Simplify coord-rotate (issue 263690043 by address@hidden)

[thomasmorley65]

Great simplification!

Though, I'd like to add two features
1)
Making it possible to rotate at a different point other than (0 . 0)
2)
Getting the needed exactness as discussed starting:
http://lists.gnu.org/archive/html/lilypond-user/2015-10/msg00320.html

Below my attempt following your advice. I tried make it as concise as
possible, but ofcourse it is now far more complex again.

(define (get-PI/4-rotated-quadrants radians)
  (cond ((>= radians TWO-PI)
         (get-PI/4-rotated-quadrants (- radians TWO-PI)))
        ((< radians 0)
         (get-PI/4-rotated-quadrants (+ radians TWO-PI )))
        (else
          (let* (;; get the octants
                 (oct (truncate (/ radians (/ PI 4)))))
            ;; get the rotated quadrants
            (if (even? oct)
                (/ oct 2)
                (/ (1+ oct) 2))))))

(define*-public
  (coord-rotate coordinate angle-in-radians #:optional (middle '(0 .
0)))
  (let* ((angle (angle-0-2pi angle-in-radians))
         (quadrant (get-PI/4-rotated-quadrants angle-in-radians))
         (moved-angle (- angle (/ (* quadrant PI) 2)))
         (x (coord-x coordinate))
         (y (coord-y coordinate))
         (c (cos moved-angle))
         (s (sin moved-angle))
         (xs (* x s))
         (xc (* x c))
         (ys (* y s))
         (yc (* y c))
         (rotated-round-zero
           (cond ((= quadrant 1)
                  (cons
                    (- (- xs) (- yc))
                    (- (+ (- xc) (- ys)))))
                 ((= quadrant 2)
                  (cons
                    (- (- xc) (- ys))
                    (+ (- xs) (- yc))))
                 ((= quadrant 3)
                  (cons
                    (- xs yc)
                    (- (+ xc ys))))
                 (else
                  (cons
                    (- xc ys)
                    (+ xs yc))))))
    (cons
     (+ (coord-x middle) (coord-x rotated-round-zero))
     (+ (coord-y middle) (coord-y rotated-round-zero)))))

https://codereview.appspot.com/263690043/