anchor.diff:  (defun untransform-angle (transformation phi)
     (multiple-value-bind (rotations remainder) (ffloor phi (* 2 pi))
       (when (reflection-transformation-p transformation)
  -      (setq rotations  (ffloor (- 1 phi) (* 2 pi))))
  +      (setq rotations  (ffloor (- phi) (* 2 pi))))
       (multiple-value-bind (ix iy) (untransform-distance transformation (cos remainder) (sin remainder))
         (multiple-value-bind (x0 y0) (untransform-distance transformation 1 0)
           (let ((my-angle (atan* ix iy))
  
positive.code: (defun transform-angle (transformation phi)
    (multiple-value-bind (rotations remainder) (ffloor phi (* 2 pi))
      (when (reflection-transformation-p transformation)
        (setq rotations  (ffloor (- 1 phi) (* 2 pi))))
      (multiple-value-bind (ix iy) (transform-distance transformation (cos remainder) (sin remainder))
        (multiple-value-bind (x0 y0) (transform-distance transformation 1 0)
          (let ((my-angle (atan* ix iy))
  
negative.code: 
  (defmethod untransform-region ((transformation transformation) region)
    (transform-region (invert-transformation transformation) region))
  
  (defmethod transform-position ((transformation standard-transformation) x y)
    (let ((x (coordinate x))
          (y (coordinate y)))
      (multiple-value-bind (mxx mxy myx myy tx ty)
          (get-transformation transformation)
        (declare (type coordinate mxx mxy myx myy tx ty))
        (values (+ (* mxx x) (* mxy y) tx)
                (+ (* myx x) (* myy y) ty)))))
  
  (defmethod untransform-position ((transformation transformation) x y)
    (transform-position (invert-transformation transformation) x y))
  
  (defmethod transform-distance ((transformation standard-transformation) dx dy)
    (let ((dx (coordinate dx))
          (dy (coordinate dy)))
      (multiple-value-bind (mxx mxy myx myy) (get-transformation transformation)
        (declare (type coordinate mxx mxy myx myy))
        (values (+ (* mxx dx) (* mxy dy))
                (+ (* myx dx) (* myy dy))))))
  
  (defmethod untransform-distance ((transformation transformation) dx dy)
    (transform-distance (invert-transformation transformation) dx dy))
  