Bitmap/Bresenham's line algorithm
< Bitmap
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 (definition on Wikipedia).
Ada
<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; </ada> The test program's <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);
</ada> 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
MODE PIXEL = STRUCT(#SHORT# BITS red,green,blue);
MODE IMAGE = [16,16]PIXEL,
POINT = STRUCT(INT x,y);
PIXEL black = (#SHORTEN# 16r00, #SHORTEN# 16r00, #SHORTEN# 16r00),
red = (#SHORTEN# 16rff, #SHORTEN# 16r00, #SHORTEN# 16r00),
green = (#SHORTEN# 16r00, #SHORTEN# 16rff, #SHORTEN# 16r00),
blue = (#SHORTEN# 16r00, #SHORTEN# 16r00, #SHORTEN# 16rff),
white = (#SHORTEN# 16rff, #SHORTEN# 16rff, #SHORTEN# 16rff);
PROC fill = (REF IMAGE image, PIXEL color)VOID:
BEGIN
FOR x TO 1 UPB image DO
FOR y TO 2 UPB image DO
image[x,y] := color
OD
OD
END;
PROC line = (REF IMAGE picture, POINT start, stop, PIXEL color)VOID:
BEGIN
REAL dx = ABS (x OF stop - x OF start);
REAL dy = ABS (y OF stop - y OF start);
REAL err;
INT x := x OF start;
INT y := y OF start;
INT step x := 1;
INT step y := 1;
IF x OF start > x OF stop THEN
step x := -1
FI;
IF y OF start > y OF stop THEN
step y := -1
FI;
IF dx > dy THEN
err := dx / 2.0;
WHILE x /= x OF stop DO
picture[x,y] := color;
err -:= dy;
IF err < 0.0 THEN
y +:= step y;
err +:= dx
FI;
x +:= step x
OD
ELSE
err := dy / 2.0;
WHILE y /= y OF stop DO
picture[x,y] := color;
err := err - dx;
IF err < 0.0 THEN
x +:= step x;
err +:= dy
FI;
y +:= step y
OD
FI;
picture[x,y] := color # ensure dots to be drawn #
END # line #;
###
the test program's
###
REF IMAGE x = LOC[1:16, 1:16]PIXEL;
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);
printf(($n(UPB x)(3(16r2d))l$, x))
END
Output:
ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffff000000ffffff000000ffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffff000000ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000000000ffffffffffffffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffff ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffff 000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000 ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffff000000ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffff000000ffffff000000ffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffff
C
<C>#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</C>
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
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
<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
- </ocaml>
Vedit macro language
// Daw a line using Bresenham's line algorithm.
// #1=x1, #2=y1; #3=x2, #4=y2
:DRAW_LINE:
if (#4-#2 < #1-#3) { // dy < -dx ?
#99=#1; #1=#3; #3=#99 // swap start and end points
#99=#2; #2=#4; #4=#99
}
#31 = abs(#3-#1) // x distance
#32 = abs(#4-#2) // y distance
if (#32 > #31) { // steep angle, step by Y
#33 = #32 / 2 // error distance
if (#1 < #3) { #34=1 } else { #34=-1 } // x step
while (#2 <= #4) {
Call("DRAW_PIXEL") // #1=x, #2=y
#33 -= #31
if (#33 < 0) {
#1 += #34 // move right
#33 += #32
}
#2++ // move up
}
} else { // not steep, step by X
#33 = #31 / 2
if (#2 < #4) { #34=1 } else { #34=-1 } // y step
while (#1 <= #3) {
Call("DRAW_PIXEL")
#33 -= #32
if (#33 < 0) {
#2 += #34 // move up
#33 += #31
}
#1++ // move right
}
}
return