/// <summary>
/// Converts a quaternion to a euler angle.
/// https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
/// </summary>
/// <param name="quaternion">The quaternion to convert from.</param>
/// <returns>An euler angle.</returns>
public static FixVec3 ToEuler(FixQuaternion quaternion)
{
FixVec3 result;
Fix t0 = 2 * (quaternion.w * quaternion.z + quaternion.x * quaternion.y);
Fix t1 = Fix.one - (2 * (quaternion.y * quaternion.y + quaternion.z * quaternion.z));
result.z = FixMath.Atan2(t0, t1);
Fix t2 = 2 * (quaternion.w * quaternion.y - quaternion.z * quaternion.x);
if (t2 >= Fix.one)
{
result.y = FixMath.PI / 2;
}
else if (t2 <= -Fix.one)
{
result.y = -(FixMath.PI / 2);
}
else
{
result.y = FixMath.Asin(t2);
}
Fix t3 = 2 * (quaternion.w * quaternion.x + quaternion.y * quaternion.z);
Fix t4 = Fix.one - (2 * (quaternion.x * quaternion.x + quaternion.y * quaternion.y));
result.x = FixMath.Atan2(t3, t4);
return(result);
}
public void AsinAverageDeviationTest()
{
var totalDiff = 0.0;
var maxDiff = double.MinValue;
for (var i = 0; i < 1000; i++)
{
var fixValue = Fix.Ratio(i, 1000);
var doubleValue = i / 1000.0;
var diff = Math.Abs((double)FixMath.Asin(fixValue) - Math.Asin(doubleValue));
totalDiff += diff;
maxDiff = Math.Max(maxDiff, Math.Abs(diff));
}
// Max & Average deviation
FixAssert.AssertEquals(maxDiff, 0, 0.005f);
FixAssert.AssertEquals(totalDiff / 360, 0, 0.002f);
}