public SCNQuaternion(ref Matrix3 matrix)
{
double scale = System.Math.Pow(matrix.Determinant, 1.0d / 3.0d);
float x, y, z;
w = (float)(System.Math.Sqrt(System.Math.Max(0, scale + matrix[0, 0] + matrix[1, 1] + matrix[2, 2])) / 2);
x = (float)(System.Math.Sqrt(System.Math.Max(0, scale + matrix[0, 0] - matrix[1, 1] - matrix[2, 2])) / 2);
y = (float)(System.Math.Sqrt(System.Math.Max(0, scale - matrix[0, 0] + matrix[1, 1] - matrix[2, 2])) / 2);
z = (float)(System.Math.Sqrt(System.Math.Max(0, scale - matrix[0, 0] - matrix[1, 1] + matrix[2, 2])) / 2);
xyz = new Vector3(x, y, z);
if (matrix[2, 1] - matrix[1, 2] < 0)
{
X = -X;
}
if (matrix[0, 2] - matrix[2, 0] < 0)
{
Y = -Y;
}
if (matrix[1, 0] - matrix[0, 1] < 0)
{
Z = -Z;
}
}
/// <summary>
/// Convert the current quaternion to axis angle representation
/// </summary>
/// <param name="axis">The resultant axis</param>
/// <param name="angle">The resultant angle</param>
public void ToAxisAngle(out SCNVector3 axis, out pfloat angle)
{
SCNVector4 result = ToAxisAngle();
axis = result.Xyz;
angle = result.W;
}
/// <summary>
/// Build a quaternion from the given axis and angle
/// </summary>
/// <param name="axis">The axis to rotate about</param>
/// <param name="angle">The rotation angle in radians</param>
/// <returns></returns>
public static SCNQuaternion FromAxisAngle(SCNVector3 axis, float angle)
{
if (axis.LengthSquared == 0.0f)
{
return(Identity);
}
SCNQuaternion result = Identity;
angle *= 0.5f;
axis.Normalize();
result.Xyz = axis * (float)System.Math.Sin(angle);
result.W = (float)System.Math.Cos(angle);
return(Normalize(result));
}
/// <summary>
/// Construct a new SCNQuaternion from vector and w components
/// </summary>
/// <param name="v">The vector part</param>
/// <param name="w">The w part</param>
public SCNQuaternion(SCNVector3 v, pfloat w)
{
this.xyz = v;
this.w = w;
}
/// <summary>
/// Do Spherical linear interpolation between two quaternions
/// </summary>
/// <param name="q1">The first quaternion</param>
/// <param name="q2">The second quaternion</param>
/// <param name="blend">The blend factor</param>
/// <returns>A smooth blend between the given quaternions</returns>
public static SCNQuaternion Slerp(SCNQuaternion q1, SCNQuaternion q2, float blend)
{
// if either input is zero, return the other.
if (q1.LengthSquared == 0.0f)
{
if (q2.LengthSquared == 0.0f)
{
return(Identity);
}
return(q2);
}
else if (q2.LengthSquared == 0.0f)
{
return(q1);
}
pfloat cosHalfAngle = q1.W * q2.W + SCNVector3.Dot(q1.Xyz, q2.Xyz);
if (cosHalfAngle >= 1.0f || cosHalfAngle <= -1.0f)
{
// angle = 0.0f, so just return one input.
return(q1);
}
else if (cosHalfAngle < 0.0f)
{
q2.Xyz = -q2.Xyz;
q2.W = -q2.W;
cosHalfAngle = -cosHalfAngle;
}
float blendA;
float blendB;
if (cosHalfAngle < 0.99f)
{
// do proper slerp for big angles
float halfAngle = (float)System.Math.Acos(cosHalfAngle);
float sinHalfAngle = (float)System.Math.Sin(halfAngle);
float oneOverSinHalfAngle = 1.0f / sinHalfAngle;
blendA = (float)System.Math.Sin(halfAngle * (1.0f - blend)) * oneOverSinHalfAngle;
blendB = (float)System.Math.Sin(halfAngle * blend) * oneOverSinHalfAngle;
}
else
{
// do lerp if angle is really small.
blendA = 1.0f - blend;
blendB = blend;
}
SCNQuaternion result = new SCNQuaternion(blendA * q1.Xyz + blendB * q2.Xyz, blendA * q1.W + blendB * q2.W);
if (result.LengthSquared > 0.0f)
{
return(Normalize(result));
}
else
{
return(Identity);
}
}
/// <summary>
/// Multiplies two instances.
/// </summary>
/// <param name="left">The first instance.</param>
/// <param name="right">The second instance.</param>
/// <param name="result">A new instance containing the result of the calculation.</param>
public static void Multiply(ref SCNQuaternion left, ref SCNQuaternion right, out SCNQuaternion result)
{
result = new SCNQuaternion(
right.W * left.Xyz + left.W * right.Xyz + SCNVector3.Cross(left.Xyz, right.Xyz),
left.W * right.W - SCNVector3.Dot(left.Xyz, right.Xyz));
}
public static SCNQuaternion Mult(SCNQuaternion left, SCNQuaternion right)
{
return(new SCNQuaternion(
right.W * left.Xyz + left.W * right.Xyz + SCNVector3.Cross(left.Xyz, right.Xyz),
left.W * right.W - SCNVector3.Dot(left.Xyz, right.Xyz)));
}
