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joslloand/Example_A20_Matrices.scd

Last active September 13, 2016 19:13
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Example_A20_Matrices.scd
// Dodecahedron
// see:
"http://neilsloane.com/sphdesigns/dim3/des.3.20.5.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_a20_decoder_matrix, soa_a20_encoder_matrix;
// a-20 decoder matrix
soa_a20_decoder_matrix = Matrix.with([
[ 0.0707106781, 0.0866025404, 0.0866025404, 0.0866025404, 0, 0.125, 0.125, 0, 0.125 ],
[ 0.0707106781, 0.0866025404, 0.0866025404, -0.0866025404, 0, -0.125, -0.125, 0, 0.125 ],
[ 0.0707106781, 0.0866025404, -0.0866025404, 0.0866025404, 0, 0.125, -0.125, 0, -0.125 ],
[ 0.0707106781, -0.0866025404, 0.0866025404, 0.0866025404, 0, -0.125, 0.125, 0, -0.125 ],
[ 0.0707106781, 0.0866025404, -0.0866025404, -0.0866025404, 0, -0.125, 0.125, 0, -0.125 ],
[ 0.0707106781, -0.0866025404, 0.0866025404, -0.0866025404, 0, 0.125, -0.125, 0, -0.125 ],
[ 0.0707106781, -0.0866025404, -0.0866025404, 0.0866025404, 0, -0.125, -0.125, 0, 0.125 ],
[ 0.0707106781, -0.0866025404, -0.0866025404, -0.0866025404, 0, 0.125, 0.125, 0, 0.125 ],
[ 0.0707106781, 0, 0.0535233135, 0.140125854, 0.202254249, 0, 0.125, -0.0238728757, 0 ],
[ 0.0707106781, 0, -0.0535233135, 0.140125854, 0.202254249, 0, -0.125, -0.0238728757, 0 ],
[ 0.0707106781, 0, 0.0535233135, -0.140125854, 0.202254249, 0, -0.125, -0.0238728757, 0 ],
[ 0.0707106781, 0, -0.0535233135, -0.140125854, 0.202254249, 0, 0.125, -0.0238728757, 0 ],
[ 0.0707106781, 0.140125854, 0, 0.0535233135, -0.0772542486, 0.125, 0, 0.163627124, 0 ],
[ 0.0707106781, 0.140125854, 0, -0.0535233135, -0.0772542486, -0.125, 0, 0.163627124, 0 ],
[ 0.0707106781, -0.140125854, 0, 0.0535233135, -0.0772542486, -0.125, 0, 0.163627124, 0 ],
[ 0.0707106781, -0.140125854, 0, -0.0535233135, -0.0772542486, 0.125, 0, 0.163627124, 0 ],
[ 0.0707106781, 0.0535233135, 0.140125854, 0, -0.125, 0, 0, -0.139754249, 0.125 ],
[ 0.0707106781, -0.0535233135, 0.140125854, 0, -0.125, 0, 0, -0.139754249, -0.125 ],
[ 0.0707106781, 0.0535233135, -0.140125854, 0, -0.125, 0, 0, -0.139754249, -0.125 ],
[ 0.0707106781, -0.0535233135, -0.140125854, 0, -0.125, 0, 0, -0.139754249, 0.125 ],]);
// a-20 encoder matrix
soa_a20_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, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781, 0.707106781 ],
[ 0.577350269, 0.577350269, 0.577350269, -0.577350269, 0.577350269, -0.577350269, -0.577350269, -0.577350269, 0, 0, 0, 0, 0.934172359, 0.934172359, -0.934172359, -0.934172359, 0.35682209, -0.35682209, 0.35682209, -0.35682209 ],
[ 0.577350269, 0.577350269, -0.577350269, 0.577350269, -0.577350269, 0.577350269, -0.577350269, -0.577350269, 0.35682209, -0.35682209, 0.35682209, -0.35682209, 0, 0, 0, 0, 0.934172359, 0.934172359, -0.934172359, -0.934172359 ],
[ 0.577350269, -0.577350269, 0.577350269, 0.577350269, -0.577350269, -0.577350269, 0.577350269, -0.577350269, 0.934172359, 0.934172359, -0.934172359, -0.934172359, 0.35682209, -0.35682209, 0.35682209, -0.35682209, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0.809016994, 0.809016994, 0.809016994, 0.809016994, -0.309016994, -0.309016994, -0.309016994, -0.309016994, -0.5, -0.5, -0.5, -0.5 ],
[ 0.666666667, -0.666666667, 0.666666667, -0.666666667, -0.666666667, 0.666666667, -0.666666667, 0.666666667, 0, 0, 0, 0, 0.666666667, -0.666666667, -0.666666667, 0.666666667, 0, 0, 0, 0 ],
[ 0.666666667, -0.666666667, -0.666666667, 0.666666667, 0.666666667, -0.666666667, -0.666666667, 0.666666667, 0.666666667, -0.666666667, -0.666666667, 0.666666667, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -0.127322004, -0.127322004, -0.127322004, -0.127322004, 0.872677996, 0.872677996, 0.872677996, 0.872677996, -0.745355992, -0.745355992, -0.745355992, -0.745355992 ],
[ 0.666666667, 0.666666667, -0.666666667, -0.666666667, -0.666666667, -0.666666667, 0.666666667, 0.666666667, 0, 0, 0, 0, 0, 0, 0, 0, 0.666666667, -0.666666667, -0.666666667, 0.666666667 ],]);
// -- test... should return identity matrix
soa_a20_encoder_matrix.mulMatrix(soa_a20_decoder_matrix)
)
/*
1st-order FuMa-MaxN A-format decoder
*/
(
var cart, spher, foa_a20_decoder_matrix;
// directions
// the original coordinates, in cartesian
cart = [
0.57735026918962576449,
0.57735026918962576449,
0.57735026918962576449,
0.57735026918962576449,
0.57735026918962576449,
-0.57735026918962576449,
0.57735026918962576449,
-0.57735026918962576449,
0.57735026918962576449,
-0.57735026918962576449,
0.57735026918962576449,
0.57735026918962576449,
0.57735026918962576449,
-0.57735026918962576449,
-0.57735026918962576449,
-0.57735026918962576449,
0.57735026918962576449,
-0.57735026918962576449,
-0.57735026918962576449,
-0.57735026918962576449,
0.57735026918962576449,
-0.57735026918962576449,
-0.57735026918962576449,
-0.57735026918962576449,
0,
0.356822089773089932,
0.934172358962715698,
0,
-0.356822089773089932,
0.934172358962715698,
0,
0.356822089773089932,
-0.934172358962715698,
0,
-0.356822089773089932,
-0.934172358962715698,
0.934172358962715698,
0,
0.356822089773089932,
0.934172358962715698,
0,
-0.356822089773089932,
-0.934172358962715698,
0,
0.356822089773089932,
-0.934172358962715698,
0,
-0.356822089773089932,
0.356822089773089932,
0.934172358962715698,
0,
-0.356822089773089932,
0.934172358962715698,
0,
0.356822089773089932,
-0.934172358962715698,
0,
-0.356822089773089932,
-0.934172358962715698,
0,
];
// 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_a20_decoder_matrix = FoaEncoderMatrix.newDirections(spher).matrix.pseudoInverse;
)
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