Bitmap/Bresenham's line algorithm: Difference between revisions
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drawLine(i, 1, 1, 3, 18, makeColor.fromFloat(0,1,1))
i.writePPM(<import:java.io.makeFileOutputStream>(<file:~/Desktop/Bresenham.ppm>))</lang>
=={{header|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>
=={{header|F Sharp|F#}}==
|
Revision as of 10:43, 18 May 2010
![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 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
<lang algol68>PRAGMAT READ "Basic_bitmap_storage.a68" PRAGMAT;
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 #;
The test program:
IF test THEN
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)
FI</lang> Output:
ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffff000000ffffff000000ffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffff000000ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000000000ffffffffffffffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffff ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffff 000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000 ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffff000000ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffff000000ffffff000000ffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff
C
To be added to imglib.h.
<lang c>void draw_line(
image img, unsigned int x0, unsigned int y0, unsigned int x1, unsigned int y1, color_component r, color_component g, color_component b );</lang>
The implementation code:
<lang c>#include "imglib.h"
- define plot(x, y) put_pixel_clip(img, x, y, r, g, b)
- define swap_uint(a, b) do{ unsigned int tmp; tmp = a; a = b; b = tmp; }while(0)
void draw_line(
image img, unsigned int x0, unsigned int y0, unsigned int x1, unsigned int y1, color_component r, color_component g, color_component b )
{
unsigned short steep; steep = abs(y1 - y0) > abs(x1 - x0); if (steep) { swap_uint(x0, y0); swap_uint(x1, y1); } if (x0 > x1) { swap_uint(x0, x1); swap_uint(y0, y1); } { int deltax = x1 - x0; int deltay = abs(y1 - y0); int error = deltax / 2; int ystep; int y = y0; int x; if (y0 < y1) ystep = 1; else ystep = -1; for (x = x0; x <= x1; ++x) { if (steep) plot(y,x); else plot(x,y); error = error - deltay; if (error < 0) { y = y + ystep; error = error + deltax; } } }
}
- undef swap_uint
- undef plot</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 (abs (- x1 x2))
dist-y (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 (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 (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>
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 (progn (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 example uses Bitmap structure template defined in Basic bitmap storage task.
This version uses direct pointers to the data to speed things up.
<lang D>// swap function template void swap(T)(ref T a, ref T b) { T t = a; a = b; b = t; } // absolute value, this could be taken from std.math or // tango.math.Math, but is placed here for convenience T labs(T)(T a) { return a < 0 ? -a : a; }
void drawLine(T)(Bitmap!(T) dest, int x0, int y0, int x1, int y1, T color) {
auto deltaY = labs(y1 - y0); auto deltaX = labs(x1 - x0); auto skew = deltaX > deltaY ? 1 : 0;
if (! skew ) { swap (deltaX, deltaY); swap (x0, y0); swap (x1, y1); }
auto d = (deltaY << 1) - deltaX; deltaX = (deltaY - deltaX) << 1; deltaY <<= 1;
if (x1 < x0) { swap (x0, x1); swap (y0, y1); }
int step = (x0 < x1 && y0 < y1) ? 1 : -1; if (skew) { T *ptr = &dest.data[y0*dest.width + x0]; for (; x0 < x1; x0++, ptr++) { *ptr = color; d += (d < 0) ? deltaY : deltaX; if (d >= 0) ptr += step*dest.width; } } else { T *ptr = &dest.data[x0*dest.width + y0]; for (; x0 < x1; x0++, ptr+=dest.width) { *ptr = color; d += (d < 0) ? deltaY : deltaX; if (d >= 0) ptr += step; }
}
}</lang>
Sample usage: <lang D>Rgb black; Rgb yellow = {[255, 255, 0]}; auto foobar = RgbBitmap(200, 100); drawLine(foobar, 20, 20, 180, 80, yellow); drawLine(foobar, 180, 20, 20, 80, yellow);</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>
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>
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>
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>
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>
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>
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>
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.
PL/I
<lang PL/I> /* Draw a line fom (x0, y0) to (x1, y1). 13 May 2010 */ /* Based on Rosetta code proforma. */ 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>
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>
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>
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>
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>