(defstruct line points)
(defstruct circle radius centre)
(defstruct polygon points)

(defun line (start-x start-y end-x end-y)
  (list (make-line :points (vector start-x start-y end-x end-y))))

(defun circle (radius centre-x centre-y)
  (list (make-circle :radius radius :centre (vector centre-x centre-y))))

(defun rectangle (left-x bottom-y width height)
  (let ((right-x (+ left-x width))
		(top-y (+ bottom-y height)))
	(list (make-polygon
           :points (vector left-x bottom-y
						   left-x top-y
						   right-x top-y
						   right-x bottom-y)))))

(defun centre-rectangle (centre-x centre-y width height)
  (let ((left-x (- centre-x (/ width 2)))
        (bottom-y (- centre-y (/ height 2))))
    (rectangle left-x bottom-y width height)))

(defun translate (delta-x delta-y drawing)
  (defun translate-points (points)
    (let ((new-points (copy-seq points)))
      (do ((i 0 (+ i 2)))
          ((>= i (length points)))
        (incf (aref new-points i) delta-x)
        (incf (aref new-points (1+ i)) delta-y))
      new-points))
  (defun translate-primitive (primitive)
    (typecase primitive
      (line (make-line :points (translate-points (line-points primitive))))
      (circle
       (make-circle
        :radius (circle-radius primitive)
        :centre (translate-points (circle-centre primitive))))
      (polygon
       (make-polygon
        :points (translate-points (polygon-points primitive))))))
  (mapcar #'translate-primitive drawing))

(defun scale (scale-factor drawing)
  (defun scale-points (points)
    (let ((new-points (copy-seq points)))
      (dotimes (i (length points))
        (setf (aref new-points i)
              (* scale-factor (aref new-points i))))
      new-points))
  (defun scale-primitive (primitive)
    (typecase primitive
      (line (make-line :points (scale-points (line-points primitive))))
      (circle
       (make-circle
        :radius (* scale-factor (circle-radius primitive))
        :centre (scale-points (circle-centre primitive))))
      (polygon
       (make-polygon
        :points (scale-points (polygon-points primitive))))))
  (mapcar #'scale-primitive drawing))

(defun overlay (&rest drawings)
  (apply #'append drawings))