Math extensions

// EXTENDED MATH FUNCTIONS
// Converts from degrees to radians.
Math.radians = function(degrees)
{
    return degrees * Math.PI / 180;
};

// Converts from radians to degrees.
Math.degrees = function(radians)
{
    return radians * 180 / Math.PI;
};

// Converts from Axis Angle in radians to Euler in degrees
Math.AxisAngleToEuler = function(x, y, z, angle)
{
    var heading,attitude,bank;
    var s=Math.sin(angle);
    var c=Math.cos(angle);
    var t=1-c;
    //  if axis is not already normalised then uncomment this
    // double magnitude = Math.sqrt(x*x + y*y + z*z);
    // if (magnitude==0) throw error;
    // x /= magnitude;
    // y /= magnitude;
    // z /= magnitude;
    if ((x*y*t + z*s) > 0.998)
    { // north pole singularity detected
        heading     = 2*atan2(x*Math.sin(angle/2),Math.cos(angle/2));
        attitude    = Math.PI/2;
        bank            = 0;
    }
    else if ((x*y*t + z*s) < -0.998)
    { // south pole singularity detected
        heading     = -2*atan2(x*Math.sin(angle/2),Math.cos(angle/2));
        attitude    = -Math.PI/2;
        bank            = 0;
    }
    else
    {
        heading     = Math.atan2(y * s- x * z * t , 1 - (y*y+ z*z ) * t);
        attitude    = Math.asin(x * y * t + z * s) ;
        bank            = Math.atan2(x * s - y * z * t , 1 - (x*x + z*z) * t);
    }

    return {'x':Math.degrees(bank),'y':Math.degrees(heading),'z':Math.degrees(attitude)};
};

// Converts from Euler in degrees to Axis Angle in radians
Math.EulerToAxisAngle = function(bankDegrees, headingDegrees, attitudeDegrees)
{
    var Xradians    = Math.radians(bankDegrees); // bank
    var Yradians    = Math.radians(headingDegrees); // heading
    var Zradians    = Math.radians(attitudeDegrees); // attitude

    // Convert Euler to Axis-Angle
    // NWN appears to use an axis angle
    // downloaded from http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToAngle/
    var c1 = Math.cos(Yradians/2); // heading
    var s1 = Math.sin(Yradians/2);
    var c2 = Math.cos(Zradians/2);// altitude
    var s2 = Math.sin(Zradians/2);
    var c3 = Math.cos(Xradians/2); // bank
    var s3 = Math.sin(Xradians/2);
    var c1c2 = c1*c2;
    var s1s2 = s1*s2;
    var w =c1c2*c3 - s1s2*s3;
    var x =c1c2*s3 + s1s2*c3;
    var y =s1*c2*c3 + c1*s2*s3;
    var z =c1*s2*c3 - s1*c2*s3;
            w = 2 * Math.acos(w);
    var norm = x*x+y*y+z*z;
    if( norm==0 || norm <= 0.0001)
    { // when all euler angles are zero angle = 0 so
        // we can set axis to anything to avoid divide by zero
        x="1.0";
        y=z="0.0";
    }
    else
    {
        norm = Math.sqrt(norm);
        x = (x/norm);
        y = (y/norm);
        z = (z/norm);
    }

    return {'x':x,'y':y,'z':z,'w':w};
};