Create(n, n, 1.0, 1.0, format, null, pixel, n) Window(Content=image, Title="Bresenham's line algorithm") |> (Application()).Run |> ignore</lang>
FBSL
1. In FBSL, successive calls to one and the same subprocedure may be concatenated to a series of argument sets as in Sub Rhombus() below.
2. In FBSL, BASIC-style logical AND and OR operators are "inclusive", i.e. they always evaluate the both of their conditions. C-style logical ANDALSO and ORELSE operators are "exclusive". ANDALSO evaluates the second condition if, and only if, its first condition is TRUE as in Sub Bresenham() below. ORELSE evaluates its second condition if, and only if, its first condition is FALSE.
Using pure FBSL's built-in graphics functions: <lang qbasic>#DEFINE WM_LBUTTONDOWN 513
- DEFINE WM_CLOSE 16
FBSLSETTEXT(ME, "Bresenham") ' Set form caption FBSLSETFORMCOLOR(ME, RGB(0, 255, 255)) ' Cyan: set persistent background color DRAWWIDTH(5) ' Adjust point size FBSL.GETDC(ME) ' Use volatile FBSL.GETDC below to avoid extra assignments
RESIZE(ME, 0, 0, 200, 235) CENTER(ME) SHOW(ME)
BEGIN EVENTS
SELECT CASE CBMSG CASE WM_LBUTTONDOWN: Rhombus() ' Draw CASE WM_CLOSE: FBSL.RELEASEDC(ME, FBSL.GETDC) ' Clean up END SELECT
END EVENTS
SUB Rhombus()
Bresenham(50, 100, 100, 190)(100, 190, 150, 100)(150, 100, 100, 10)(100, 10, 50, 100)
SUB Bresenham(x0, y0, x1, y1)
DIM dx = ABS(x0 - x1), sx = SGN(x0 - x1)
DIM dy = ABS(y0 - y1), sy = SGN(y0 - y1)
DIM tmp, er = IIF(dx > dy, dx, -dy) / 2
WHILE NOT (x0 = x1 ANDALSO y0 = y1)
PSET(FBSL.GETDC, x0, y0, &HFF) ' Red: Windows stores colors in BGR order
tmp = er
IF tmp > -dx THEN: er = er - dy: x0 = x0 + sx: END IF
IF tmp < +dy THEN: er = er + dx: y0 = y0 + sy: END IF
WEND
END SUB
END SUB</lang>
Output: 
Factor
A very ugly imperative implementation similar to the wikipedia pseudocode.. <lang factor>USING: accessors arrays kernel locals math math.functions math.ranges math.vectors rosettacode.raster.display rosettacode.raster.storage sequences ui.gadgets ; IN: rosettacode.raster.line
- line-points ( pt1 pt2 -- points )
pt1 first2 :> y0! :> x0!
pt2 first2 :> y1! :> x1!
y1 y0 - abs x1 x0 - abs > :> steep
steep [
y0 x0 y0! x0!
y1 x1 y1! x1!
] when
x0 x1 > [
x0 x1 x0! x1!
y0 y1 y0! y1!
] when
x1 x0 - :> deltax
y1 y0 - abs :> deltay
0 :> current-error!
deltay deltax / abs :> deltaerr
0 :> ystep!
y0 :> y!
y0 y1 < [ 1 ystep! ] [ -1 ystep! ] if
x0 x1 1 <range> [
y steep [ swap ] when 2array
current-error deltaerr + current-error!
current-error 0.5 >= [
ystep y + y!
current-error 1 - current-error!
] when
] { } map-as ;
! Needs rosettacode.raster.storage for the set-pixel function and to create the image
- draw-line ( {R,G,B} pt1 pt2 image -- )
[ line-points ] dip [ set-pixel ] curry with each ;</lang>
Forth
<lang forth>defer steep \ noop or swap defer ystep \ 1+ or 1-
- line ( x0 y0 x1 y1 color bmp -- )
{ color bmp }
rot swap
( x0 x1 y0 y1 )
2dup - abs >r
2over - abs r> <
if ['] swap \ swap use of x and y
else 2swap ['] noop
then is steep
( y0 y1 x0 x1 )
2dup >
if swap 2swap swap \ ensure x1 > x0
else 2swap
then
( x0 x1 y0 y1 )
2dup >
if ['] 1-
else ['] 1+
then is ystep
over - abs { y deltay }
swap 2dup - dup { deltax }
2/ rot 1+ rot
( error x1+1 x0 )
do color i y steep bmp b!
deltay -
dup 0<
if y ystep to y
deltax +
then
loop
drop ;
5 5 bitmap value test 0 test bfill 1 0 4 1 red test line 4 1 3 4 red test line 3 4 0 3 red test line 0 3 1 0 red test line test bshow cr
** * **
- *
- *
**
ok</lang>
Fortran
<lang fortran>module RCImagePrimitive
use RCImageBasic
implicit none
type point
integer :: x, y
end type point
private :: swapcoord
contains
subroutine swapcoord(p1, p2) integer, intent(inout) :: p1, p2 integer :: t
t = p2 p2 = p1 p1 = t end subroutine swapcoord
subroutine draw_line(img, from, to, color) type(rgbimage), intent(inout) :: img type(point), intent(in) :: from, to type(rgb), intent(in) :: color
type(point) :: rfrom, rto integer :: dx, dy, error, ystep, x, y logical :: steep
rfrom = from
rto = to
steep = (abs(rto%y - rfrom%y) > abs(rto%x - rfrom%x))
if ( steep ) then
call swapcoord(rfrom%x, rfrom%y)
call swapcoord(rto%x, rto%y)
end if
if ( rfrom%x > rto%x ) then
call swapcoord(rfrom%x, rto%x)
call swapcoord(rfrom%y, rto%y)
end if
dx = rto%x - rfrom%x dy = abs(rto%y - rfrom%y) error = dx / 2 y = rfrom%y
if ( rfrom%y < rto%y ) then
ystep = 1
else
ystep = -1
end if
do x = rfrom%x, rto%x
if ( steep ) then
call put_pixel(img, y, x, color)
else
call put_pixel(img, x, y, color)
end if
error = error - dy
if ( error < 0 ) then
y = y + ystep
error = error + dx
end if
end do
end subroutine draw_line
end module RCImagePrimitive</lang>
Usage example:
<lang fortran>program BasicImageTests
use RCImageBasic use RCImageIO use RCImagePrimitive
implicit none
type(rgbimage) :: animage integer :: x, y
call alloc_img(animage, 200, 200) call fill_img(animage, rgb(255,255,255))
call draw_line(animage, point(0,0), point(199,199), rgb(0,0,0))
do y=0,219,20
call draw_line(animage, point(0,0), point(199, y), &
rgb(0,0,0))
end do
open(unit=10, file='outputimage.ppm', status='new') call output_ppm(10, animage) close(10)
call free_img(animage)
end program BasicImageTests</lang>
FreeBASIC
<lang freebasic>' version 16-09-2015 ' compile with: fbc -s console
' Ported from the C version Sub Br_line(x0 As Integer, y0 As Integer, x1 As Integer, y1 As Integer, Col As Integer = &HFFFFFF)
Dim As Integer dx = Abs(x1 - x0), dy = Abs(y1 - y0) Dim As Integer sx = IIf(x0 < x1, 1, -1) Dim As Integer sy = IIf(y0 < y1, 1, -1) Dim As Integer er = IIf(dx > dy, dx, -dy) \ 2, e2
Do
PSet(x0, y0), col
If (x0 = x1) And (y0 = y1) Then Exit Do
e2 = er
If e2 > -dx Then Er -= dy : x0 += sx
If e2 < dy Then Er += dx : y0 += sy
Loop
End Sub
' ------=< MAIN >=------
Dim As Double x0, y0, x1, y1
ScreenRes 400, 400, 32 WindowTitle" Press key to end demo" Randomize Timer
Do
Cls
For a As Integer = 1 To 20
Br_line(Rnd*380+10, Rnd*380+10, Rnd*380+10, Rnd*380+10, Rnd*&hFFFFFF)
Next
Sleep 2000
Loop Until InKey <> "" ' loop until a key is pressed
End</lang>
Go
<lang go>package raster
// Line draws line by Bresenham's algorithm. func (b *Bitmap) Line(x0, y0, x1, y1 int, p Pixel) {
// implemented straight from WP pseudocode
dx := x1 - x0
if dx < 0 {
dx = -dx
}
dy := y1 - y0
if dy < 0 {
dy = -dy
}
var sx, sy int
if x0 < x1 {
sx = 1
} else {
sx = -1
}
if y0 < y1 {
sy = 1
} else {
sy = -1
}
err := dx - dy
for {
b.SetPx(x0, y0, p)
if x0 == x1 && y0 == y1 {
break
}
e2 := 2 * err
if e2 > -dy {
err -= dy
x0 += sx
}
if e2 < dx {
err += dx
y0 += sy
}
}
}
func (b *Bitmap) LineRgb(x0, y0, x1, y1 int, c Rgb) {
b.Line(x0, y0, x1, y1, c.Pixel())
}</lang> A demonstration program: <lang go>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(0xdfefff)
blue := raster.Rgb(0x8fcfff)
b.LineRgb(7, 12, 307, 122, blue)
b.LineRgb(177, 12, 127, 222, blue)
err := b.WritePpmFile("bresenham.ppm")
if err != nil {
fmt.Println(err)
}
}</lang>
Haskell
<lang haskell>module Bitmap.Line(line) where
import Bitmap import Control.Monad import Control.Monad.ST import qualified Data.STRef
var = Data.STRef.newSTRef get = Data.STRef.readSTRef mutate = Data.STRef.modifySTRef
line :: Color c => Image s c -> Pixel -> Pixel -> c -> ST s () line i (Pixel (xa, ya)) (Pixel (xb, yb)) c = do
yV <- var y1
errorV <- var $ deltax `div` 2
forM_ [x1 .. x2] (\x -> do
y <- get yV
setPix i (Pixel $ if steep then (y, x) else (x, y)) c
mutate errorV $ subtract deltay
error <- get errorV
when (error < 0) (do
mutate yV (+ ystep)
mutate errorV (+ deltax)))
where steep = abs (yb - ya) > abs (xb - xa)
(xa', ya', xb', yb') = if steep
then (ya, xa, yb, xb)
else (xa, ya, xb, yb)
(x1, y1, x2, y2) = if xa' > xb'
then (xb', yb', xa', ya')
else (xa', ya', xb', yb')
deltax = x2 - x1
deltay = abs $ y2 - y1
ystep = if y1 < y2 then 1 else -1</lang>
J
Solution:
Using definitions from Basic bitmap storage. <lang j>thru=: <./ + -~ i.@+ _1 ^ > NB. integers from x through y
NB.*getBresenhamLine v Returns points for a line given start and end points NB. y is: y0 x0 ,: y1 x1 getBresenhamLine=: monad define
steep=. ([: </ |@-~/) y
points=. |."1^:steep y
slope=. %~/ -~/ points
ypts=. thru/ {."1 points
xpts=. ({: + 0.5 <.@:+ slope * ypts - {.) {.points
|."1^:steep ypts,.xpts
)
NB.*drawLines v Draws lines (x) on image (y) NB. x is: 2-item list (start and end points) ; (color) drawLines=: (1&{:: ;~ [: ; [: <@getBresenhamLine"2 (0&{::))@[ setPixels ]</lang>
Example Usage: <lang j> myimg=: 0 255 0 makeRGB 20 32 NB. 32 by 20 green image
myimg=: ((1 1 ,: 5 11) ; 255 0 0 ) drawLines myimg NB. draw red line from xy point 1 1 to 11 5
NB. Works for lists of 2 by 2 arrays each defining a line's start and end point.
Diamond=: _2]\ _2]\ 9 5 5 15 , 5 15 9 25 , 9 25 13 15 , 13 15 9 5 Square =: _2]\ _2]\ 5 5 5 25 , 5 25 13 25 , 13 25 13 5 , 13 5 5 5 viewRGB myimg=: (Diamond;255 0 0) drawLines myimg NB. draw 4 red lines to form a diamond viewRGB myimg=: (Square;0 0 255) drawLines myimg NB. draw 4 blue lines to form a square viewRGB (Diamond;255 0 0) drawLines (Square;0 0 255) drawLines myimg</lang>
Java
<lang java>import java.awt.*; import javax.swing.*;
public class Bresenham extends JFrame {
public static void main(String[] args) {
SwingUtilities.invokeLater(new Runnable() {
@Override
public void run() {
JFrame f = new Bresenham();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setVisible(true);
f.add(new BresenhamPanel(), BorderLayout.CENTER);
f.setTitle("Bresenham");
f.setResizable(false);
f.pack();
f.setLocationRelativeTo(null);
}
});
}
}
class BresenhamPanel extends JPanel {
final int centerX, centerY;
public BresenhamPanel() {
int w = 600;
int h = 500;
centerX = w / 2;
centerY = h / 2;
setPreferredSize(new Dimension(w, h));
setBackground(Color.white);
}
@Override
public void paintComponent(Graphics g) {
super.paintComponent(g);
drawLine(g, 0, 0, 8, 19); // NNE
drawLine(g, 0, 0, 19, 8); // ENE
drawLine(g, 0, 0, 19, -8); // ESE
drawLine(g, 0, 0, 8, -19); // SSE
drawLine(g, 0, 0, -8, -19); // SSW
drawLine(g, 0, 0, -19, -8); // WSW
drawLine(g, 0, 0, -19, 8); // WNW
drawLine(g, 0, 0, -8, 19); // NNW
}
private void plot(Graphics g, int x, int y) {
g.setColor(Color.black);
g.drawOval(centerX + (x * 10), centerY + (-y * 10), 10, 10);
}
private void drawLine(Graphics g, int x1, int y1, int x2, int y2) {
// delta of exact value and rounded value of the dependant variable
int d = 0;
int dy = Math.abs(y2 - y1);
int dx = Math.abs(x2 - x1);
int dy2 = (dy << 1); // slope scaling factors to avoid floating
int dx2 = (dx << 1); // point
int ix = x1 < x2 ? 1 : -1; // increment direction
int iy = y1 < y2 ? 1 : -1;
if (dy <= dx) {
for (;;) {
plot(g, x1, y1);
if (x1 == x2)
break;
x1 += ix;
d += dy2;
if (d > dx) {
y1 += iy;
d -= dx2;
}
}
} else {
for (;;) {
plot(g, x1, y1);
if (y1 == y2)
break;
y1 += iy;
d += dx2;
if (d > dy) {
x1 += ix;
d -= dy2;
}
}
}
}
}</lang>
JavaScript
Instead of swaps in the initialisation use error calculation for both directions x and y simultaneously: <lang javascript>function bline(x0, y0, x1, y1) {
var dx = Math.abs(x1 - x0), sx = x0 < x1 ? 1 : -1; var dy = Math.abs(y1 - y0), sy = y0 < y1 ? 1 : -1; var err = (dx>dy ? dx : -dy)/2;
while (true) {
setPixel(x0,y0);
if (x0 === x1 && y0 === y1) break;
var e2 = err;
if (e2 > -dx) { err -= dy; x0 += sx; }
if (e2 < dy) { err += dx; y0 += sy; }
}
}</lang>
Julia
<lang Julia>function line(img, x0::Int, y0::Int, x1::Int, y1::Int, col) dx = int(abs(x1-x0)) dy = int(abs(y1-y0))
sx = x0<x1 ? 1 : -1 sy = y0<y1 ? 1 : -1;
err = (dx>dy ? dx : -dy)/2
while true @inbounds img[x0,y0]=col if (x0==x1 && y0==y1); break; end e2 = err; if e2 > -dx err -= dy x0 += sx end if e2 < dy err += dx y0 += sy end end end </lang>
Korn Shell
<lang>function line {
x0=$1; y0=$2 x1=$3; y1=$4
if (( x0 > x1 ))
then
((dx = x0 - x1)); ((sx = -1))
else
((dx = x1 - x0)); ((sx = 1))
fi
if (( y0 > y1 ))
then
((dy = y0 - y1)); ((sy = -1))
else
((dy = y1 - y0)); ((sy = 1))
fi
if (( dx > dy ))
then
((err = dx))
else
((err = -dy))
fi
((err /= 2)); ((e2 = 0))
while /bin/true
do
echo $x0 $y0
(( x0 == x1 && y0 == y1 )) && return
((e2 = err))
(( e2 > -dx)) && { ((err -= dy )); (( x0 += sx )) }
(( e2 < dy)) && { ((err += dx )); (( y0 += sy )) }
done
}</lang>
Output from the statement:-
line 0 0 3 4
(which could be piped to another program) <lang>0 0 1 1 1 2 2 3 3 4</lang>
Maple
<lang maple>SegmentBresenham := proc (img, x0, y0, x1, y1)
local deltax, deltay, x, y, ystep, steep, err, img2, x02, y02, x12, y12;
x02, x12, y02, y12 := y0, y1, x0, x1;
steep := abs(x12 - x02) < abs(y12 - y02);
img2 := copy(img);
if steep then
x02, y02 := y02, x02;
x12, y12 := y12, x12;
end if;
if x12 < x02 then
x02, x12 := x12, x02;
y02, y12 := y12, y02;
end if;
deltax := x12 - x02;
deltay := abs(y12 - y02);
err := deltax / 2;
y := y02;
if y02 < y12 then
ystep := 1
else
ystep := -1
end if;
for x from x02 to x12 do
if steep then
img2[y, x] := 0
else
img2[x, y] := 0
end if;
err := err - deltay;
if err < 0 then
y := y + ystep;
err := err + deltax
end if;
end do;
return img2;
end proc:</lang>
Mathematica / Wolfram Language
<lang Mathematica>Rasterize[ Style[Graphics[Line[{{0, 0}, {20, 10}}]], Antialiasing -> False]] </lang>
MATLAB
Note: Store this function in a file named "bresenhamLine.m" in the @Bitmap folder for the Bitmap class defined here.
<lang MATLAB> %screen = Bitmap object %startPoint = [x0,y0] %endPoint = [x1,y1] %color = [red,green,blue]
function bresenhamLine(screen,startPoint,endPoint,color)
if( any(color > 255) )
error 'RGB colors must be between 0 and 255';
end
%Check for vertical line, x0 == x1
if( startPoint(1) == endPoint(1) )
%Draw vertical line
for i = (startPoint(2):endPoint(2))
setPixel(screen,[startPoint(1) i],color);
end
end
%Simplified Bresenham algorithm
dx = abs(endPoint(1) - startPoint(1));
dy = abs(endPoint(2) - startPoint(2));
if(startPoint(1) < endPoint(1))
sx = 1;
else
sx = -1;
end
if(startPoint(2) < endPoint(2))
sy = 1;
else
sy = -1;
end
err = dx - dy;
pixel = startPoint;
while(true)
screen.setPixel(pixel,color); %setPixel(x0,y0)
if( pixel == endPoint )
break;
end
e2 = 2*err;
if( e2 > -dy )
err = err - dy;
pixel(1) = pixel(1) + sx;
end
if( e2 < dx )
err = err + dx;
pixel(2) = pixel(2) + sy;
end
end
assignin('caller',inputname(1),screen); %saves the changes to the object
end </lang>
Sample Usage: <lang MATLAB> >> img = Bitmap(800,600); >> img.bresenhamLine([400 550],[200 400],[255 255 255]); >> img.bresenhamLine([400 550],[600 400],[255 255 255]); >> img.bresenhamLine([200 400],[350 150],[255 255 255]); >> img.bresenhamLine([600 400],[450 150],[255 255 255]); >> img.bresenhamLine([350 150],[450 150],[255 255 255]); >> img.bresenhamLine([400 550],[400 150],[255 255 255]); >> disp(img) </lang>
MAXScript
<lang maxscript>fn plot img coord steep col = (
if steep then
(
swap coord[1] coord[2]
)
setPixels img coord col
)
fn drawLine img start end col = (
local steep = (abs (end.y - start.y)) > (abs (end.x - start.x))
if steep then
(
swap start.x start.y
swap end.x end.y
)
if start.x > end.x then
(
swap start.x end.x
swap start.y end.y
)
local deltaX = end.x - start.x
local deltaY = abs (end.y - start.y)
local error = deltaX / 2.0
local yStep = -1
local y = start.y
if start.y < end.y then
(
yStep = 1
)
for x in start.x to end.x do
(
plot img [x, y] steep col
error -= deltaY
if error < 0 then
(
y += yStep
error += deltaX
)
)
img
)
myBitmap = bitmap 512 512 color:(color 0 0 0) myBitmap = drawLine myBitmap [0, 511] [511, 0] #((color 255 255 255)) display myBitmap</lang>
Metal
For drawing lines between points in an Apple Metal compute shader.
<lang metal>void drawLine(texture2d<float, access::write> targetTexture, uint2 start, uint2 end);
void drawLine(texture2d<float, access::write> targetTexture, uint2 start, uint2 end) {
int x = int(start.x);
int y = int(start.y);
int dx = abs(x - int(end.x));
int dy = abs(y - int(end.y));
int sx = start.x < end.x ? 1 : -1;
int sy = start.y < end.y ? 1 : -1;
int err = (dx > dy ? dx : -dy) / 2;
while (true)
{
targetTexture.write(float4(1.0), uint2(x, y));
if (x == int(end.x) && y == int(end.y))
{
break;
}
int e2 = err;
if (e2 > -dx)
{
err -= dy;
x += sx;
}
if (e2 < dy)
{
err += dx;
y += sy;
}
}
}</lang>
Nim
<lang nim>import math
proc line(img: var Image, p, q: Point) =
let dx = abs(q.x - p.x) sx = if p.x < q.x: 1 else: -1 dy = abs(q.y - p.y) sy = if p.y < q.y: 1 else: -1
var p = p q = q err = (if dx > dy: dx else: -dy) div 2 e2 = 0
while true:
img[p] = Black
if p == q:
break
e2 = err
if e2 > -dx:
err -= dy
p.x += sx
if e2 < dy:
err += dx
p.y += sy</lang>
OCaml
<lang ocaml>let draw_line ~img ~color ~p0:(x0,y0) ~p1:(x1,y1) =
let steep = abs(y1 - y0) > abs(x1 - x0) in
let plot = if steep then (fun x y -> put_pixel img color y x) else (fun x y -> put_pixel img color x y) in
let x0, y0, x1, y1 = if steep then y0, x0, y1, x1 else x0, y0, x1, y1 in let x0, x1, y0, y1 = if x0 > x1 then x1, x0, y1, y0 else x0, x1, y0, y1 in
let delta_x = x1 - x0
and delta_y = abs(y1 - y0) in
let error = -delta_x / 2
and y_step =
if y0 < y1 then 1 else -1
in
let rec loop x y error =
plot x y;
if x <= x1 then
let error = error + delta_y in
let y, error =
if error > 0
then (y + y_step), (error - delta_x)
else y, error
in
loop (succ x) y error
in
loop x0 y0 error
- </lang>
Pascal
Perl
<lang perl>#! /usr/bin/perl use strict; use Image::Imlib2;
sub my_draw_line {
my ( $img, $x0, $y0, $x1, $y1) = @_;
my $steep = (abs($y1 - $y0) > abs($x1 - $x0));
if ( $steep ) {
( $y0, $x0 ) = ( $x0, $y0);
( $y1, $x1 ) = ( $x1, $y1 );
}
if ( $x0 > $x1 ) {
( $x1, $x0 ) = ( $x0, $x1 );
( $y1, $y0 ) = ( $y0, $y1 );
}
my $deltax = $x1 - $x0;
my $deltay = abs($y1 - $y0);
my $error = $deltax / 2;
my $ystep;
my $y = $y0;
my $x;
$ystep = ( $y0 < $y1 ) ? 1 : -1;
for( $x = $x0; $x <= $x1; $x += 1 ) {
if ( $steep ) {
$img->draw_point($y, $x);
} else {
$img->draw_point($x, $y);
}
$error -= $deltay;
if ( $error < 0 ) {
$y += $ystep;
$error += $deltax;
}
}
}
- test
my $img = Image::Imlib2->new(160, 160); $img->set_color(255, 255, 255, 255); # white $img->fill_rectangle(0,0,160,160);
$img->set_color(0,0,0,255); # black my_draw_line($img, 10, 80, 80, 160); my_draw_line($img, 80, 160, 160, 80); my_draw_line($img, 160, 80, 80, 10); my_draw_line($img, 80, 10, 10, 80);
$img->save("test0.png");
- let's try the same using its internal algo
$img->set_color(255, 255, 255, 255); # white $img->fill_rectangle(0,0,160,160); $img->set_color(0,0,0,255); # black $img->draw_line(10, 80, 80, 160); $img->draw_line(80, 160, 160, 80); $img->draw_line(160, 80, 80, 10); $img->draw_line(80, 10, 10, 80);
$img->save("test1.png");
exit 0;</lang>
Images test0.png and test1.png look different since Imlib2 draw lines with antialiasing.
Perl 6
<lang perl6>sub line(Bitmap $bitmap, $x0 is copy, $x1 is copy, $y0 is copy, $y1 is copy) {
my $steep = abs($y1 - $y0) > abs($x1 - $x0);
if $steep {
($x0, $y0) = ($y0, $x0);
($x1, $y1) = ($y1, $x1);
}
if $x0 > $x1 {
($x0, $x1) = ($x1, $x0);
($y0, $y1) = ($y1, $y0);
}
my $Δx = $x1 - $x0;
my $Δy = abs($y1 - $y0);
my $error = 0;
my $Δerror = $Δy / $Δx;
my $y-step = $y0 < $y1 ?? 1 !! -1;
my $y = $y0;
for $x0 .. $x1 -> $x {
my $pix = Pixel.new(R => 100, G => 200, B => 0);
if $steep {
$bitmap.set-pixel($y, $x, $pix);
} else {
$bitmap.set-pixel($x, $y, $pix);
}
$error += $Δerror;
if $error >= 0.5 {
$y += $y-step;
$error -= 1.0;
}
}
}</lang>
Phix
Modified copy of Euphoria, with a bigger bitmap and a simpler pattern. Requires new_image() from Bitmap, write_ppm() from Write_a_PPM_file. Included as demo\rosetta\Bresenham_line.exw, results may be verified with demo\rosetta\viewppm.exw <lang Phix>function bresLine(sequence screenData, integer x0, integer y0, integer x1, integer y1, integer colour) -- The line algorithm integer deltaX = abs(x1-x0),
deltaY = abs(y1-y0),
stepX = iff(x0<x1,1,-1),
stepY = iff(y0<y1,1,-1),
lineError = iff(deltaX>deltaY,deltaX,-deltaY),
prevle
lineError = round(lineError/2,1)
while 1 do
if x0>=1 and x0<=length(screenData)
and y0>=1 and y0<=length(screenData[x0]) then
screenData[x0][y0] = colour
end if
if x0=x1 and y0=y1 then exit end if
prevle = lineError
if prevle>-deltaX then
lineError -= deltaY
x0 += stepX
end if
if prevle<deltaY then
lineError += deltaX
y0 += stepY
end if
end while
return screenData
end function
sequence screenData = new_image(400,300,black)
screenData = bresLine(screenData,100,1,50,300,red)
screenData = bresLine(screenData,1,180,400,240,green)
screenData = bresLine(screenData,200,1,400,150,white)
screenData = bresLine(screenData,195,1,205,300,blue)
write_ppm("bresenham.ppm",screenData)</lang>
PicoLisp
<lang PicoLisp>(de brez (Img X Y DX DY)
(let SX
(cond
((=0 DX) 0)
((gt0 DX) 1)
(T (setq DX (- DX)) -1) )
(let SY
(cond
((=0 DY) 0)
((gt0 DY) 1)
(T (setq DY (- DY)) -1) )
(if (>= DX DY)
(let E (- (* 2 DY) DX)
(do DX
(set (nth Img Y X) 1)
(when (ge0 E)
(inc 'Y SY)
(dec 'E (* 2 DX)) )
(inc 'X SX)
(inc 'E (* 2 DY)) ) )
(let E (- (* 2 DX) DY)
(do DY
(set (nth Img Y X) 1)
(when (ge0 E)
(inc 'X SX)
(dec 'E (* 2 DY)) )
(inc 'Y SY)
(inc 'E (* 2 DX)) ) ) ) ) ) )
(let Img (make (do 90 (link (need 120 0)))) # Create image 120 x 90
(brez Img 10 10 100 30) # Draw five lines
(brez Img 10 10 100 50)
(brez Img 10 10 100 70)
(brez Img 10 10 60 70)
(brez Img 10 10 20 70)
(out "img.pbm" # Write to bitmap file
(prinl "P1")
(prinl 120 " " 90)
(mapc prinl Img) ) )</lang>
PL/I
version 1
<lang PL/I> /* Draw a line from (x0, y0) to (x1, y1). 13 May 2010 */ /* Based on Rosetta code proforma. */
/* Declarations for image and selected color, for 4-bit colors. */
declare image(40,40) bit (4), color bit (4) static initial ('1000'b);
draw_line: procedure (xi, yi, xf, yf );
declare (xi, yi, xf, yf) fixed binary (31) nonassignable; declare (x0, y0, x1, y1) fixed binary (31); declare (deltax, deltay, x, y, ystep) fixed binary; declare (error initial (0), delta_error) float; declare steep bit (1);
x0 = xi; y = YI; y0 = yi; x1 = xf; y1 = yf;
steep = abs(y1 - y0) > abs (x1 - x0);
if steep then
do; call swap (x0, y0); call swap (x1, y1); end;
if x0 > x1 then
do; call swap (x0, x1); call swap (y0, y1); end;
deltax = x1 - x0; deltay = abs(y1 - y0);
delta_error = deltay/deltax;
if y0 < y1 then ystep = 1; else ystep = -1;
do x = x0 to x1;
if steep then image(y, x) = color; else image(x, y) = color;
if steep then put skip list (y, x); else put skip list (x, y);
error = error + delta_error;
if error >= 0.5 then do; y = y + ystep; error = error - 1; end;
end;
swap: procedure (a, b);
declare (a, b) fixed binary (31); declare t fixed binary (31); t = a; a = b; b = t;
end swap;
end draw_line; </lang>
Output from the statement:-
call draw_line(-1, -3, 6, 10);
for a -10:10 x -10:10 grid: <lang> ..........|.......... ..........|.......... ..........|.......... ..........|.......... ..........|.......... ..........|.......... ..........|.........* ..........|.......**. ..........|.....**... ..........|...**.....
+-**-------
..........**......... ........**|.......... .......*..|.......... ..........|.......... ..........|.......... ..........|.......... ..........|.......... ..........|.......... ..........|.......... ..........|.......... </lang>
version 2
<lang PL/I>*process source xref or(!);
brbn:Proc Options(main); /********************************************************************* * 21.05.2014 Walter Pachl * Implementing the pseudo code of * http://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm * under 'Simplification' (see also REXX version 2) *********************************************************************/
grid.=
dcl image(-2:7,-4:11) char(1);
image='.';
image(*,0)='-';
image(0,*)='|';
image(0,0)='+';
call draw_line(-1,-3,6,10);
Dcl (i,j) Bin Fixed(31);
Do j=11 To -4 By -1;
Put Edit(j,' ')(Skip,f(2),a);
Do i=-2 To 7;
Put Edit(image(i,j))(a);
End;
End;
Put Edit(' 2101234567')(Skip,a);
draw_line: procedure (x0,y0,x1,y1); dcl (x0,y0,x1,y1) fixed binary(31); dcl (dx,dy,sx,sy,err,e2) fixed binary(31);
dx = abs(x1-x0);
dy = abs(y1-y0);
if x0 < x1 then sx = 1;
else sx = -1;
if y0 < y1 then sy = 1;
else sy = -1;
err = dx-dy;
Do Until(x0=x1&y0=y1);
image(x0,y0)='X';
e2=err*2;
if e2>-dy then do;
err=err-dy;
x0=x0+sx;
End;
if e2<dx then do;
err=err+dx;
y0=y0+sy;
End;
End;
image(x0,y0)='X';
end;
end;</lang>
output
11 ..|....... 10 ..|.....X. 9 ..|....X.. 8 ..|....X.. 7 ..|...X... 6 ..|...X... 5 ..|..X.... 4 ..|..X.... 3 ..|.X..... 2 ..|.X..... 1 ..|X...... 0 --+X------ -1 ..X....... -2 ..X....... -3 .X|....... -4 ..|....... 2101234567
Prolog
Works with SWI-prolog.
<lang Prolog> use_module(library(pce)). lindraw(X1,Y1,X2,Y2):- new(Win,window("Line")), new(Pix,pixmap(@nil,black,white,X2+30,Y2+30)), send(Win,size,size(400,400)), draw_line(Pix,X1,Y1,X2,Y2), new(Bmp,bitmap(Pix)), send(Win,display,Bmp,point(0,0)), send(Win,open).
draw_recursive_line(_Pict,X,X,_DX,_DY,Y,Y,_D,_Sx,_Sy).%Don't iterate if X and X2 are the same number draw_recursive_line(Pict,X,X2,DX,DY,Y,Y2,C,Sx,Sy):- ( C>0->%If the difference is greater than one, add Y one to Y. Y1 is Y+Sy, send(Pict,pixel(X,Y1,colour(black))), C2 is C+(2*DY-2*DX); Y1 is Y, send(Pict,pixel(X,Y,colour(black))), C2 is C+(2*DY)), X0 is X+Sx,%The next iteration draw_recursive_line(Pict,X0,X2,DX,DY,Y1,Y2,C2,Sx,Sy). isneg(X,O):- ( X<0->
O is -1; ( X\==0-> O is 1; O is 0)).
draw_line(Pict,X1,Y1,X2,Y2):- DY is abs(Y2-Y1), DX is abs(X2-X1), isneg(DX,Sx), isneg(DY,Sy), D = 2*DY-DX,%The slope of the line draw_recursive_line(Pict,X1,X2,DX,DY,Y1,Y2,D,Sx,Sy). </lang>
PureBasic
<lang PureBasic>Procedure BresenhamLine(x0 ,y0 ,x1 ,y1)
If Abs(y1 - y0) > Abs(x1 - x0);
steep =#True
Swap x0, y0
Swap x1, y1
EndIf
If x0 > x1
Swap x0, x1
Swap y0, y1
EndIf
deltax = x1 - x0
deltay = Abs(y1 - y0)
error = deltax / 2
y = y0
If y0 < y1
ystep = 1
Else
ystep = -1
EndIf
For x = x0 To x1
If steep
Plot(y,x)
Else
Plot(x,y)
EndIf
error - deltay
If error < 0
y + ystep
error + deltax
EndIf
Next
EndProcedure
- Window1 = 0
- Image1 = 0
- ImgGadget = 0
- width = 300
- height = 300
Define.i Event Define.f Angle
If OpenWindow(#Window1, 0, 0, #width, #height, "Bresenham's Line PureBasic Example", #PB_Window_SystemMenu|#PB_Window_ScreenCentered)
If CreateImage(#Image1, #width, #height)
ImageGadget(#ImgGadget, 0, 0, #width, #height, ImageID(#Image1))
StartDrawing(ImageOutput(#Image1))
FillArea(0,0,-1,$FFFFFF) :FrontColor(0)
While Angle < 2*#PI
BresenhamLine(150,150,150+Cos(Angle)*120,150+Sin(Angle)*120)
Angle + #PI/60
Wend
StopDrawing()
SetGadgetState(#ImgGadget, ImageID(#Image1))
Repeat
Event = WaitWindowEvent()
Until Event = #PB_Event_CloseWindow
EndIf
EndIf</lang>
Python
Extending the example given here and using the algorithm from the Ada solution:
<lang python>def line(self, x0, y0, x1, y1):
"Bresenham's line algorithm"
dx = abs(x1 - x0)
dy = abs(y1 - y0)
x, y = x0, y0
sx = -1 if x0 > x1 else 1
sy = -1 if y0 > y1 else 1
if dx > dy:
err = dx / 2.0
while x != x1:
self.set(x, y)
err -= dy
if err < 0:
y += sy
err += dx
x += sx
else:
err = dy / 2.0
while y != y1:
self.set(x, y)
err -= dx
if err < 0:
x += sx
err += dy
y += sy
self.set(x, y)
Bitmap.line = line
bitmap = Bitmap(17,17) for points in ((1,8,8,16),(8,16,16,8),(16,8,8,1),(8,1,1,8)):
bitmap.line(*points)
bitmap.chardisplay()
The origin, 0,0; is the lower left, with x increasing to the right, and Y increasing upwards.
The chardisplay above produces the following output : +-----------------+ | @ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @ | | @ @| | @ @ | | @ @ | | @ @@ | | @ @ | | @ @ | | @ @ | | @ | | | +-----------------+ </lang>
Not relying on floats
Extending the example given here.
<lang python> from fractions import Fraction
def line(self, x0, y0, x1, y1):
rev = reversed
if abs(y1 - y0) <= abs(x1 - x0):
x0, y0, x1, y1 = y0, x0, y1, x1
rev = lambda x: x
if x1 < x0:
x0, y0, x1, y1 = x1, y1, x0, y0
leny = abs(y1 - y0)
for i in range(leny + 1):
self.set(*rev((round(Fraction(i, leny) * (x1 - x0)) + x0, (1 if y1 > y0 else -1) * i + y0)))
Bitmap.line = line
- see test code above
</lang>
Racket
Port of the Python version. <lang racket>
- lang racket
(require racket/draw)
(define (draw-line dc x0 y0 x1 y1)
(define dx (abs (- x1 x0)))
(define dy (abs (- y1 y0)))
(define sx (if (> x0 x1) -1 1))
(define sy (if (> y0 y1) -1 1))
(cond
[(> dx dy)
(let loop ([x x0] [y y0] [err (/ dx 2.0)])
(unless (= x x1)
(send dc draw-point x y)
(define newerr (- err dy))
(if (< newerr 0)
(loop (+ x sx) (+ y sy) (+ newerr dx))
(loop (+ x sx) y newerr))))]
[else
(let loop ([x x0] [y y0] [err (/ dy 2.0)])
(unless (= y y1)
(send dc draw-point x y)
(define newerr (- err dy))
(if (< newerr 0)
(loop (+ x sx) (+ y sy) newerr)
(loop x (+ y sy) (+ newerr dy)))))]))
(define bm (make-object bitmap% 17 17)) (define dc (new bitmap-dc% [bitmap bm])) (send dc set-smoothing 'unsmoothed) (send dc set-pen "red" 1 'solid) (for ([points '((1 8 8 16) (8 16 16 8) (16 8 8 1) (8 1 1 8))])
(apply draw-line (cons dc points)))
bm </lang>
RapidQ
Use this routine together with the code from Basic bitmap storage to create a full application.
<lang rapidq>SUB draw_line(x1, y1, x2, y2, colour)
x_dist = abs(x2-x1)
y_dist = abs(y2-y1)
IF y2-y1 < -x_dist OR x2-x1 <= -y_dist THEN
SWAP x1, x2 ' Swap start and end points
SWAP y1, y2
END IF
IF x1 < x2 THEN x_step = 1 ELSE x_step = -1
IF y1 < y2 THEN y_step = 1 ELSE y_step = -1
IF y_dist > x_dist THEN ' steep angle, step by y
error = y_dist/2
x = x1
FOR y = y1 TO y2
canvas.Pset(x, y, colour)
error = error - x_dist
IF error < 0 THEN
x = x + x_step
error = error + y_dist
END IF
NEXT y
ELSE ' not steep, step by x
error = x_dist/2
y = y1
FOR x = x1 TO x2
canvas.Pset(x, y, colour)
error = error - y_dist
IF error < 0 THEN
y = y + y_step
error = error + x_dist
END IF
NEXT y
END IF
END SUB</lang>
Example usage:
<lang rapidq>SUB PaintCanvas
draw_line 200, 10, 100, 200, &H00ff00 draw_line 100, 200, 200, 400, &H00ff00 draw_line 200, 400, 300, 200, &H00ff00 draw_line 300, 200, 200, 10, &H00ff00
END SUB</lang>
REXX
version 1
This REXX version has automatic scaling (for displaying the plot), and it also handles multiple line segments. <lang rexx>/*REXX program plots/draws line segments using the Bresenham's line algorithm.*/ @.='·' /*fill the array with middle─dots chars*/ parse arg data /*allow the data point specifications. */ if data= then data= '(1,8) (8,16) (16,8) (8,1) (1,8)' /*◄────rhombus.*/ data=translate(data,,'()[]{}/,:;') /*elide chaff from the data points. */
/* [↓] data point pairs ───► !.array. */ do points=1 while data\= /*put the data points into an array (!)*/ parse var data x y data; !.points=x y /*extract the line segments. */ if points==1 then do; minX=x; maxX=x; minY=y; maxY=y; end /*1st case.*/ minX=min(minX,x); maxX=max(maxX,x); minY=min(minY,y); maxY=max(maxY,y) end /*points*/ /* [↑] data points pairs in array !. */
border=2 /*border: is extra space around plot. */ minX=minX-border*2; maxX=maxX+border*2 /*min and max X for the plot display.*/ minY=minY-border ; maxY=maxY+border /* " " " Y " " " " */
do x=minX to maxX; @.x.0='─'; end /*draw a dash from left ───► right.*/ do y=minY to maxY; @.0.y='│'; end /*draw a pipe from lowest ───► highest*/
@.0.0='┼' /*define the plot's origin axis point. */
do seg=2 to points-1; _=seg-1 /*obtain the X and Y line coördinates*/
call draw_line !._, !.seg /*draw (plot) a line segment. */
end /*seg*/ /* [↑] drawing the line segments. */
/* [↓] display the plot to terminal. */
do y=maxY to minY by -1; _= /*display the plot one line at a time. */
do x=minX to maxX /*build line by examining the X axis.*/
_=_ || @.x.y /*construct/build a line of the plot. */
end /*x*/ /* (a line is a "row" of points.) */
say _ /*display a line of the plot──►terminal*/
end /*y*/ /* [↑] all done plotting the points. */
exit /*stick a fork in it, we're all done. */ /*────────────────────────────────────────────────────────────────────────────*/ draw_line: procedure expose @.; parse arg x y,xf yf; plotChar='Θ' dx=abs(xf-x); if x<xf then sx=+1 /*obtain X range, determine the slope*/
else sx=-1
dy=abs(yf-y); if y<yf then sy=+1 /*obtain Y range, determine the slope*/
else sy=-1
err=dx-dy /*calculate error between adjustments. */
do forever; @.x.y=plotChar /*plot the points until it's complete. */
if x=xf & y=yf then return /*are the plot points at the finish? */
err2=err+err /*addition is faster than: err*2. */
if err2 > -dy then do; err=err-dy; x=x+sx; end
if err2 < dx then do; err=err+dx; y=y+sy; end
end /*forever*/</lang>
output when using the default input:
···│···················· ···│···················· ···│·······Θ············ ···│······Θ·Θ··········· ···│·····Θ···Θ·········· ···│····Θ·····Θ········· ···│···Θ·······Θ········ ···│···Θ········Θ······· ···│··Θ··········Θ······ ···│·Θ············Θ····· ···│Θ··············Θ···· ···│·Θ············Θ····· ···│··Θ··········Θ······ ···│···Θ·······ΘΘ······· ···│····Θ·····Θ········· ···│·····Θ···Θ·········· ···│······Θ·Θ··········· ···│·······Θ············ ───┼──────────────────── ···│····················
version 2
<lang rexx>/* REXX ***************************************************************
- 21.05.2014 Walter Pachl
- Implementing the pseudo code of
- http://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm
- under 'Simplification'
- /
grid.='.' Do i=-2 To 7; grid.i.0='-'; End Do j=-4 To 11; grid.0.j='|'; End grid.0.0='+' Call line -1,-3,6,10 Do j=11 To -4 By -1
ol=format(j,2)' ' Do i=-2 To 7 ol=ol||grid.i.j End Say ol End
Say ' 2101234567' Exit line: Procedure Expose grid. Parse Arg x0, y0, x1, y1 dx = abs(x1-x0) dy = abs(y1-y0) if x0 < x1 then sx = 1
else sx = -1
if y0 < y1 then sy = 1
else sy = -1
err = dx-dy
Do Forever
grid.x0.y0='X' if x0 = x1 & y0 = y1 Then Leave e2 = 2*err if e2 > -dy then do err = err - dy x0 = x0 + sx end if e2 < dx then do err = err + dx y0 = y0 + sy end end
Return</lang> output
11 ..|....... 10 ..|.....X. 9 ..|....X.. 8 ..|....X.. 7 ..|...X... 6 ..|...X... 5 ..|..X.... 4 ..|..X.... 3 ..|.X..... 2 ..|.X..... 1 ..|X...... 0 --+X------ -1 ..X....... -2 ..X....... -3 .X|....... -4 ..|....... 2101234567
Ruby
<lang ruby>Pixel = Struct.new(:x, :y)
class Pixmap
def draw_line(p1, p2, colour) validate_pixel(p1.x, p2.y) validate_pixel(p2.x, p2.y)
x1, y1 = p1.x, p1.y
x2, y2 = p2.x, p2.y
steep = (y2 - y1).abs > (x2 - x1).abs
if steep
x1, y1 = y1, x1
x2, y2 = y2, x2
end
if x1 > x2
x1, x2 = x2, x1
y1, y2 = y2, y1
end
deltax = x2 - x1
deltay = (y2 - y1).abs
error = deltax / 2
ystep = y1 < y2 ? 1 : -1
y = y1
x1.upto(x2) do |x|
pixel = steep ? [y,x] : [x,y]
self[*pixel] = colour
error -= deltay
if error < 0
y += ystep
error += deltax
end
end
end
end
bitmap = Pixmap.new(500, 500) bitmap.fill(RGBColour::BLUE) 10.step(430, 60) do |a|
bitmap.draw_line(Pixel[10, 10], Pixel[490,a], RGBColour::YELLOW) bitmap.draw_line(Pixel[10, 10], Pixel[a,490], RGBColour::YELLOW)
end bitmap.draw_line(Pixel[10, 10], Pixel[490,490], RGBColour::YELLOW)</lang>
Scala
Uses the Scala Basic Bitmap Storage class. <lang scala>object BitmapOps {
def bresenham(bm:RgbBitmap, x0:Int, y0:Int, x1:Int, y1:Int, c:Color)={
val dx=math.abs(x1-x0)
val sx=if (x0<x1) 1 else -1
val dy=math.abs(y1-y0)
val sy=if (y0<y1) 1 else -1
def it=new Iterator[Tuple2[Int,Int]]{
var x=x0; var y=y0
var err=(if (dx>dy) dx else -dy)/2
def next={
val res=(x,y)
val e2=err;
if (e2 > -dx) {err-=dy; x+=sx}
if (e2<dy) {err+=dx; y+=sy}
res;
}
def hasNext = (sx*x <= sx*x1 && sy*y <= sy*y1)
}
for((x,y) <- it)
bm.setPixel(x, y, c)
}
}</lang>
Sidef
<lang ruby>func my_draw_line(img, x0, y0, x1, y1) {
var steep = (abs(y1 - y0) > abs(x1 - x0))
if (steep) {
(y0, x0) = (x0, y0)
(y1, x1) = (x1, y1)
}
if (x0 > x1) {
(x1, x0) = (x0, x1)
(y1, y0) = (y0, y1)
}
var deltax = (x1 - x0) var deltay = abs(y1 - y0) var error = (deltax / 2) var y = y0 var ystep = (y0 < y1 ? 1 : -1)
x0.to(x1).each { |x|
img.draw_point(steep ? ((y, x)) : ((x, y)))
error -= deltay
if (error < 0) {
y += ystep
error += deltax
}
}
}
require('Image::Imlib2')
var img = %s'Image::Imlib2'.new(160, 160) img.set_color(255, 255, 255, 255) # white img.fill_rectangle(0,0,160,160)
img.set_color(0,0,0,255) # black my_draw_line(img, 10, 80, 80, 160) my_draw_line(img, 80, 160, 160, 80) my_draw_line(img, 160, 80, 80, 10) my_draw_line(img, 80, 10, 10, 80)
img.save("test0.png");
- let's try the same using its internal algo
img.set_color(255, 255, 255, 255) # white img.fill_rectangle(0,0,160,160) img.set_color(0,0,0,255) # black img.draw_line(10, 80, 80, 160) img.draw_line(80, 160, 160, 80) img.draw_line(160, 80, 80, 10) img.draw_line(80, 10, 10, 80)
img.save("test1.png")</lang>
Tcl
ref Basic bitmap storage#Tcl <lang tcl>package require Tcl 8.5 package require Tk
proc drawLine {image colour point0 point1} {
lassign $point0 x0 y0
lassign $point1 x1 y1
set steep [expr {abs($y1 - $y0) > abs($x1 - $x0)}]
if {$steep} {
lassign [list $x0 $y0] y0 x0
lassign [list $x1 $y1] y1 x1
}
if {$x0 > $x1} {
lassign [list $x0 $x1] x1 x0
lassign [list $y0 $y1] y1 y0
}
set deltax [expr {$x1 - $x0}]
set deltay [expr {abs($y1 - $y0)}]
set error [expr {$deltax / 2}]
set ystep [expr {$y0 < $y1 ? 1 : -1}]
for {set x $x0; set y $y0} {$x <= $x1} {incr x} {
setPixel $image $colour [expr {$steep ? [list $y $x] : [list $x $y]}]
incr error -$deltay
if {$error < 0} {
incr y $ystep
incr error $deltax
}
}
}
- create the image and display it
set img [newImage 200 100] label .l -image $img pack .l
fill $img black drawLine $img yellow {20 20} {180 80} drawLine $img yellow {180 20} {20 80}</lang>
TI-89 BASIC
<lang ti89b>(lx0, ly0, lx1, ly1) Prgm
Local steep, x, y, dx, dy, ystep, error, tmp
abs(ly1 - ly0) > abs(lx1 - lx0) → steep
If steep Then
lx0 → tmp
ly0 → lx0
tmp → ly0
lx1 → tmp
ly1 → lx1
tmp → ly1
EndIf
If lx0 > lx1 Then
lx0 → tmp
lx1 → lx0
tmp → lx1
ly0 → tmp
ly1 → ly0
tmp → ly1
EndIf
lx1 - lx0 → dx
abs(ly1 - ly0) → dy
when(ly0 < ly1, 1, –1) → ystep
intDiv(dx, 2) → error
ly0 → y
For x,lx0,lx1
If steep Then: PxlChg x, y :Else: PxlChg y, x :EndIf
error - dy → error
If error < 0 Then
y + ystep → y
error + dx → error
EndIf
EndFor
EndPrgm</lang>
Vedit macro language
<lang vedit>// Daw a line using Bresenham's line algorithm. // #1=x1, #2=y1; #3=x2, #4=y2
- DRAW_LINE:
Num_Push(31,35)
- 31 = abs(#3-#1) // x distance
- 32 = abs(#4-#2) // y distance
if (#4-#2 < -#31 || #3-#1 <= -#32) {
#99=#1; #1=#3; #3=#99 // swap start and end points #99=#2; #2=#4; #4=#99
} if (#1 < #3) { #34=1 } else { #34=-1 } // x step if (#2 < #4) { #35=1 } else { #35=-1 } // y step
if (#32 > #31) { // steep angle, step by Y
#33 = #32 / 2 // error distance
while (#2 <= #4) {
Call("DRAW_PIXEL")
#33 -= #31
if (#33 < 0) {
#1 += #34 // move right
#33 += #32
}
#2++ // move up
}
} else { // not steep, step by X
#33 = #31 / 2
while (#1 <= #3) {
Call("DRAW_PIXEL")
#33 -= #32
if (#33 < 0) {
#2 += #35 // move up
#33 += #31
}
#1++ // move right
}
} Num_Pop(31,35) return</lang>
Wart
<lang wart># doesn't handle vertical lines def (line x0 y0 x1 y1)
let steep ((> abs) y1-y0 x1-x0)
when steep
swap! x0 y0
swap! x1 y1
when (x0 > x1)
swap! x0 x1
swap! y0 y1
withs (deltax x1-x0
deltay (abs y1-y0)
error deltax/2
ystep (if (y0 < y1) 1 -1)
y y0)
for x x0 (x <= x1) ++x
if steep
plot y x
plot x y
error -= deltay
when (error < 0)
y += ystep
error += deltax</lang>
XPL0
Bresenham line draw is built-in. <lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations [SetVid($112); \set 640x480 graphics in 24-bit color Move(10, 20); \set start of line segment Line(600, 400, $123456);\draw line segment, red=$12, green=$34, blue=$56 if ChIn(1) then []; \wait for keystroke while viewing graphic screen SetVid(3); \restore normal text mode ]</lang>
zkl
Algorithm from Wikipedia plus other functions so I can reference this code in other examples. <lang zkl>ppm:=PPM(200,200,0xFF|FF|FF); ppm.line(50,100, 100,190, 0); ppm.line(100,190, 150,100, 0); ppm.line(150,100, 100,10, 0); ppm.line(100,10, 50,100, 0);
ppm.writeJPGFile("line.jpg");</lang> <lang zkl>class PPM{ // (0,0) is logically bottom left
fcn init(width,height,rgb=0){
sz:=width*height;
var [const]
data=Data(sz*3).fill(rgb.toBigEndian(3).toData()), // initialize to 24bit Black (RGB=000)
w=width, h=height;
}
fcn fill(rgb){ data.fill(rgb.toBigEndian(3).toData()) }
fcn __sGet(x,y) { data.toBigEndian(3*y*w + 3*x,3); } //ppm[x,y]
fcn __sSet(rgb,x,y){ data[3*y*w + x*3,3]=rgb.toBigEndian(3); rgb } //ppm[x,y]=rgb
fcn write(out,raw=False){ // write bottom to top to move (0,0) from top left to bottom left
out.write("P6\n#rosettacode PPM\n%d %d\n255\n".fmt(w,h));
if(raw) out.write(data);
else [h-1..0, -1].pump(out,'wrap(h){ data.seek(3*h*w); data.read(3*w) });
}
fcn writeJPGFile(fname){ // Linux, using imagemagick
System.popen(0'|convert ppm:- jpg:"%s"|.fmt(fname),"w") :
write(_,vm.pasteArgs(1));
}
fcn readPPMFile(fileName){
f:=File(fileName,"rb"); ppm:=readPPM(f); f.close();
ppm
}
fcn readPPM(image){ // image is a PPM byte stream
// header is "P6\n[#comment\n]<w> <h>\nmaxPixelValue\n
image.readln(); // "P6"
while("#"==(text:=image.readln().strip())[0]){}
w,h:=text.split().apply("toInt");
image.readln(); // max pixel value
ppm,sz,buffer:=PPM(w,h), 3*w, Data(sz);
ppm.data.clear(); // gonna write file image data
// image is stored upside down in my data structure
do(h){ ppm.data.insert(0, image.read(sz,buffer)) }
ppm
}
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); }
}
}
fcn line(x0,y0, x1,y1, rgb){
dx:=(x1-x0).abs();
dy:=(y1-y0).abs();
if(x0 < x1) sx:=1 else sx:=-1;
if(y0 < y1) sy:=1 else sy:=-1;
err:=dx - dy;
while(1){
__sSet(rgb,x0,y0); if(x0==x1 and y0==y1) break; e2:=2*err; if(e2 > -dy){ err=err - dy; x0=x0 + sx; } if(e2 < dx) { err=err + dx; y0=y0 + sy; }
}
}
fcn flood(x,y, repl){ // slow!
targ:=self[x,y];
(stack:=List.createLong(10000)).append(T(x,y));
while(stack){
x,y:=stack.pop(); if((0<=y<h) and (0<=x<w)){ p:=self[x,y]; if(p==targ){ self[x,y]=repl; stack.append( T(x-1,y), T(x+1,y), T(x, y-1), T(x, y+1) ); } }
} }
}</lang>
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