Use an ambisonics-based panning method

For mono sources, third-order ambisonics is utilized to generate panning gains.
The general idea is that a panned mono sound can be encoded into b-format
ambisonics as:

w[i] = sample[i] * 0.7071;
x[i] = sample[i] * dir[0];
y[i] = sample[i] * dir[1];
...

and subsequently rendered using:

output[chan][i] = w[i] * w_coeffs[chan] +
                  x[i] * x_coeffs[chan] +
                  y[i] * y_coeffs[chan] +
                  ...;

By reordering the math, channel gains can be generated by doing:

gain[chan] = 0.7071 * w_coeffs[chan] +
             dir[0] * x_coeffs[chan] +
             dir[1] * y_coeffs[chan] +
             ...;

which then get applied as normal:

output[chan][i] = sample[i] * gain[chan];

One of the reasons to use ambisonics for panning is that it provides arguably
better reproduction for sounds emanating from between two speakers. As well,
this makes it easier to pan in all 3 dimensions, with for instance a "3D7.1" or
8-channel cube speaker configuration by simply providing the necessary
coefficients (this will need some work since some methods still use angle-based
panpot, particularly multi-channel sources).

Unfortunately, the math to reliably generate the coefficients for a given
speaker configuration is too costly to do at run-time. They have to be pre-
generated based on a pre-specified speaker arangement, which means the config
options for tweaking speaker angles are no longer supportable. Eventually I
hope to provide config options for custom coefficients, which can either be
generated and written in manually, or via alsoft-config from user-specified
speaker positions.

The current default set of coefficients were generated using the MATLAB scripts
(compatible with GNU Octave) from the excellent Ambisonic Decoder Toolbox, at
https://bitbucket.org/ambidecodertoolbox/adt/

1 files changed, 110 insertions, 115 deletions

diff --git a/Alc/panning.c b/Alc/panning.c
index a3f6d09a..d0c89071 100644
--- a/Alc/panning.c
+++ b/Alc/panning.c
@@ -33,111 +33,51 @@
 
 extern inline void SetGains(const ALCdevice *device, ALfloat ingain, ALfloat gains[MaxChannels]);
 
-static void SetSpeakerArrangement(const char *name, ALCdevice *device)
-{
-    char *confkey, *next;
-    char *layout_str;
-    char *sep, *end;
-    enum Channel val;
-    const char *str;
-    ALuint i;
-
-    if(!ConfigValueStr(NULL, name, &str) && !ConfigValueStr(NULL, "layout", &str))
-        return;
-
-    layout_str = strdup(str);
-    next = confkey = layout_str;
-    while(next && *next)
-    {
-        confkey = next;
-        next = strchr(confkey, ',');
-        if(next)
-        {
-            *next = 0;
-            do {
-                next++;
-            } while(isspace(*next) || *next == ',');
-        }
-
-        sep = strchr(confkey, '=');
-        if(!sep || confkey == sep)
-        {
-            ERR("Malformed speaker key: %s\n", confkey);
-            continue;
-        }
-
-        end = sep - 1;
-        while(isspace(*end) && end != confkey)
-            end--;
-        *(++end) = 0;
-
-        if(strcmp(confkey, "fl") == 0 || strcmp(confkey, "front-left") == 0)
-            val = FrontLeft;
-        else if(strcmp(confkey, "fr") == 0 || strcmp(confkey, "front-right") == 0)
-            val = FrontRight;
-        else if(strcmp(confkey, "fc") == 0 || strcmp(confkey, "front-center") == 0)
-            val = FrontCenter;
-        else if(strcmp(confkey, "bl") == 0 || strcmp(confkey, "back-left") == 0)
-            val = BackLeft;
-        else if(strcmp(confkey, "br") == 0 || strcmp(confkey, "back-right") == 0)
-            val = BackRight;
-        else if(strcmp(confkey, "bc") == 0 || strcmp(confkey, "back-center") == 0)
-            val = BackCenter;
-        else if(strcmp(confkey, "sl") == 0 || strcmp(confkey, "side-left") == 0)
-            val = SideLeft;
-        else if(strcmp(confkey, "sr") == 0 || strcmp(confkey, "side-right") == 0)
-            val = SideRight;
-        else
-        {
-            ERR("Unknown speaker for %s: \"%s\"\n", name, confkey);
-            continue;
-        }
-
-        *(sep++) = 0;
-        while(isspace(*sep))
-            sep++;
-
-        for(i = 0;i < device->NumSpeakers;i++)
-        {
-            if(device->Speaker[i].ChanName == val)
-            {
-                long angle = strtol(sep, NULL, 10);
-                if(angle >= -180 && angle <= 180)
-                    device->Speaker[i].Angle = DEG2RAD(angle);
-                else
-                    ERR("Invalid angle for speaker \"%s\": %ld\n", confkey, angle);
-                break;
-            }
-        }
-    }
-    free(layout_str);
-    layout_str = NULL;
-
-    for(i = 0;i < device->NumSpeakers;i++)
-    {
-        ALuint min = i;
-        ALuint i2;
 
-        for(i2 = i+1;i2 < device->NumSpeakers;i2++)
-        {
-            if(device->Speaker[i2].Angle < device->Speaker[min].Angle)
-                min = i2;
-        }
+static inline void Set0thOrder(ALfloat coeffs[16], ALfloat w)
+{
+    coeffs[0] = w;
+}
 
-        if(min != i)
-        {
-            ALfloat tmpf;
-            enum Channel tmpc;
+static inline void Set1stOrder(ALfloat coeffs[16], ALfloat w, ALfloat x, ALfloat y, ALfloat z)
+{
+    coeffs[0] = w;
+    coeffs[1] = x;
+    coeffs[2] = y;
+    coeffs[3] = z;
+}
 
-            tmpf = device->Speaker[i].Angle;
-            device->Speaker[i].Angle = device->Speaker[min].Angle;
-            device->Speaker[min].Angle = tmpf;
+static inline void Set2ndOrder(ALfloat coeffs[16], ALfloat w, ALfloat x, ALfloat y, ALfloat z, ALfloat r, ALfloat s, ALfloat t, ALfloat u, ALfloat v)
+{
+    coeffs[0] = w;
+    coeffs[1] = x;
+    coeffs[2] = y;
+    coeffs[3] = z;
+    coeffs[4] = r;
+    coeffs[5] = s;
+    coeffs[6] = t;
+    coeffs[7] = u;
+    coeffs[8] = v;
+}
 
-            tmpc = device->Speaker[i].ChanName;
-            device->Speaker[i].ChanName = device->Speaker[min].ChanName;
-            device->Speaker[min].ChanName = tmpc;
-        }
-    }
+static inline void Set3rdOrder(ALfloat coeffs[16], ALfloat w, ALfloat x, ALfloat y, ALfloat z, ALfloat r, ALfloat s, ALfloat t, ALfloat u, ALfloat v, ALfloat k, ALfloat l, ALfloat m, ALfloat n, ALfloat o, ALfloat p, ALfloat q)
+{
+    coeffs[0] = w;
+    coeffs[1] = x;
+    coeffs[2] = y;
+    coeffs[3] = z;
+    coeffs[4] = r;
+    coeffs[5] = s;
+    coeffs[6] = t;
+    coeffs[7] = u;
+    coeffs[8] = v;
+    coeffs[9] = k;
+    coeffs[10] = l;
+    coeffs[11] = m;
+    coeffs[12] = n;
+    coeffs[13] = o;
+    coeffs[14] = p;
+    coeffs[15] = q;
 }
 
 
@@ -155,12 +95,13 @@ void ComputeAngleGains(const ALCdevice *device, ALfloat angle, ALfloat hwidth, A
     for(i = 0;i < device->NumSpeakers;i++)
         SpeakerAngle[i] = device->Speaker[i].Angle;
 
+    for(i = 0;i < MaxChannels;i++)
+        gains[i] = 0.0f;
+
     /* Some easy special-cases first... */
     if(device->NumSpeakers <= 1 || hwidth >= F_PI)
     {
         /* Full coverage for all speakers. */
-        for(i = 0;i < MaxChannels;i++)
-            gains[i] = 0.0f;
         for(i = 0;i < device->NumSpeakers;i++)
         {
             enum Channel chan = Speaker2Chan[i];
@@ -171,8 +112,6 @@ void ComputeAngleGains(const ALCdevice *device, ALfloat angle, ALfloat hwidth, A
     if(hwidth <= 0.0f)
     {
         /* Infinitely small sound point. */
-        for(i = 0;i < MaxChannels;i++)
-            gains[i] = 0.0f;
         for(i = 0;i < device->NumSpeakers-1;i++)
         {
             if(angle >= SpeakerAngle[i] && angle < SpeakerAngle[i+1])
@@ -338,10 +277,45 @@ void ComputeAngleGains(const ALCdevice *device, ALfloat angle, ALfloat hwidth, A
     }
 }
 
+void ComputeDirectionalGains(const ALCdevice *device, const ALfloat dir[3], ALfloat ingain, ALfloat gains[MaxChannels])
+{
+    ALfloat coeffs[MAX_AMBI_COEFFS];
+    ALuint i, j;
+
+    /* Convert from OpenAL coords to Ambisonics. */
+    coeffs[0] = 0.7071f; /* sqrt(1.0 / 2.0) */
+    coeffs[1] = -dir[2]; /* X */
+    coeffs[2] = -dir[0]; /* Y */
+    coeffs[3] =  dir[1]; /* Z */
+    coeffs[4] = 0.5f * (3.0f*dir[1]*dir[1] - 1.0f); /* 0.5 * (3*Z*Z - 1) */
+    coeffs[5] = 2.0f *  dir[1] * -dir[2]; /* 2*Z*X */
+    coeffs[6] = 2.0f * -dir[0] *  dir[1]; /* 2*Y*Z */
+    coeffs[7] = dir[2]*dir[2] - dir[0]*dir[0]; /* X*X - Y*Y */
+    coeffs[8] = 2.0f * -dir[2] * -dir[0]; /* 2*X*Y */
+    coeffs[9] = 0.5f *  dir[1] * (5.0f*dir[1]*dir[1] - 3.0f); /* 0.5 * Z * (5*Z*Z - 3) */
+    coeffs[10] = 0.7262f * -dir[2] * (5.0f*dir[1]*dir[1] - 1.0f); /* sqrt(135.0 / 256.0) * X * (5*Z*Z - 1) */
+    coeffs[11] = 0.7262f * -dir[0] * (5.0f*dir[1]*dir[1] - 1.0f); /* sqrt(135.0 / 256.0) * Y * (5*Z*Z - 1) */
+    coeffs[12] = 2.5981f *  dir[1] * (dir[2]*dir[2] - dir[0]*dir[0]); /* sqrt(27.0 / 4.0) * Z * (X*X - Y*Y) */
+    coeffs[13] = 5.1962f * -dir[2] * -dir[0] * dir[1]; /* sqrt(27) * X * Y * Z */
+    coeffs[14] = -dir[2] * (dir[2]*dir[2] - 3.0f*dir[0]*dir[0]); /* X * (X*X - 3*Y*Y) */
+    coeffs[15] = -dir[0] * (3.0f*dir[2]*dir[2] - dir[0]*dir[0]); /* Y * (3*X*X - Y*Y) */
+
+    for(i = 0;i < MaxChannels;i++)
+        gains[i] = 0.0f;
+    for(i = 0;i < device->NumSpeakers;i++)
+    {
+        enum Channel chan = device->Speaker[i].ChanName;
+        for(j = 0;j < MAX_AMBI_COEFFS;j++)
+            gains[chan] += device->Speaker[i].Coeff[j]*coeffs[j];
+        gains[chan] = maxf(gains[chan], 0.0f) * ingain;
+    }
+}
+
 
 ALvoid aluInitPanning(ALCdevice *device)
 {
-    const char *layoutname = NULL;
+    memset(device->Speaker, 0, sizeof(device->Speaker));
+    device->NumSpeakers = 0;
 
     switch(device->FmtChans)
     {
@@ -349,7 +323,7 @@ ALvoid aluInitPanning(ALCdevice *device)
             device->NumSpeakers = 1;
             device->Speaker[0].ChanName = FrontCenter;
             device->Speaker[0].Angle = DEG2RAD(0.0f);
-            layoutname = NULL;
+            Set0thOrder(device->Speaker[0].Coeff, 1.4142f);
             break;
 
         case DevFmtStereo:
@@ -358,7 +332,8 @@ ALvoid aluInitPanning(ALCdevice *device)
             device->Speaker[1].ChanName = FrontRight;
             device->Speaker[0].Angle = DEG2RAD(-90.0f);
             device->Speaker[1].Angle = DEG2RAD( 90.0f);
-            layoutname = "layout_stereo";
+            Set1stOrder(device->Speaker[0].Coeff, 0.7071f, -0.5f, 0.0f, 0.0f);
+            Set1stOrder(device->Speaker[1].Coeff, 0.7071f,  0.5f, 0.0f, 0.0f);
             break;
 
         case DevFmtQuad:
@@ -371,7 +346,10 @@ ALvoid aluInitPanning(ALCdevice *device)
             device->Speaker[1].Angle = DEG2RAD( -45.0f);
             device->Speaker[2].Angle = DEG2RAD(  45.0f);
             device->Speaker[3].Angle = DEG2RAD( 135.0f);
-            layoutname = "layout_quad";
+            Set2ndOrder(device->Speaker[0].Coeff, 0.353543f, -0.306192f,  0.306181f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.117193f);
+            Set2ndOrder(device->Speaker[1].Coeff, 0.353558f,  0.306181f,  0.306192f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.117183f);
+            Set2ndOrder(device->Speaker[2].Coeff, 0.353543f,  0.306181f, -0.306192f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.117193f);
+            Set2ndOrder(device->Speaker[3].Coeff, 0.353558f, -0.306192f, -0.306181f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.117183f);
             break;
 
         case DevFmtX51:
@@ -386,7 +364,11 @@ ALvoid aluInitPanning(ALCdevice *device)
             device->Speaker[2].Angle = DEG2RAD(   0.0f);
             device->Speaker[3].Angle = DEG2RAD(  30.0f);
             device->Speaker[4].Angle = DEG2RAD( 110.0f);
-            layoutname = "layout_surround51";
+            Set3rdOrder(device->Speaker[0].Coeff, 0.470934f, -0.369630f,  0.349383f, 0.0f, 0.0f, 0.0f, 0.0f, -0.031379f, -0.058143f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.007116f, -0.043968f);
+            Set3rdOrder(device->Speaker[1].Coeff, 0.208954f,  0.212846f,  0.238350f, 0.0f, 0.0f, 0.0f, 0.0f, -0.017738f,  0.204014f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.051023f,  0.047490f);
+            Set3rdOrder(device->Speaker[2].Coeff, 0.109403f,  0.179490f, -0.000002f, 0.0f, 0.0f, 0.0f, 0.0f,  0.142031f, -0.000002f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.072024f, -0.000001f);
+            Set3rdOrder(device->Speaker[3].Coeff, 0.208950f,  0.212842f, -0.238350f, 0.0f, 0.0f, 0.0f, 0.0f, -0.017740f, -0.204011f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.051022f, -0.047489f);
+            Set3rdOrder(device->Speaker[4].Coeff, 0.470936f, -0.369626f, -0.349386f, 0.0f, 0.0f, 0.0f, 0.0f, -0.031375f,  0.058144f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.007119f,  0.043968f);
             break;
 
         case DevFmtX51Side:
@@ -401,7 +383,11 @@ ALvoid aluInitPanning(ALCdevice *device)
             device->Speaker[2].Angle = DEG2RAD(  0.0f);
             device->Speaker[3].Angle = DEG2RAD( 30.0f);
             device->Speaker[4].Angle = DEG2RAD( 90.0f);
-            layoutname = "layout_side51";
+            Set3rdOrder(device->Speaker[0].Coeff, 0.289151f, -0.081301f,  0.401292f, 0.0f, 0.0f, 0.0f, 0.0f, -0.188208f, -0.071420f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.010099f, -0.032897f);
+            Set3rdOrder(device->Speaker[1].Coeff, 0.167065f,  0.200583f,  0.172695f, 0.0f, 0.0f, 0.0f, 0.0f,  0.029855f,  0.186407f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.039241f,  0.068910f);
+            Set3rdOrder(device->Speaker[2].Coeff, 0.109403f,  0.179490f, -0.000002f, 0.0f, 0.0f, 0.0f, 0.0f,  0.142031f, -0.000002f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.072024f, -0.000001f);
+            Set3rdOrder(device->Speaker[3].Coeff, 0.167058f,  0.200580f, -0.172701f, 0.0f, 0.0f, 0.0f, 0.0f,  0.029846f, -0.186405f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.039241f, -0.068904f);
+            Set3rdOrder(device->Speaker[4].Coeff, 0.289157f, -0.081298f, -0.401295f, 0.0f, 0.0f, 0.0f, 0.0f, -0.188208f,  0.071419f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.010099f,  0.032897f);
             break;
 
         case DevFmtX61:
@@ -418,7 +404,12 @@ ALvoid aluInitPanning(ALCdevice *device)
             device->Speaker[3].Angle = DEG2RAD( 30.0f);
             device->Speaker[4].Angle = DEG2RAD( 90.0f);
             device->Speaker[5].Angle = DEG2RAD(180.0f);
-            layoutname = "layout_surround61";
+            Set3rdOrder(device->Speaker[0].Coeff, 0.289151f, -0.081301f,  0.401292f, 0.0f, 0.0f, 0.0f, 0.0f, -0.188208f, -0.071420f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.010099f, -0.032897f);
+            Set3rdOrder(device->Speaker[1].Coeff, 0.167065f,  0.200583f,  0.172695f, 0.0f, 0.0f, 0.0f, 0.0f,  0.029855f,  0.186407f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.039241f,  0.068910f);
+            Set3rdOrder(device->Speaker[2].Coeff, 0.109403f,  0.179490f, -0.000002f, 0.0f, 0.0f, 0.0f, 0.0f,  0.142031f, -0.000002f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.072024f, -0.000001f);
+            Set3rdOrder(device->Speaker[3].Coeff, 0.167058f,  0.200580f, -0.172701f, 0.0f, 0.0f, 0.0f, 0.0f,  0.029846f, -0.186405f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.039241f, -0.068904f);
+            Set3rdOrder(device->Speaker[4].Coeff, 0.289157f, -0.081298f, -0.401295f, 0.0f, 0.0f, 0.0f, 0.0f, -0.188208f,  0.071419f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.010099f,  0.032897f);
+            Set3rdOrder(device->Speaker[5].Coeff, 0.353556f, -0.461940f, -0.000006f, 0.0f, 0.0f, 0.0f, 0.0f,  0.165723f, -0.000000f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.000000f,  0.000005f);
             break;
 
         case DevFmtX71:
@@ -437,9 +428,13 @@ ALvoid aluInitPanning(ALCdevice *device)
             device->Speaker[4].Angle = DEG2RAD(  30.0f);
             device->Speaker[5].Angle = DEG2RAD(  90.0f);
             device->Speaker[6].Angle = DEG2RAD( 150.0f);
-            layoutname = "layout_surround71";
+            Set3rdOrder(device->Speaker[0].Coeff, 0.224752f, -0.295009f,  0.170325f, 0.0f, 0.0f, 0.0f, 0.0f,  0.105349f, -0.182473f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.000000f,  0.065799f);
+            Set3rdOrder(device->Speaker[1].Coeff, 0.224739f,  0.000002f,  0.340644f, 0.0f, 0.0f, 0.0f, 0.0f, -0.210697f,  0.000002f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.000000f, -0.065795f);
+            Set3rdOrder(device->Speaker[2].Coeff, 0.167065f,  0.200583f,  0.172695f, 0.0f, 0.0f, 0.0f, 0.0f,  0.029855f,  0.186407f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.039241f,  0.068910f);
+            Set3rdOrder(device->Speaker[3].Coeff, 0.109403f,  0.179490f, -0.000002f, 0.0f, 0.0f, 0.0f, 0.0f,  0.142031f, -0.000002f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.072024f, -0.000001f);
+            Set3rdOrder(device->Speaker[4].Coeff, 0.167058f,  0.200580f, -0.172701f, 0.0f, 0.0f, 0.0f, 0.0f,  0.029846f, -0.186405f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.039241f, -0.068904f);
+            Set3rdOrder(device->Speaker[5].Coeff, 0.224754f,  0.000004f, -0.340647f, 0.0f, 0.0f, 0.0f, 0.0f, -0.210697f, -0.000004f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.000000f,  0.065796f);
+            Set3rdOrder(device->Speaker[6].Coeff, 0.224739f, -0.295005f, -0.170331f, 0.0f, 0.0f, 0.0f, 0.0f,  0.105342f,  0.182470f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.000000f, -0.065792f);
             break;
     }
-    if(layoutname && device->Type != Loopback)
-        SetSpeakerArrangement(layoutname, device);
 }