Example_A12_Matrices.scd

// Icosahedron
// see:
"http://neilsloane.com/sphdesigns/dim3/des.3.12.5.txt".openOS

// Matrix Author: Ambisonic Toolkit
// --J Anderson
"http://www.ambisonictoolkit.net".openOS

/*

2nd-order FuMa-MaxN A-format decoder & encoder

Use in conjunction with AtkMatrixMix*ar

*/

(
var soa_a12_decoder_matrix, soa_a12_encoder_matrix;

// a-12 decoder matrix
soa_a12_decoder_matrix = Matrix.with([
	[ 0.11785113, 0.212662702, 0, -0.131432778, -0.0355875819, -0.279508497, 0, 0.226127124, 0 ],
	[ 0.11785113, 0.131432778, -0.212662702, 0, -0.208333333, 0, 0, -0.139754249, -0.279508497 ],
	[ 0.11785113, 0, -0.131432778, 0.212662702, 0.243920915, 0, -0.279508497, -0.0863728757, 0 ],
	[ 0.11785113, 0.212662702, 0, 0.131432778, -0.0355875819, 0.279508497, 0, 0.226127124, 0 ],
	[ 0.11785113, -0.131432778, -0.212662702, 0, -0.208333333, 0, 0, -0.139754249, 0.279508497 ],
	[ 0.11785113, 0, 0.131432778, -0.212662702, 0.243920915, 0, -0.279508497, -0.0863728757, 0 ],
	[ 0.11785113, -0.212662702, 0, -0.131432778, -0.0355875819, 0.279508497, 0, 0.226127124, 0 ],
	[ 0.11785113, -0.131432778, 0.212662702, 0, -0.208333333, 0, 0, -0.139754249, -0.279508497 ],
	[ 0.11785113, 0, 0.131432778, 0.212662702, 0.243920915, 0, 0.279508497, -0.0863728757, 0 ],
	[ 0.11785113, -0.212662702, 0, 0.131432778, -0.0355875819, -0.279508497, 0, 0.226127124, 0 ],
	[ 0.11785113, 0.131432778, 0.212662702, 0, -0.208333333, 0, 0, -0.139754249, 0.279508497 ],
	[ 0.11785113, 0, -0.131432778, -0.212662702, 0.243920915, 0, 0.279508497, -0.0863728757, 0 ],
]);

// a-12 encoder matrix
soa_a12_encoder_matrix = Matrix.with([
	[ 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781 ],
	[ 0.850650808, 0.525731112, 0, 0.850650808, -0.525731112, 0, -0.850650808, -0.525731112, 0, -0.850650808, 0.525731112, 0 ],
	[ 0, -0.850650808, -0.525731112, 0, -0.850650808, 0.525731112, 0, 0.850650808, 0.525731112, 0, 0.850650808, -0.525731112 ],
	[ -0.525731112, 0, 0.850650808, 0.525731112, 0, -0.850650808, -0.525731112, 0, 0.850650808, 0.525731112, 0, -0.850650808 ],
	[ -0.0854101966, -0.5, 0.585410197, -0.0854101966, -0.5, 0.585410197, -0.0854101966, -0.5, 0.585410197, -0.0854101966, -0.5, 0.585410197 ],
	[ -0.894427191, 0, 0, 0.894427191, 0, 0, 0.894427191, 0, 0, -0.894427191, 0, 0 ],
	[ 0, 0, -0.894427191, 0, 0, -0.894427191, 0, 0, 0.894427191, 0, 0, 0.894427191 ],
	[ 0.723606798, -0.447213596, -0.276393202, 0.723606798, -0.447213596, -0.276393202, 0.723606798, -0.447213596, -0.276393202, 0.723606798, -0.447213596, -0.276393202 ],
	[ 0, -0.894427191, 0, 0, 0.894427191, 0, 0, -0.894427191, 0, 0, 0.894427191, 0 ],
]);

// -- test... should return identity matrix
soa_a12_encoder_matrix.mulMatrix(soa_a12_decoder_matrix)
)


/*

1st-order FuMa-MaxN A-format decoder

*/

(
var cart, spher, foa_a12_decoder_matrix;

// directions
// the original coordinates, in cartesian
cart = [
	0.850650808352E+00,
	0,
	-0.525731112119E+00,
	0.525731112119E+00,
	-0.850650808352E+00,
	0.000000000000E+00,
	0,
	-0.525731112119E+00,
	0.850650808352E+00,
	0.850650808352E+00,
	0,
	0.525731112119E+00,
	-0.525731112119E+00,
	-0.850650808352E+00,
	0,
	0,
	0.525731112119E+00,
	-0.850650808352E+00,
	-0.850650808352E+00,
	0,
	-0.525731112119E+00,
	-0.525731112119E+00,
	0.850650808352E+00,
	0,
	0,
	0.525731112119E+00,
	0.850650808352E+00,
	-0.850650808352E+00,
	0,
	0.525731112119E+00,
	0.525731112119E+00,
	0.850650808352E+00,
	0,
	0,
	-0.525731112119E+00,
	-0.850650808352E+00
];

// convert to angles -- use these directions
spher = cart.clump(3).collect({ arg cart, i;
	cart.asCartesian.asSpherical.angles;
});

// make a 1st-order decoder matrix
foa_a12_decoder_matrix = FoaEncoderMatrix.newDirections(spher).matrix.pseudoInverse;
)