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coordinate-frame-converter's Issues

Redundant Quaternion.Euler(Quaternion.eulerAngles) is needed

The ToQuaternion function requires that the formed quaternion be stuff into Quaternion.Euler(Quaternnion.eulerAngles) to avoid inconsistencies when using the AngleExtraction class functions. For example

Quaternion q = Quaternion.Euler(90, -27, 170);
Matrix4x4 mat;

// Outputs (0, -90, 0), which is not equivalent!
mat = Matrix4x4.TRS(Vector3.zero, q, Vector3.one);
Debug.Log(AngleExtraction.ExtractEulerZXY(mat, out eulerResult) * Mathf.Rad2Deg);

// Outputs (163, -27, 170), which is!
mat = Matrix4x4.TRS(Vector3.zero, Quaternion.Euler(q.eulerAngles), Vector3.one);
Debug.Log(AngleExtraction.ExtractEulerZXY(mat, out eulerResult) * Mathf.Rad2Deg);

Why is this happening?

Address the floating point precision issue

Unity uses floats for a lot of its operations, which means there can be quite a bit of accumulated error as rotations are converted. If the quaternions, vectors, and matrices were all doubles it would address the problem.

Right now the extractAngleXYZ functions check against an epsilon when checking how to extract.

Consider removing `ToQuaternion`

ToQuaternion basically only works with properly with Unity-frame axes because we have to assume certain conventions when pulling the new rotation order out of the axis.

There even seem to be subtle rotation offsets when consistently converting to a different frame like XYZ instead of XY-Z. Possibly because the euler application for quaternions assumes the axis conventions? This should be investigated (the problem can be seen when rotating like in the example image)

Either way, it might make things less confusing if it wasn't there

Convert matrix

How to convert right hand matrix to left hand matrix(Unity) and back? Right hand matrix: right-handed coordinate system where positive X-axis points to the right, positive Y-axis away from the viewer and positive Z-axis points up. In the context of characters this means that positive X is right, positive Y is forward, and positive Z is up.

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