/// <summary>
/// Build a rotation matrix from the specified quaternion.
/// </summary>
/// <param name="q">Quaternion to translate.</param>
/// <returns>A matrix instance.</returns>
public static Matrix3d CreateFromQuaternion(Quaterniond q)
{
CreateFromQuaternion(ref q, out Matrix3d result);
return(result);
}
/// <summary>
/// Returns the rotation component of this instance. Quite slow.
/// </summary>
/// <param name="row_normalise">Whether the method should row-normalise (i.e. remove scale from) the Matrix. Pass false if you know it's already normalised.</param>
public Quaterniond ExtractRotation(bool row_normalise = true)
{
var row0 = Row0;
var row1 = Row1;
var row2 = Row2;
if (row_normalise)
{
row0 = row0.Normalized();
row1 = row1.Normalized();
row2 = row2.Normalized();
}
// code below adapted from Blender
Quaterniond q = new Quaterniond();
double trace = 0.25 * (row0[0] + row1[1] + row2[2] + 1.0);
if (trace > 0)
{
double sq = Math.Sqrt(trace);
q.W = sq;
sq = 1.0 / (4.0 * sq);
q.X = (row1[2] - row2[1]) * sq;
q.Y = (row2[0] - row0[2]) * sq;
q.Z = (row0[1] - row1[0]) * sq;
}
else if (row0[0] > row1[1] && row0[0] > row2[2])
{
double sq = 2.0 * Math.Sqrt(1.0 + row0[0] - row1[1] - row2[2]);
q.X = 0.25 * sq;
sq = 1.0 / sq;
q.W = (row2[1] - row1[2]) * sq;
q.Y = (row1[0] + row0[1]) * sq;
q.Z = (row2[0] + row0[2]) * sq;
}
else if (row1[1] > row2[2])
{
double sq = 2.0 * Math.Sqrt(1.0 + row1[1] - row0[0] - row2[2]);
q.Y = 0.25 * sq;
sq = 1.0 / sq;
q.W = (row2[0] - row0[2]) * sq;
q.X = (row1[0] + row0[1]) * sq;
q.Z = (row2[1] + row1[2]) * sq;
}
else
{
double sq = 2.0 * Math.Sqrt(1.0 + row2[2] - row0[0] - row1[1]);
q.Z = 0.25 * sq;
sq = 1.0 / sq;
q.W = (row1[0] - row0[1]) * sq;
q.X = (row2[0] + row0[2]) * sq;
q.Y = (row2[1] + row1[2]) * sq;
}
q.Normalize();
return(q);
}
/// <summary>
/// Build a rotation matrix from the specified quaternion.
/// </summary>
/// <param name="q">Quaternion to translate.</param>
/// <param name="result">Matrix result.</param>
public static void CreateFromQuaternion(ref Quaterniond q, out Matrix3d result)
{
q.ToAxisAngle(out Vector3d axis, out double angle);
CreateFromAxisAngle(axis, angle, out result);
}
/// <summary>
/// Transforms a vector by a quaternion rotation.
/// </summary>
/// <param name="vec">The vector to transform.</param>
/// <param name="quat">The quaternion to rotate the vector by.</param>
/// <returns>The result of the operation.</returns>
public static Vector2d Transform(Vector2d vec, Quaterniond quat)
{
Transform(ref vec, ref quat, out Vector2d result);
return(result);
}