How to convert 1D-UP CGA to a homogeneous matrix?

[WY-2022]

I noticed that in the "test" phase of the code you provided, the displacement "x" from the annotations is used to recover the translation_rotor and further obtain the rotation_rotor. So, what I would like to ask is, if we use the trained network for a regular inference (meaning, without any annotations), how can we obtain translation_rotor and rotation_rotor from the resulting 1-UP CGA? Or in other words, how can we convert the 1-UP CGA into a homogeneous matrix that represents rigid motion?

I eagerly await your response.

[WY-2022]

@albertomariapepe

[albertomariapepe]

hi there! That's actually a good point, as that is not necessarily known information.
The reason why we split it into rotational and translational component is to compare it with other approaches. Once you have a motor, however, you don't actually need to split it in two components to roto-translate something in 3D, as long as you project your points in spherical space from x to X and then roto-translate them it as Y = MX\tilde{M}.

Also, remember that the translation component is relative to an arbitrary reference frame which is dataset-dependent. You could try using the training data rather than testing for your scaling and see how much the results differ, or eventually try some sort of interpolation between the x values in the training set and the motor coefficients of Ta, so you can go back to t from the predicted Ta based on the interpolated values.

I hope I was clear enough!