Bitmap/Midpoint circle algorithm

Bitmap/Midpoint circle algorithm
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, write an implementation of the midpoint circle algorithm (also known as Bresenham's circle algorithm).
(definition on Wikipedia).

Ada

<lang ada> procedure Circle

         (  Picture : in out Image;
            Center  : Point;
            Radius  : Natural;
            Color   : Pixel
         )  is
  F     : Integer := 1 - Radius;
  ddF_X : Integer := 0;
  ddF_Y : Integer := -2 * Radius;
  X     : Integer := 0;
  Y     : Integer := Radius;

begin

  Picture (Center.X, Center.Y + Radius) := Color;
  Picture (Center.X, Center.Y - Radius) := Color;
  Picture (Center.X + Radius, Center.Y) := Color;
  Picture (Center.X - Radius, Center.Y) := Color; 
  while X < Y loop
     if F >= 0 then
        Y := Y - 1;
        ddF_Y := ddF_Y + 2;
        F := F + ddF_Y;
     end if;
     X := X + 1;
     ddF_X := ddF_X + 2;
     F := F + ddF_X + 1;    
     Picture (Center.X + X, Center.Y + Y) := Color;
     Picture (Center.X - X, Center.Y + Y) := Color;
     Picture (Center.X + X, Center.Y - Y) := Color;
     Picture (Center.X - X, Center.Y - Y) := Color;
     Picture (Center.X + Y, Center.Y + X) := Color;
     Picture (Center.X - Y, Center.Y + X) := Color;
     Picture (Center.X + Y, Center.Y - X) := Color;
     Picture (Center.X - Y, Center.Y - X) := Color;
  end loop;

end Circle; </lang> The following illustrates use: <lang ada>

  X : Image (1..16, 1..16);

begin

  Fill (X, White);
  Circle (X, (8, 8), 5, Black);
  Print (X);

</lang> Sample output:

     HHHHH
    H     H
   H       H
  H         H
  H         H
  H         H
  H         H
  H         H
   H       H
    H     H
     HHHHH

ALGOL 68

Translation of: Ada

Works with: ALGOL 68 version Standard - pragmat read is an extension

Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386

<lang>PRAGMAT READ "Basic_bitmap_storage.a68" PRAGMAT;

circle OF class image :=

         (  REF IMAGE picture,
            POINT center,
            INT radius,
            PIXEL color
         )VOID:

BEGIN

  INT f     := 1 - radius,
  POINT ddf := (0, -2 * radius), 
        df := (0, radius);
  picture [x OF center, y OF center + radius] :=
  picture [x OF center, y OF center - radius] :=
  picture [x OF center + radius, y OF center] :=
  picture [x OF center - radius, y OF center] := color; 
  WHILE x OF df < y OF df DO
     IF f >= 0 THEN
        y OF df -:= 1;
        y OF ddf +:= 2;
        f +:= y OF ddf
     FI;
     x OF df +:= 1;
     x OF ddf +:= 2;
     f +:= x OF ddf + 1;    
     picture [x OF center + x OF df, y OF center + y OF df] :=
     picture [x OF center - x OF df, y OF center + y OF df] :=
     picture [x OF center + x OF df, y OF center - y OF df] :=
     picture [x OF center - x OF df, y OF center - y OF df] :=
     picture [x OF center + y OF df, y OF center + x OF df] :=
     picture [x OF center - y OF df, y OF center + x OF df] :=
     picture [x OF center + y OF df, y OF center - x OF df] :=
     picture [x OF center - y OF df, y OF center - x OF df] := color
  OD

END # circle #;

The following illustrates use:

IF test THEN

  REF IMAGE x = INIT LOC [1:16, 1:16] PIXEL;
  (fill OF class image)(x, (white OF class image));
  (circle OF class image)(x, (8, 8), 5, (black OF class image));
  (print OF class image)(x)

FI</lang> Output:

ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffff000000000000000000000000000000ffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff
ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffff000000ffffffffffffffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffff
ffffffffffffffffff000000ffffffffffffffffffffffffffffffffffffffffff000000ffffffffffffffffffffffff
ffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff000000ffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffff000000000000000000000000000000ffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

C

Interface:

<lang c>void raster_circle(

       image img,
       unsigned int x0,
       unsigned int y0,
       unsigned int radius,
       color_component r,
       color_component g,
       color_component b );</lang>

Implementation:

<lang c>#define plot(x, y) put_pixel_clip(img, x, y, r, g, b)

void raster_circle(

       image img,
       unsigned int x0,
       unsigned int y0,
       unsigned int radius,
       color_component r,
       color_component g,
       color_component b )

{

   int f = 1 - radius;
   int ddF_x = 0;
   int ddF_y = -2 * radius;
   int x = 0;
   int y = radius;

   plot(x0, y0 + radius);
   plot(x0, y0 - radius);
   plot(x0 + radius, y0);
   plot(x0 - radius, y0);

   while(x < y) 
   {
       if(f >= 0) 
       {
           y--;
           ddF_y += 2;
           f += ddF_y;
       }
       x++;
       ddF_x += 2;
       f += ddF_x + 1;    
       plot(x0 + x, y0 + y);
       plot(x0 - x, y0 + y);
       plot(x0 + x, y0 - y);
       plot(x0 - x, y0 - y);
       plot(x0 + y, y0 + x);
       plot(x0 - y, y0 + x);
       plot(x0 + y, y0 - x);
       plot(x0 - y, y0 - x);
   }

}

1. undef plot</lang>

Forth

: circle { x y r color bmp -- }
  1 r -  0 r 2* negate  0 r  { f ddx ddy dx dy }
  color x     y r + bmp b!
  color x     y r - bmp b!
  color x r + y     bmp b!
  color x r - y     bmp b!
  begin dx dy < while
    f 0< 0= if
      dy  1-      to dy
      ddy 2 + dup to ddy
      f +         to f
    then
    dx 1+       to dx
    ddx 2 + dup to ddx
    f 1+ +      to f
    color x dx + y dy + bmp b!
    color x dx - y dy + bmp b!
    color x dx + y dy - bmp b!
    color x dx - y dy - bmp b!
    color x dy + y dx + bmp b!
    color x dy - y dx + bmp b!
    color x dy + y dx - bmp b!
    color x dy - y dx - bmp b!
  repeat ;

12 12 bitmap value test
0 test bfill
6 6 5 blue test circle
test bshow cr

Fortran

This code should be inside RCImagePrimitive (see here). The private subroutine draw_circle_toch, which writes to a channel, is used by both draw_circle_rgb and draw_circle_sc and the interface allows to use draw_circle with rgb images and grayscale images.

<lang fortran> interface draw_circle

    module procedure draw_circle_sc, draw_circle_rgb
 end interface

 private :: plot, draw_circle_toch</lang>

<lang fortran> subroutine plot(ch, p, v)

   integer, dimension(:,:), intent(out) :: ch
   type(point), intent(in) :: p
   integer, intent(in) :: v

   integer :: cx, cy
   ! I've kept the default 1-based array, but top-left corner pixel
   ! is labelled as (0,0).
   cx = p%x + 1
   cy = p%y + 1

   if ( (cx > 0) .and. (cx <= ubound(ch,1)) .and. &
        (cy > 0) .and. (cy <= ubound(ch,2)) ) then
      ch(cx,cy) = v
   end if
 end subroutine plot
 
 subroutine draw_circle_toch(ch, c, radius, v)
   integer, dimension(:,:), intent(out) :: ch
   type(point), intent(in) :: c
   integer, intent(in) :: radius, v

   integer :: f, ddf_x, ddf_y, x, y

   f = 1 - radius
   ddf_x = 0
   ddf_y = -2 * radius
   x = 0
   y = radius

   call plot(ch, point(c%x, c%y + radius), v)
   call plot(ch, point(c%x, c%y - radius), v)
   call plot(ch, point(c%x + radius, c%y), v)
   call plot(ch, point(c%x - radius, c%y), v)

   do while ( x < y )
      if ( f >= 0 ) then
         y = y - 1
         ddf_y = ddf_y + 2
         f = f + ddf_y
      end if
      x = x + 1
      ddf_x = ddf_x + 2
      f = f + ddf_x + 1
      call plot(ch, point(c%x + x, c%y + y), v)
      call plot(ch, point(c%x - x, c%y + y), v)
      call plot(ch, point(c%x + x, c%y - y), v)
      call plot(ch, point(c%x - x, c%y - y), v)
      call plot(ch, point(c%x + y, c%y + x), v)
      call plot(ch, point(c%x - y, c%y + x), v)
      call plot(ch, point(c%x + y, c%y - x), v)
      call plot(ch, point(c%x - y, c%y - x), v)
   end do
   
 end subroutine draw_circle_toch

 subroutine draw_circle_rgb(img, c, radius, color)
   type(rgbimage), intent(out) :: img
   type(point), intent(in) :: c
   integer, intent(in) :: radius
   type(rgb), intent(in) :: color
   
   call draw_circle_toch(img%red, c, radius, color%red)
   call draw_circle_toch(img%green, c, radius, color%green)
   call draw_circle_toch(img%blue, c, radius, color%blue)
 end subroutine draw_circle_rgb

 subroutine draw_circle_sc(img, c, radius, lum)
   type(scimage), intent(out) :: img
   type(point), intent(in) :: c
   integer, intent(in) :: radius, lum
   
   call draw_circle_toch(img%channel, c, radius, lum)
 end subroutine draw_circle_sc</lang>

Modula-3

<lang modula3>INTERFACE Circle;

IMPORT Bitmap;

PROCEDURE Draw(

 img: Bitmap.T; 
 center: Bitmap.Point; 
 radius: CARDINAL; 
 color: Bitmap.Pixel);

END Circle.</lang> <lang modula3>MODULE Circle;

IMPORT Bitmap;

PROCEDURE Draw(

 img: Bitmap.T; 
 center: Bitmap.Point; 
 radius: CARDINAL; 
 color: Bitmap.Pixel) = 
 VAR f := 1 - radius;
     ddfx := 0;
     ddfy := - 2 * radius;
     x := 0;
     y := radius;
 BEGIN
   Bitmap.SetPixel(img, Bitmap.Point{center.x, center.y + radius}, color);
   Bitmap.SetPixel(img, Bitmap.Point{center.x, center.y - radius}, color);
   Bitmap.SetPixel(img, Bitmap.Point{center.x + radius, center.y}, color);
   Bitmap.SetPixel(img, Bitmap.Point{center.x - radius, center.y}, color);
   WHILE x < y DO
     IF f >= 0 THEN
       y := y - 1;
       ddfy := ddfy + 2;
       f := f + ddfy;
     END;
     x := x + 1;
     ddfx := ddfx + 2;
     f := f + ddfx + 1;
     Bitmap.SetPixel(img, Bitmap.Point{center.x + x, center.y + y}, color);
     Bitmap.SetPixel(img, Bitmap.Point{center.x - x, center.y + y}, color);
     Bitmap.SetPixel(img, Bitmap.Point{center.x + x, center.y - y}, color);
     Bitmap.SetPixel(img, Bitmap.Point{center.x - x, center.y - y}, color);
     Bitmap.SetPixel(img, Bitmap.Point{center.x + y, center.y + x}, color);
     Bitmap.SetPixel(img, Bitmap.Point{center.x - y, center.y + x}, color);
     Bitmap.SetPixel(img, Bitmap.Point{center.x + y, center.y - x}, color);
     Bitmap.SetPixel(img, Bitmap.Point{center.x - y, center.y - x}, color);
   END;
 END Draw;

BEGIN END Circle.</lang>

Example (outputs a PPM image): <lang modula3>MODULE Main;

IMPORT Circle, Bitmap, PPM;

VAR testpic: Bitmap.T;

BEGIN

 testpic := Bitmap.NewImage(32, 32);
 Bitmap.Fill(testpic, Bitmap.White);
 Circle.Draw(testpic, Bitmap.Point{16, 16}, 10, Bitmap.Black);
 PPM.Create("testpic.ppm", testpic);

END Main.</lang>

OCaml

<lang ocaml>let raster_circle ~img ~color ~c:(x0, y0) ~r =

 let plot = put_pixel img color in
 let x = 0
 and y = r
 and m = 5 - 4 * r
 in
 let rec loop x y m =
   plot (x0 + x) (y0 + y);
   plot (x0 + y) (y0 + x);
   plot (x0 - x) (y0 + y);
   plot (x0 - y) (y0 + x);
   plot (x0 + x) (y0 - y);
   plot (x0 + y) (y0 - x);
   plot (x0 - x) (y0 - y);
   plot (x0 - y) (y0 - x);
   let y, m =
     if m > 0
     then (y - 1), (m - 8 * y)
     else y, m
   in
   if x <= y then
     let x = x + 1 in
     let m = m + 8 * x + 4 in
     loop x y m
 in
 loop x y m

</lang>

Vedit macro language

<lang vedit> // Draw a circle using Bresenham's circle algorithm. // #21 = center x, #22 = center y; #23 = radius

DRAW_CIRCLE:

1. 30 = 1 - #23 // f
2. 31 = 0 // ddF_x
3. 32 = -2 * #23 // ddF_y
4. 41 = 0 // x
5. 42 = #23 // y

while (#41 <= #42) {

   #1 = #21+#41; #2 = #22+#42; Call("DRAW_PIXEL")
   #1 = #21-#41; #2 = #22+#42; Call("DRAW_PIXEL")
   #1 = #21+#41; #2 = #22-#42; Call("DRAW_PIXEL")
   #1 = #21-#41; #2 = #22-#42; Call("DRAW_PIXEL")
   #1 = #21+#42; #2 = #22+#41; Call("DRAW_PIXEL")
   #1 = #21-#42; #2 = #22+#41; Call("DRAW_PIXEL")
   #1 = #21+#42; #2 = #22-#41; Call("DRAW_PIXEL")
   #1 = #21-#42; #2 = #22-#41; Call("DRAW_PIXEL")
   if (#30 >= 0) {

#42-- #32 += 2 #30 += #32

   }
   #41++
   #31 += 2
   #30 += #31 + 1

}

return </lang>