; hw7#1
; CS 381 homework 7 problem 1
; Jacob Lundberg

;;
;; Problem One
;;

; MAKE-POINT creates a list ordered correctly to represent a point (x y).
(defun MAKE-POINT (&key (x 0) (y 0))
  ; If x any y are not a valid locus we will fail and return nil.
  (if (and (numberp x) (numberp y))
    ; valid numbers so make a list
    (list x y)
    ; invalid locus so return nil
    nil
  )
)

; POINT-P is a predicate to determine if a list has the correct form to be a point.
; That is, a point as defined by MAKE-POINT, which creates two dimentsional points.
(defun POINT-P (point1)
  (cond ; nothing there
        ((null point1) nil)
        ; only one dimension
        ((null (cdr point1)) nil)
        ; too many dimensions
        ((not (null (cddr point1))) nil)
        ; first dimension is not a number
        ((not (numberp (car point1))) nil)
        ; second dimension is not a number
        ((not (numberp (cadr point1))) nil)
        ; if we survive all the tests above, it is a point
        (T)
  )
)

; POINT-X and POINT-Y are accessors for a point made with MAKE-POINT.
(defun POINT-X (point1) (if (POINT-P point1) (car point1) nil))
(defun POINT-Y (point1) (if (POINT-P point1) (cadr point1) nil))

; MAKE-SEGMENT creates a list of two points as created by MAKE-POINT, thus defining a line segment.
(defun MAKE-SEGMENT (&key (point1 '(0 0)) (point2 '(0 0)))
  ; if point1 and point2 are not valid points then fail and return nil
  (if (and (POINT-P point1) (POINT-P point2))
    ; we have valid points
    (list point1 point2)
    ; we have invalid points
    nil
  )
)

; SEGMENT-P is a predicate to determine if a list has the correct form to be a segment.
; That is, a segment as defined by MAKE-SEGMENT, which creates two dimentsional segments.
(defun SEGMENT-P (seg1)
  (cond ; nothing there
        ((null seg1) nil)
        ; only one point
        ((null (cdr seg1)) nil)
        ; too many points
        ((not (null (cddr seg1))) nil)
        ; first point isn't
        ((not (POINT-P (car seg1))) nil)
        ; second point isn't
        ((not (POINT-P (cadr seg1))) nil)
        ; if we survive all the tests above, it is a segment
        (T)
  )
)

; SEGMENT-POINT1 and SEGMENT-POINT2 are accessors for a segment made with MAKE-SEGMENT.
(defun SEGMENT-POINT1 (seg1) (if (SEGMENT-P seg1) (car seg1) nil))
(defun SEGMENT-POINT2 (seg2) (if (SEGMENT-P seg2) (cadr seg2) nil))

; MIDPOINT returns the midpoint of a line segment created using MAKE-SEGMENT.
; Care has been taken to mimic structure access syntax here.
(defun MIDPOINT (seg1)
  (MAKE-POINT ; find center X value
              :x (/ (+ (POINT-X (SEGMENT-POINT1 seg1)) (POINT-X (SEGMENT-POINT2 seg1))) 2)
              ; find center Y value
              :y (/ (+ (POINT-Y (SEGMENT-POINT1 seg1)) (POINT-Y (SEGMENT-POINT2 seg1))) 2)
  )
)