Bitmap/Bresenham's line algorithm: Difference between revisions
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drawLine(foobar, 180, 20, 20, 80, yellow); |
drawLine(foobar, 180, 20, 20, 80, yellow); |
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</lang> |
</lang> |
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=={{header|E}}== |
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{{trans|C}} |
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<lang e>def swap(&left, &right) { # From [[Generic swap]] |
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def t := left |
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left := right |
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right := t |
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} |
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def drawLine(image, var x0, var y0, var x1, var y1, color) { |
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def steep := (y1 - y0).abs() > (x1 - x0).abs() |
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if (steep) { |
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swap(&x0, &y0) |
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swap(&x1, &y1) |
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} |
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if (x0 > x1) { |
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swap(&x0, &x1) |
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swap(&y0, &y1) |
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} |
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def deltax := x1 - x0 |
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def deltay := (y1 - y0).abs() |
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def ystep := if (y0 < y1) { 1 } else { -1 } |
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var error := deltax // 2 |
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var y := y0 |
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for x in x0..x1 { |
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if (steep) { image[y, x] := color } else { image[x, y] := color } |
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error -= deltay |
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if (error < 0) { |
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y += ystep |
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error += deltax |
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} |
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} |
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}</lang> |
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<lang e>def i := makeImage(5, 20) |
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drawLine(i, 1, 1, 3, 18, makeColor.fromFloat(0,1,1)) |
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i.writePPM(<import:java.io.makeFileOutputStream>(<file:~/Desktop/Bresenham.ppm>))</lang> |
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=={{header|Forth}}== |
=={{header|Forth}}== |
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Revision as of 13:38, 26 July 2009
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
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H
ALGOL 68
<lang algol>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>
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>
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
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>
Maple
<lang maple> SegmentBresenham := proc (img, x0, y0, x1, y1) local deltax, deltay, x, y, ystep, bool, e, img2, swap, x02, y02, x12, y12; x02 := y0; x12 := y1; y12 := x1; y02 := x0; bool := abs(x12-x02) < abs(y12-y02); img2 := copy(img); if bool then
swap := x02; x02 := y02; y02 := swap; swap := x12; x12 := y12; y12 := swap;
end if; if x12 < x02 then
swap := x02; x02 := x12; x12 := swap; swap := y02; y02 := y12; y12 := swap;
end if; deltax := x12-x02; deltay := abs(y12-y02); e := (1/2)*deltax; y := y02; if y02 < y12 then
ystep := 1 else ystep := -1; end if;
for x from x02 to x12 do
if bool then
img2[y, x] := 0
else
img2[x, y] := 0;
end if;
e := e-deltay;
if e < 0 then
y := y+ystep;
e := e+deltax;
end if;
end do; img2; end proc:</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
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.
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>
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>
Vedit macro language
// 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