Bitmap/Bézier curves/Cubic
< 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 images, and the draw_line function defined in this other one, draw a cubic bezier curves (definition on Wikipedia).
Ada
<lang ada> procedure Cubic_Bezier
( Picture : in out Image;
P1, P2, P3, P4 : Point;
Color : Pixel;
N : Positive := 20
) is
Points : array (0..N) of Point;
begin
for I in Points'Range loop
declare
T : constant Float := Float (I) / Float (N);
A : constant Float := (1.0 - T)**3;
B : constant Float := 3.0 * T * (1.0 - T)**2;
C : constant Float := 3.0 * T**2 * (1.0 - T);
D : constant Float := T**3;
begin
Points (I).X := Positive (A * Float (P1.X) + B * Float (P2.X) + C * Float (P3.X) + D * Float (P4.X));
Points (I).Y := Positive (A * Float (P1.Y) + B * Float (P2.Y) + C * Float (P3.Y) + D * Float (P4.Y));
end;
end loop;
for I in Points'First..Points'Last - 1 loop
Line (Picture, Points (I), Points (I + 1), Color);
end loop;
end Cubic_Bezier; </lang> The following test <lang ada>
X : Image (1..16, 1..16);
begin
Fill (X, White); Cubic_Bezier (X, (16, 1), (1, 4), (3, 16), (15, 11), Black); Print (X);
</lang> should produce output:
HH
HH HH
H H
H H
H H
H H
H H
H H
H H
H H
H H
H
ALGOL 68
<lang algol>PRAGMAT READ "Bresenhams_line_algorithm.a68" PRAGMAT;
PROC cubic bezier =
( REF IMAGE picture,
POINT p1, p2, p3, p4,
PIXEL color,
UNION(INT, VOID) in n
)VOID:
BEGIN
INT n = (in n|(INT n):n|20); # default 20 #
[0:n]POINT points;
FOR i FROM LWB points TO UPB points DO
REAL t = i / n,
a = (1 - t)**3,
b = 3 * t * (1 - t)**2,
c = 3 * t**2 * (1 - t),
d = t**3;
x OF points [i] := ENTIER (a * x OF p1 + b * x OF p2 + c * x OF p3 + d * x OF p4);
y OF points [i] := ENTIER (a * y OF p1 + b * y OF p2 + c * y OF p3 + d * y OF p4)
OD;
FOR i FROM LWB points TO UPB points - 1 DO
line (picture, points (i), points (i + 1), color)
OD
END # cubic bezier #;
The following test
BEGIN
REF IMAGE x = INIT LOC[16,16]PIXEL; (fill OF class image)(x, (white OF class image)); cubic bezier (x, (16, 1), (1, 4), (3, 16), (15, 11), (black OF class image), EMPTY); (print OF class image) (x)
END</lang> Output:
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffffffffffffffff000000000000000000000000ffffffffffffffffffffffffffffffffffff ffffffffffffffffffffffff000000000000ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff ffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff 000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff 000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff 000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff 000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
C
"Interface" imglib.h.
<lang c>void cubic_bezier(
image img,
unsigned int x1, unsigned int y1,
unsigned int x2, unsigned int y2,
unsigned int x3, unsigned int y3,
unsigned int x4, unsigned int y4,
color_component r,
color_component g,
color_component b );</lang>
<lang c>#include <math.h>
/* number of segments for the curve */
- define N_SEG 20
- define plot(x, y) put_pixel_clip(img, x, y, r, g, b)
- define line(x0,y0,x1,y1) draw_line(img, x0,y0,x1,y1, r,g,b)
void cubic_bezier(
image img,
unsigned int x1, unsigned int y1,
unsigned int x2, unsigned int y2,
unsigned int x3, unsigned int y3,
unsigned int x4, unsigned int y4,
color_component r,
color_component g,
color_component b )
{
unsigned int i;
double pts[N_SEG+1][2];
for (i=0; i <= N_SEG; ++i)
{
double t = (double)i / (double)N_SEG;
double a = pow((1.0 - t), 3.0);
double b = 3.0 * t * pow((1.0 - t), 2.0);
double c = 3.0 * pow(t, 2.0) * (1.0 - t);
double d = pow(t, 3.0);
double x = a * x1 + b * x2 + c * x3 + d * x4;
double y = a * y1 + b * y2 + c * y3 + d * y4;
pts[i][0] = x;
pts[i][1] = y;
}
- if 0
/* draw only points */
for (i=0; i <= N_SEG; ++i)
{
plot( pts[i][0],
pts[i][1] );
}
- else
/* draw segments */
for (i=0; i < N_SEG; ++i)
{
int j = i + 1;
line( pts[i][0], pts[i][1],
pts[j][0], pts[j][1] ); }
- endif
}
- undef plot
- undef line</lang>
Fortran
This subroutine should go inside the RCImagePrimitive module (see Bresenham's line algorithm)
<lang fortran> subroutine cubic_bezier(img, p1, p2, p3, p4, color)
type(rgbimage), intent(inout) :: img type(point), intent(in) :: p1, p2, p3, p4 type(rgb), intent(in) :: color
integer :: i, j real :: pts(0:N_SEG,0:1), t, a, b, c, d, x, y
do i = 0, N_SEG
t = real(i) / real(N_SEG)
a = (1.0 - t)**3.0
b = 3.0 * t * (1.0 - t)**2.0
c = 3.0 * (1.0 - t) * t**2.0
d = t**3.0
x = a * p1%x + b * p2%x + c * p3%x + d * p4%x
y = a * p1%y + b * p2%y + c * p3%y + d * p4%y
pts(i,0) = x
pts(i,1) = y
end do
do i = 0, N_SEG-1
j = i + 1
call draw_line(img, point(pts(i,0), pts(i,1)), &
point(pts(j,0), pts(j,1)), color)
end do
end subroutine cubic_bezier</lang>
OCaml
<lang ocaml>let cubic_bezier ~img ~color
~p1:(_x1, _y1)
~p2:(_x2, _y2)
~p3:(_x3, _y3)
~p4:(_x4, _y4) =
let x1, y1, x2, y2, x3, y3, x4, y4 =
(float _x1, float _y1,
float _x2, float _y2,
float _x3, float _y3,
float _x4, float _y4)
in
let bz t =
let a = (1.0 -. t) ** 3.0
and b = 3.0 *. t *. ((1.0 -. t) ** 2.0)
and c = 3.0 *. (t ** 2.0) *. (1.0 -. t)
and d = t ** 3.0
in
let x = a *. x1 +. b *. x2 +. c *. x3 +. d *. x4
and y = a *. y1 +. b *. y2 +. c *. y3 +. d *. y4
in
(int_of_float x, int_of_float y)
in
let rec loop _t acc =
if _t > 20 then acc else
begin
let t = (float _t) /. 20.0 in
let x, y = bz t in
loop (succ _t) ((x,y)::acc)
end
in
let pts = loop 0 [] in
(* (* draw only points *) List.iter (fun (x, y) -> put_pixel img color x y) pts; *)
(* draw segments *)
let line = draw_line ~img ~color in
let by_pair li f =
let rec aux prev = function
| [] -> ()
| x::xs ->
f prev x;
aux x xs
in
aux (List.hd li) (List.tl li)
in
by_pair pts (fun p0 p1 -> line ~p0 ~p1);
- </lang>