gkjohnson / coordinate-frame-converter Goto Github PK

Verify that simply reversing the order of rotations properly applies a rotation in an intrinsic order.

https://en.wikipedia.org/wiki/Euler_angles#Intrinsic_rotations
https://en.wikibooks.org/wiki/Cg_Programming/Unity/Rotations
http://danceswithcode.net/engineeringnotes/rotations_in_3d/rotations_in_3d_part1.html

Right now you have to create negative or reversed rotation order frames to account for left handed or intrinsic rotation coordinate systems.

It might be less confusing to allow for setting constructor arguments that specify whether the frame is leftHanded or intrinsic / movingBody

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?

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.

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.

For use in any platform.

When extracting the euler angles using the angle extraction functions, the order doesn't seem quite right. We have to swap the row and col indices, for example, and there seem to be a few inconsistencies in the resultant values.

This needs some investigation.

http://danceswithcode.net/engineeringnotes/rotations_in_3d/rotations_in_3d_part1.html

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