;Authors: A. Nguyen, 2025.

; Design limitations:
; 1) Sounds must have identical sample rate; otherwise, SoX fails silently, literally.

; Questions:
; 1) Is there a built-in (flatten lst)-function?
; 2) Implement up to which order? <=> CLI issues to be expected (e.g., maximum command character length)?

(in-package :om)

;;; SOX-HOAENCODE ========================

; Util
(defun flatten (structure)
    (cond 
        ((null structure) 
            nil)
        ((atom structure) 
            (list structure))
        (t 
            (mapcan #'flatten structure))
    )
)

(defun sox-hoaencode-deg-to-rad (x)
    (* (/ x 180) pi)
)

(defun sox-hoaencode-double-to-float (lst)
    (mapcar 
        (lambda (x) (float x 0.0S0)) 
        lst
    )
)

; Ambisonics
(defun sox-hoaencode-sn3d-factor (order degree)
    (ecase order
        (0 1)
        (1 1)
        (2 
            (ecase (abs degree)
                (2 (/ (sqrt 3) 6))
                (1 (/ (sqrt 3) 3))
                (0 1)
            ))
        (3 
            (ecase (abs degree)
                (3 (/ (sqrt 10) 60))
                (2 (/ (sqrt 15) 30))
                (1 (/ (sqrt 6) 6))
                (0 1)
            )
        )
    )
)

(defun sox-hoaencode-azimuth-factor (degree theta_deg)
    (let* 
        (
            (theta (sox-hoaencode-deg-to-rad theta_deg))
        )
        (if (< degree 0) 
            (sin (* (abs degree) theta)) 
            (cos (* (abs degree) theta))
        )
    )
)

(defun sox-hoaencode-elevation-factor (order degree phi_deg)
    (let* 
        (
            (phi (sox-hoaencode-deg-to-rad phi_deg))
        )
        (ecase order
            (0 1)
            (1 
                (ecase (abs degree)
                    (0 (sin phi))
                    (1 (cos phi))
                ))
            (2 
                (ecase (abs degree)
                    (0 (- (/ (* 3 (expt (sin phi) 2)) 2) (/ 1 2)))
                    (1 (/ (* 3 (expt (sin phi) 2)) 2))
                    (2 (* 3 (expt (cos phi) 2)))
                ))
            (3 
                (ecase (abs degree)
                    (0 (/ (* (sin phi) (- (* 5 (expt (sin phi) 2)) 3)) 2))
                    (1 (- (* 6 (cos phi)) (/ (* 15 (expt (cos phi) 3)) 2)))
                    (2 (* -15 (sin phi) (- (expt (sin phi) 2) 1)))
                    (3 (* 15 (expt (cos phi) 3)))
                ))
        )
    ))

; Convenience functions

; Ensures that positions are given as '((azimuth elevation) ...) (in degrees), i.e.
; 1) if list of list of three values, input is assumed to be '(x y z) coordinates and will be transformed to '(azimuth elevation) coordinates (in the navigational spherical coordinate system).
; 2) if list of list of two values, input is assumed to be '(azimuth elevation) coordinates and won't be transformed any further.
; 3) if 3dc, input is transformed to '(azimuth elevation) coordinates.
(defun sox-hoaencode-auto-convert-positions (positions)
    (cond 
        ((subtypep (type-of positions) '3dc)  
            (progn ; convert xyz->aed, keep azimuth and elevation only.
                (mat-trans 
                    (butlast 
                        (mat-trans 
                            (mapcar 
                                (lambda (xyz) (multiple-value-list (om:xyz->aed (first xyz) (second xyz) (third xyz)))) 
                                (mat-trans (list (x-points positions) (y-points positions) (z-points positions)))
                            ))))))
        ((subtypep (type-of positions) 'list) 
            (cond
                ((= 2 (length (first positions)))
                    positions)
                ((= 3 (length (first positions))) 
                    (mat-trans 
                        (butlast 
                            (mat-trans 
                                (mapcar 
                                    (lambda (xyz) (multiple-value-list (om:xyz->aed (first xyz) (second xyz) (third xyz)))) 
                                    positions
                                )))))
                (t (error "Positions must consist of lists of length 2 (ae) or 3 (xyz)."))
            ))
        (t (error "Positions must be of type 3dc or list."))))

; High-level API
; Returns the gain value (linear, -1 to 1) for a single ACN-channel
(defun sox-hoaencode-gain-single-component (order degree azimuth_deg elevation_deg)
    (let
        (
            ; It is assumed that azimuth_deg follows the implementation details of SpatDIF, 
            ; where azimuth_deg runs counterclockwise. 
            ; However, the formulas inside assume that azimuth_deg runs clockwise, i.e. 
            ; the sign of azimuth_deg must be inverted.
            (azimuth_deg_inverted (* -1 azimuth_deg))
        )
        (* 
            (sox-hoaencode-sn3d-factor order degree) 
            (sox-hoaencode-azimuth-factor degree azimuth_deg_inverted) 
            (sox-hoaencode-elevation-factor order degree elevation_deg)))
    )

; Returns the gain values for all components at a specific order
(defun sox-hoaencode-gains-by-order (order azimuth_deg elevation_deg)
    (loop for degree from (* -1 order) to order collect 
        (sox-hoaencode-gain-single-component order degree azimuth_deg elevation_deg)))

; Returns the gain values for all components up to a specific order
(defun sox-hoaencode-gains-up-to-order (order azimuth_deg elevation_deg)
    (sox-hoaencode-double-to-float 
        (flatten
            (loop for ord from 0 to order collect 
                (sox-hoaencode-gains-by-order ord azimuth_deg elevation_deg)))))


(defclass! sox-hoaencode (sox-input)
    (
        (positions :accessor positions :initarg :positions :initform nil :documentation *sox-hoaencode-positions-doc*)
        (order :accessor order :initarg :order :initform nil :documentation *sox-hoaencode-order-doc*)
    )
    (:icon 100)
    (:documentation "Sox-hoaencode transforms <sound> into a <order>-th ambisonic (HOA) signal at <positions>.

    The signal follows the ambiX convention, i.e. it uses SN3D normalization and ACN channel ordering. The resulting file has (<order>+1)^2 channels (order 0: 1 channel, order 1: 4 channels, order 2: 9 channels, order 3: 16 channels, ...).")
)

(defmethod initialize-instance :after ((self sox-hoaencode) &rest l)
    (declare (ignore l))
    (when (sound self)
        (sox-init-sound self 'list)
    )
)