Bitmap/Bresenham's line algorithm: Difference between revisions
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===version 2===
<lang rexx>/* REXX ***************************************************************
* 21.05.2014 Walter Pachl
* Implementing the pseudo code of
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Revision as of 22:11, 22 May 2015
![Task](http://static.miraheze.org/rosettacodewiki/thumb/b/ba/Rcode-button-task-crushed.png/64px-Rcode-button-task-crushed.png)
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>
BASIC
<lang basic>
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>
BASIC
<lang basic>
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>
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>
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
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>
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>
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
<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.
![](http://static.miraheze.org/rosettacodewiki/thumb/d/d4/Bresenham.png/300px-Bresenham.png)
<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>
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>
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 handles multiple line segments. <lang rexx>/*REXX program plots/draws line(s) using the Bresenham's line algorithm.*/ @.='·' /*fill the array with middle─dots*/ parse arg data /*allow data point specifications*/ if data= then data= '(1,8) (8,16) (16,8) (8,1) (1,8)' /*rhombus*/ data=translate(data,,'()[]{}/,:;') /*elide chaff from data points. */
/* [↓] data pt pairs ──► !.array.*/ do points=1 while data\= /*put data points into an array. */ parse var data x y data; !.points=x y /*extract 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 !. */
border=2 /*border=extra space around plot.*/ minX=minX-border*2; maxX=maxX+border*2 /*min,max X for the plot display.*/ minY=minY-border ; maxY=maxY+border /* " " Y " " " " */
do x=minX to maxX; @.x.0='─'; end /*draw dash from left──► right.*/ do y=minY to maxY; @.0.y='│'; end /*draw pipe from lowest──►highest*/
@.0.0='┼' /*define the plot's axis point. */
do seg=2 to points-1; _=seg-1 /*obtain the X,Y line coördinates*/ call draw_line !._, !.seg /*draw (plot) a line segment. */ end /*seg*/ /* [↑] drawing the line segments*/ /* [↓] display the plot to term.*/ do y=maxY to minY by -1; _= /*display plot one line at a time*/ do x=minX to maxX /*traipse throught the X axis. */ _=_ || @.x.y /*construct a "line" of the plot.*/ end /*x*/ /*(a line is a "row" of points.) */ say _ /*display a "line" of the plot. */ end /*y*/ /* [↑] all done ploting the pts.*/
exit /*stick a fork in it, we're done.*/ /*────────────────────────────────DRAW_LINE subroutine──────────────────*/ 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 slope*/
else sx=-1
dy=abs(yf-y); if y<yf then sy=+1 /*obtain Y range, determine slope*/
else sy=-1
err=dx-dy /*calc error between adjustments.*/
do forever; @.x.y=plotChar /*plot the points until complete.*/ if x=xf & y=yf then leave /*are plot points at the finish? */ err2=err+err /*this 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*/
return</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=(x<=x1 && y<=y1) }
for((x,y) <- it) bm.setPixel(x, y, c) }
}</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>def line(x0 y0 x1 y1)
let steep ((> abs) y1-y0 x1-x0) if steep swap x0 y0 swap x1 y1 if (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 if (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. <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.write(File("foo.ppm","wb"));</lang> <lang zkl>class PPM{ // (0,0) is logically bottom left
fcn init(width,height,rgb=0){ sz:=width*height; var [const] data=sz.pump(Data(sz*3),T(Void,rgb.toBigEndian(3))), // initialize to Black (RGB=000)
w=width, h=height;
} fcn fill(rgb){ sz:=data.len()/3; data.clear(); sz.pump(data,T(Void,rgb.toBigEndian(3))); } 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); } //ppm[x,y]=rgb fcn write(out){ // 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)); [h-1..0, -1].pump(out,'wrap(h){ data.seek(3*h*w); data.read(3*w) }); } 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; }
} }
}</lang>
- Output:
Image cribbed from BBC BASIC, minus the ">"
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