/// <summary>
/// Interpolates between two quaternions, using spherical linear interpolation
/// </summary>
/// <param name="start">Start quaternion</param>
/// <param name="end">End quaternion</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/></param>
/// <returns>The spherical linear interpolation of the two quaternions</returns>
public static Quaternion Slerp(Quaternion start, Quaternion end, float amount)
{
float opposite;
float inverse;
float dot = DotProduct(start, end);
if (Mathematics.Abs(dot) > 1f - 0f)
{
inverse = 1f - amount;
opposite = amount * Mathematics.Sign(dot);
}
else
{
float acos = Mathematics.Acos(Mathematics.Abs(dot));
float invSin = (float)(1f / Mathematics.Sin(acos));
inverse = Mathematics.Sin((1f - amount) * acos) * invSin;
opposite = Mathematics.Sin(amount * acos) * invSin * Mathematics.Sign(dot);
}
return(new Quaternion(
(inverse * start.X) + (opposite * end.X),
(inverse * start.Y) + (opposite * end.Y),
(inverse * start.Z) + (opposite * end.Z),
(inverse * start.W) + (opposite * end.W)
));
}
/// <summary>
/// Calculates the natural logarithm of the specified quaternion
/// </summary>
/// <param name="value">The quaternion whose logarithm will be calculated</param>
/// <returns>The natural logarithm of the quaternion</returns>
public static Quaternion Logarithm(Quaternion value)
{
Quaternion result = new Quaternion();
if (Mathematics.Abs(value.W) < 1f)
{
float angle = Mathematics.Acos(value.W);
float sin = Mathematics.Sin(angle);
if (Mathematics.Abs(sin) >= 0f)
{
float coeff = angle / sin;
result.X = value.X * coeff;
result.Y = value.Y * coeff;
result.Z = value.Z * coeff;
}
else
{
result = value;
}
}
else
{
result = value;
}
result.W = 0f;
return(result);
}
/// <summary>
/// Exponentiates a quaternion
/// </summary>
/// <param name="value">The quaternion to exponentiate</param>
/// <returns>The exponentiated quaternion</returns>
public static Quaternion Exponential(Quaternion value)
{
Quaternion result = new Quaternion();
float angle = Mathematics.Sqrt((value.X * value.X) + (value.Y * value.Y) + (value.Z * value.Z));
float sin = Mathematics.Sin(angle);
if (Mathematics.Abs(sin) >= 0f)
{
float coeff = sin / angle;
result.X = coeff * value.X;
result.Y = coeff * value.Y;
result.Z = coeff * value.Z;
}
else
{
result = value;
}
result.W = Mathematics.Cos(angle);
return(result);
}
/// <summary> /// Get's a value indicting whether this instance is normalized /// </summary> public bool IsNormalized() => Mathematics.Abs(X * X + Y * Y + Z * Z + W * W - 1f) < 0f;