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#1
August 9th, 2008, 05:59 PM
 paulscode
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Location: Fort Meade, MD
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3D sound, calculating pan

Anyone out there good with 3D math? Unfortunately, I am definitely not.

I need a formula to calculate pan, a value between -1 and 1.

-1 is full sound on left speaker
0 is equal sound on both speakers
1 is full sound on right speaker

Given values are:
The source's 3D position
The listener's 3D position
The "look-at" direction (a normal vector)
The "up" direction (also normal)

Any help with this would be greatly appreciated. I know a number of computer languages, so it doesn't matter what language you write in, I am mainly just looking for the math.

#2
August 22nd, 2008, 04:02 AM
 disablek
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I'm not sure that there are any free algorithms for placement of sounds in a 3D space for stereo, it'd be really great to know if you've found any, but there are the usual panning laws for placing sound in stereo. Just google for those.

#3
August 22nd, 2008, 04:04 AM
 disablek
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Oh in which case just project your sound in 3D space to the horizontal plane of the camera and use those panning laws.

#4
August 31st, 2008, 12:59 PM
 paulscode
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Solution

For anyone who is interested, I found a couple of friendly mathematicians who helped me come up with the following formula (written in Java):

Code:
```side = listenerUpVector.cross( listenerLookAtVector );
side.normalize();

float x = sourcePositionVector.dot( sourcePositionVector.subtract( listenerPositionVector ), side );

float z = sourcePositionVector.dot( sourcePositionVector.subtract( listenerPositionVector ), listenerLookAtVector );

float angle = (float) Math.atan2( x, z );

pan = (float) - Math.sin( angle );```

The above code uses the following Vector3D class:
Code:
```public class Vector3D
{

/**
* The vector's X coordinate.
*/
public float x;

/**
* The vector's Y coordinate.
*/
public float y;

/**
* The vector's Z coordinate.
*/
public float z;

/**
* Constructor:  Places the vector at the origin.
*/
public Vector3D()
{
x = 0.0f;
y = 0.0f;
z = 0.0f;
}

/**
* Constructor:  Places the vector at the specified 3D coordinates.
* @param nx X coordinate for the new vector.
* @param ny Y coordinate for the new vector.
* @param nz Z coordinate for the new vector.
*/
public Vector3D( float nx, float ny, float nz )
{
x = nx;
y = ny;
z = nz;
}

/**
* Returns a new instance containing the same information as this one.
* @return A new Vector3D.
*/
@Override
public Vector3D clone()
{
return new Vector3D( x, y, z );
}

/**
* Returns a vector containing the cross-product: A cross B.
* @param A First vector in the cross product.
* @param B Second vector in the cross product.
* @return A new Vector3D.
*/
public Vector3D cross( Vector3D A, Vector3D B )
{
return new Vector3D(
A.y * B.z - B.y * A.z,
A.z * B.x - B.z * A.x,
A.x * B.y - B.x * A.y );
}

/**
* Returns a vector containing the cross-product: (this) cross B.
* @param B Second vector in the cross product.
* @return A new Vector3D.
*/
public Vector3D cross( Vector3D B )
{
return new Vector3D(
y * B.z - B.y * z,
z * B.x - B.z * x,
x * B.y - B.x * y );

}

/**
* Returns the dot-product result of: A dot B.
* @param A First vector in the dot product.
* @param B Second vector in the dot product.
* @return Dot product.
*/
public float dot( Vector3D A, Vector3D B )
{
return( (A.x * B.x) + (A.y * B.y) + (A.z * B.z) );
}

/**
* Returns the dot-product result of: (this) dot B.
* @param B Second vector in the dot product.
* @return Dot product.
*/
public float dot( Vector3D B )
{
return( (x * B.x) + (y * B.y) + (z * B.z) );
}

/**
* Returns the vector represented by: A + B.
* @param A First vector.
* @param B Vector to add to A.
* @return A new Vector3D.
*/
public Vector3D add( Vector3D A, Vector3D B )
{
return new Vector3D( A.x + B.x, A.y + B.y, A.z + B.z );
}

/**
* Returns the vector represented by: (this) + B.
* @param B Vector to add to this one.
* @return A new Vector3D.
*/
public Vector3D add( Vector3D B )
{
return new Vector3D( x + B.x, y + B.y, z + B.z );
}

/**
* Returns the vector represented by: A - B.
* @param A First vector.
* @param B Vector to subtract from A.
* @return A new Vector3D.
*/
public Vector3D subtract( Vector3D A, Vector3D B )
{
return new Vector3D( A.x - B.x, A.y - B.y, A.z - B.z );
}

/**
* Returns the vector represented by: (this) - B.
* @param B Vector to subtract from this one.
* @return A new Vector3D.
*/
public Vector3D subtract( Vector3D B )
{
return new Vector3D( x - B.x, y - B.y, z - B.z );
}

/**
* Changes the length of this vector to 1.0.
*/
public void normalize()
{
double t = Math.sqrt( x*x + y*y + z*z );
x = (float) (x / t);
y = (float) (y / t);
z = (float) (z / t);
}
}```

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