diff --git a/README.md b/README.md
index 90600a8..f3af5ca 100644
--- a/README.md
+++ b/README.md
@@ -2,13 +2,14 @@
##### Version :
-Hoa.lib 1.1 for Faust (Download). The hoa.lib file contains the high order ambisonics functions in FAUST. This file should already be included in the last FAUST distribution. You just need to include hoa.lib before coding to use it.
+Hoa.lib 1.3 for Faust (Download). The hoa.lib file contains the high order ambisonics functions in FAUST. This version isn't included in the Faust distribution (for now).
+Home of the project : https://framagit.org/wargreen/hoalibrary-faust
##### Authors :
-Julien Colafrancesco, Pierre Guillot, Eliott Paris
+Julien Colafrancesco, Pierre Guillot, Eliott Paris, Wargreen
##### Licence :
@@ -30,3 +31,6 @@ The hoa.library in under the p = 1
+ // If l = m => p = -1 * (2 * (l-1) + 1) * sqrt(1 - cphi*cphi) * p(l-1, l-1, cphi)
+ // If l = m+1 => p = phi * (2 * (l-1) + 1) * p(l-1, l-1, cphi)
+ // Else => p = (cphi * (2 * (l-1) + 1) * p(l-1, abs(m), cphi) - ((l-1) + abs(m)) * p(l-2, abs(m), cphi)) / ((l-1) - abs(m) + 1)
+ p(l, m, cphi) = pcalcul(((l != 0) & (l == abs(m))) + ((l != 0) & (l == abs(m)+1)) * 2 + ((l != 0) & (l != abs(m)) & (l != abs(m)+1)) * 3, l, m, cphi)
+ with
+ {
+ pcalcul(0, l, m, cphi) = 1;
+ pcalcul(1, l, m, cphi) = -1 * (2 * (l-1) + 1) * sqrt(1 - cphi*cphi) * p(l-1, l-1, cphi);
+ pcalcul(2, l, m, cphi) = cphi * (2 * (l-1) + 1) * p(l-1, l-1, cphi);
+ pcalcul(s, l, m, cphi) = (cphi * (2 * (l-1) + 1) * p(l-1, abs(m), cphi) - ((l-1) + abs(m)) * p(l-2, abs(m), cphi)) / ((l-1) - abs(m) + 1);
+ };
+
+ // The exponential imaginary
+ // If m > 0 => e^i*m*theta = cos(m * theta)
+ // If m < 0 => e^i*m*theta = sin(-m * theta)
+ // If m = 0 => e^i*m*theta = 1
+ e(m, theta) = ecalcul((m > 0) * 2 + (m < 0), m, theta)
+ with
+ {
+ ecalcul(2, m, theta) = cos(m * theta);
+ ecalcul(1, m, theta) = sin(abs(m) * theta);
+ ecalcul(s, m, theta) = 1;
+ };
+
+ // The normalization
+ // If m = 0 => k(l, m) = 1
+ // If m != 0 => k(l, m) = sqrt((l - abs(m))! / l + abs(m))!) * sqrt(2)
+ k(l, m) = kcalcul((m != 0), l, m)
+ with
+ {
+ kcalcul(0, l, m) = 1;
+ kcalcul(1, l, m) = sqrt(fact(l - abs(m)) / fact(l + abs(m))) * sqrt(2)
+ with
+ {
+ fact(0) = 1;
+ fact(n) = n * fact(n-1);
+ };
+ };
+
+
+ };
+};
+
+// Usage : n is the order, x the signal, theta and phi the angle of azimuth and elevation in radiant
+// Exemple : HoaEncoder3D(3, _, azimuth, elevation)
+// Informations : It encode the signal in a 3D
+
+
+//----------------------- 3D basic optimisation ------------------------------//
+
+optimBasic3D(N) = par(i, (N+1) * (N+1), _);
+
+// Usage : n is the order
+// Exemple : optimBasic3D(3)
+// Informations : The basic optimization has no effect and should be used for a perfect circle of loudspeakers with one listener at the perfect center loudspeakers array.
+
+
+//----------------------------- 3D MaxRe -------------------------------------//
+
+optimMaxRe3D(N) = par(i, (N+1) * (N+1), MaxRe(N, degree(i), _))
+with
+{
+ // The degree l of the harmonic[l, m]
+ degree(index) = int(sqrt(index));
+ MaxRe(N, l, _)= _ * cos(l / (2*N+2) * PI);
+};
+
+// Usage : n is the order
+// Exemple : optimMaxRe3D(3)
+// Informations : The maxRe optimization optimize energy vector. It should be used for an auditory confined in the center of the loudspeakers array.
+
+
+//----------------------------3D inPhase--------------------------------------//
+
+optimInPhase3D(N) = par(i, (N+1) * (N+1), InPhase(N, degree(i), _))
+with
+{
+ // The degree l of the harmonic[l, m]
+ degree(index) = int(sqrt(index));
+ InPhase(N, l, _)= _ * (fact(N) * fact(N)) / (fact(N - l) * fact(N + l))
+ with
+ {
+ fact(0) = 1;
+ fact(n) = n * fact(n-1);
+ };
+};
+
+// Usage : n is the order
+// Exemple : optimInPhase3D(3)
+// Informations : The inPhase Optimization optimize energy vector and put all loudspeakers signals in phase. It should be used for an auditory
+
+