I’m trying to derive the 3d pose of a detected april tag. In my opinion, there are some issues with the documentation - and possibly with the code as well. But most importantly I’m missing a explicit definition of the april tag’s coordinate frame. So one after the other:

- What is the coordinate frame of an april tag? Where is its origin and where are its x-, y- and z-axis pointing at? (This important since it defines its rotation values, e.g. is x-/y-rotation 0 or 180 degrees when looking straight at it.)
- I think the documentation describing [xyz]_translation and [xyz]_rotation is incorrect:

- apriltag.y_translation(): “Note that this is the up-to-down direction.” - I think Y is pointing up, since it is increasing when the tag is moving upwards within the camera image.
- apriltag.x_rotation(): “Returns the rotation in radians of the apriltag in the X plane. E.g. moving the camera left-to-right while looking at the tag.” - I think it’s the rotation around the X axis. (What is the X plane anyway?) Also: Whether it increases or decreases depends on whether z_rotation is e.g. 0 or 180 degrees.
- apriltag.y_rotation(): Like with x_rotation axis and direction are incorrectly described.

- I converted tag translations and rotations to 4x4 motion matrices, did some computations and transformations and printed resulting translations and rotations: The results were pretty strange until I found this line in your code: https://github.com/openmv/openmv/blob/master/src/omv/img/apriltag.c#L11946

Instead I’d compute the yaw as

```
fast_atan2f(MATD_EL(pose, 1, 0), MATD_EL(pose, 0, 0))
```

(no minus sign). When replacing z_rotation with -z_rotation in my code, my results are as expected. I think you shouldn’t confuse the tag’s rotation within the image (which is a left-handed coordinate frame) and around the world’s z-axis (which is a right-handed system). I assume dropping the minus sign in that line of code yields a consistent rotation as it is usually used in computer vision applications: increasing angles when rotating from positive x to positive y, positive y to positive z and positive z to positive x.

I hope my post is not too confusing and it is of some value for you and the project.

Over all I’m totally amazed by OpenMV, its community and your awesome support!

Cheers!