racket/collects/deinprogramm/turtle.rkt

#lang scheme
 
(require mzlib/math
         (only-in deinprogramm/image rectangle line overlay image-color? image image-color)
         (only-in lang/private/imageeq image?)
         deinprogramm/signature/signature-syntax)

(provide set-color 
         turn
         draw
         move
         run
         sequence
         turtle
         image
         image-color)

 ; used to convert angles 
 (define pi/180 (/ pi 180))

 ; convert angle value
 ; (: grad->rad (number -> number))
 (define grad->rad
   (lambda (grad)
     (* pi/180 grad)))

 (define turtle (signature
		 (predicate (lambda (x)
			      (and (vector? x)
				   (= (vector-length x) 8)
				   (number? (vector-ref x 0))
				   (number? (vector-ref x 1))
				   (number? (vector-ref x 2))
				   (number? (vector-ref x 3))
				   (number? (vector-ref x 4))
				   (image? (vector-ref x 5))
				   (image-color? (vector-ref x 6)))))))

 ; This function is only for internal use.
 ; (new-turtle-priv h w x y angle img color state)
 ; creates a new turtle with hight h, width w.
 ; The cursor is at position (x,y) and the view direction
 ; is defined by an angle value relative to the vector (1,0) .
 ; The two next componets represents the image and the
 ; color of the pen. The last component represents an abritary
 ; value, that allows to transport state with the turtle.
 (: new-turtle-priv (number number number number number image image-color %A -> turtle))
 (define new-turtle-priv 
   (lambda (h w x y angle img color state)
     (vector h w x y angle img color state)))

 
 ; (new-turtle h w color)
 ; creates a new turtle with the pen color color and sets the
 ; width of the image to w and the hight to h.
 ; The background of the image is gray and the position of the
 ; cursor is (0,0) and the view direction is (1,0).
 (: new-turtle (number number image-color -> turtle))
 (define new-turtle 
   (lambda (h w color)
     (let ((x (floor (/ w 2)))
           (y (floor (/ h 2))))
       (new-turtle-priv h w x y 0 (rectangle w h "solid" "gray") color #f))))

 ; (new-turtle-complex h w color bgcolor x y angle)
 ; creates a new turtle with the pen color color and sets the
 ; width of the image to w and the hight to h.
 ; The background of the image is bgcolor and the position of the
 ; cursor is (x,y) and the view direction is (1,0) * e^(- i angle).
 (: new-turtle (number number image-color image-color number number number -> turtle))
 (define new-turtle-complex 
   (lambda (h w color bgcolor x y angle)
     (new-turtle-priv h w x y angle (rectangle w h "solid" bgcolor) color #f)))

 
 ; For internal use only
 (: get-h (turtle -> number))
 (define get-h (lambda (t) (vector-ref t 0)))
 (: get-w (turtle -> number))
 (define get-w (lambda (t) (vector-ref t 1)))
 (: get-x (turtle -> number))
 (define get-x (lambda (t) (vector-ref t 2)))
 (: get-y (turtle -> number))
 (define get-y (lambda (t) (vector-ref t 3)))
 (: get-angle (turtle -> number))
 (define get-angle (lambda (t) (vector-ref t 4)))
 (: get-iamge (turtle -> image))
 (define get-image (lambda (t) (vector-ref t 5)))
 (: get-color (turtle -> image-color))
 (define get-color (lambda (t) (vector-ref t 6)))
 (: get-state (turtle -> %A))
 (define get-state (lambda (t) (vector-ref t 7)))

 ; (set-color color)
 ; returns a function of type turtle -> turtle.
 ; Use the result to change the color of the pen.
 (: set-color (image-color -> (turtle -> turtle)))
 (define set-color
   (lambda (color)
     (lambda (t)
       (let* ((h (get-h t))
              (w (get-w t))
              (x (get-x t))
              (y (get-y t))
              (angle (get-angle t))
              (image (get-image t)))
         (new-turtle-priv h w x y angle image color #f)))))
 
 ; (turn angle) 
 ; returns a function of type turtle -> turtle.
 ; Use the result to turn the view of the turtle (counter-clockwise).
 (: turn (number -> (turtle -> turtle)))
 (define turn
   (lambda (grad)
     (lambda (t)
             (let* ((h (get-h t))
                    (w (get-w t))
                    (x (get-x t))
                    (y (get-y t))
                    (angle (get-angle t))
                    (image (get-image t))
                    (color (get-color t))
                    (state (get-state t)))
               (new-turtle-priv h w x y (- angle grad) image color state)))))
     
 ; For internal use only
 ; (move-cursor turtle length)
 ; returns a new turtle where the cursor 
 ; is moved length steps along the view vector.
 (: move-cursor (turtle number -> turtle))
 (define move-cursor
   (lambda (t length)
     (let* ((h (get-h t))
            (w (get-w t))
            (x (get-x t))
            (y (get-y t))
            (angle (get-angle t))
            (image (get-image t))
            (color (get-color t))
            (state (get-state t))
            (newx (+ x (* length (cos (grad->rad angle)))))
            (newy (+ y (* length (sin (grad->rad angle))))))
       (new-turtle-priv h w newx newy angle image color state))))
     
 ; (draw length)
 ; returns a function of type turtle -> turtle.
 ; The result can be used to move the turtle and draw a line.
 (: draw (number -> (turtle -> turtle)))
 (define draw
   (lambda (length)
     (lambda (t)
       (let* ((h (get-h t))
             (w (get-w t))
             (x (get-x t))
             (y (get-y t))
             (angle (get-angle t))
             (image (get-image t))
             (color (get-color t))
             (state (get-state t))
             ; Compute new coordinats
             (newx (+ x (* length (cos (grad->rad angle)))))
             (newy (+ y (* length (sin (grad->rad angle))))))
         (new-turtle-priv
          h w 
          newx newy angle 
          ; Compute new image
          (overlay image
                   (line w h x y newx newy color) 0 0)
          color state)))))

 ; (move length)
 ; returns a function of type turtle -> turtle.
 ; The result can be used to move the turtle without drawing a line.
 (: move (number -> (turtle -> turtle)))
 (define move
   (lambda (length)
     (lambda (t)
       (move-cursor t length)))) 
 
 ; runs a turtle function 
 (: run ((turtle -> turtle) number number image-color -> image))
 (define run 
   (lambda (t->t h w color) 
     (get-image (t->t (new-turtle h w color)))))

;   ; runs a turtle function 
;   ; (: run* ((turtle -> turtle) -> turtle -> image))
;   (define run*
;     (lambda (t->t h w color bgcolor x y angle) 
;       (get-image (t->t (new-turtle h w color bgcolor x y angle)))))

 ; This function is only for internal use.
 (define comp_priv_2 
   (lambda (f1 f2)
     (lambda (t)
       (f2 (f1 t)))))
 
 ; This function is only for internal use.
 (define comp_priv
   (lambda (l)
     (cond 
       ((null? l) (error "sequence erwartet mind. ein Argument"))
       ((list? l) 
        (let ((head (car l))
              (tail (cdr l)))
          (if (null? tail)
              head 
              (comp_priv_2 head (comp_priv tail))))))))

 ; This function allows to do a list of
 ; turtle -> turtle 
 ; functions into one new function, that do
 ; one action of the turtle, then later the rest.
 ; Define the type alias tip = turtle -> turtle.
 (define tip (signature (turtle -> turtle)))
 (: do (tip ... -> tip))
 (define sequence (lambda l (comp_priv l)))