;;--------------------- aboveline ---------------------------------------
;;      Purpose: given 2D points p1,p2,p3
;;               determines if p3 lies above or below the line defined
;;               by p1,p2
;;      Needs: two points p1,p2 to determine the line
;;             point p3 to test
;;             fuzz to determine required proximity to line
;;      Returns: 1 if p3 is above the line
;;               0 if on the line
;;              -1 if below the line
;;               nil if the line is vertical or p1,p2 are coincident
;;----------------------------------------------------------------
(defun aboveline (p1 p2 p3 fuzz / m ret y3 yprime)
  (if (= (car p1) (car p2)) (setq ret nil)
    (progn
      (setq m (/ (- (cadr p2) (cadr p1)) (- (car p2) (car p1)))
            yprime (+ (cadr p1) (* m (- (car p3) (car p1))))
            y3 (cadr p3)
      )
      (cond ((equal y3 yprime fuzz) (setq ret 0))
            ((> y3 yprime) (setq ret 1))
            ((< y3 yprime) (setq ret -1))
      );cond
    );progn
  );if
  ret
);aboveline

;;--------------------- rightofline ---------------------------------------
;;      Purpose: given 2D points p1,p2,p3
;;               determines if p3 lies right or left of the line defined
;;               by p1,p2
;;      Needs: two points p1,p2 to determine the line
;;             point p3 to test
;;             fuzz to determine required proximity to line
;;      Returns: 1 if p3 is right of the line
;;               0 if on the line
;;              -1 if left of the line
;;               nil if the line is horizontal or p1,p2 are coincident
;;----------------------------------------------------------------
(defun rightofline (p1 p2 p3 fuzz / m ret x3 xprime)
  (if (= (car p1) (car p2)) (setq ret nil)
    (progn
      (setq m (/ (- (cadr p2) (cadr p1)) (- (car p2) (car p1)))
            xprime (+ (car p1) (/ (- (cadr p3) (cadr p1)) m))
            x3 (car p3)
      )
      (cond ((equal x3 xprime fuzz) (setq ret 0))
            ((> x3 xprime) (setq ret 1))
            ((< x3 xprime) (setq ret -1))
      );cond
    );progn
  );if
  ret
);rightofline