utilities.lisp~

(defun sq (x) (* x x))

(defun mag (&rest lst)
  (sqrt (apply #'+ (mapcar #'sq lst))))

(defun list-copies (thing n)
  (if (= n 0)
      nil
      (cons thing (list-copies thing (- n 1)))))

(defun vdif (v1 v2)
  (mapcar #'- v1 v2))

(defun vdot (v1 v2)
  (apply #'+ (mapcar #'* v1 v2)))

(defmacro v+ (&rest list-of-vecs)
  `(mapcar #'+ @list-of-vecs))

(defun vs* (s v)
  (mapcar #'* v (list-copies s (length v))))

(defun unitize (v)
  (vs* (/ 1 (mag v)) v))

(defun vcross (x y)
  (list
   (- (* (nth 2 x) (nth 1 y)) (* (nth 1 x) (nth 2 y)))
   (- (* (nth 0 x) (nth 2 y)) (* (nth 2 x) (nth 0 y)))
   (- (* (nth 0 x) (nth 1 y)) (* (nth 1 x) (nth 0 y)))))

(defun random-elt (choices)
  "Choose an element from a list at random."
  (elt choices (random (length choices))))

(defun average (&rest lst)
  (/ (apply #'+ lst) (length lst)))

(defun vdistance (v1 v2)
  (mag (vdif v1 v2)))

(defun minroot (a b c)
  (if (zerop a)
      (/ (- c) b)
      (let ((disc (- (sq b) (* 4 a c))))
	(unless (minusp disc)
	  (let ((discrt (sqrt disc)))
	    (min (/ (+ (- b) discrt) (* 2 a))
		 (/ (- (- b) discrt) (* 2 a))))))))

(defmacro mand (macro-args)
  `(and ,@macro-args))