Area for quads

[sbriseid]

Hi @lucidrains and @MarcusLoppe!

The calculation of the area for a quad in get_derived_face_features is missing a shift. The current code will calculate the area for the triangle defined by v0, v1 & v3, with v2 missing from edge1 & edge2.

By using a shift value of 2 for the quad case the edges will be the required diagonals v0 - v2 & v1 - v3. Since the single shift version is needed for the computation of the angles a second shift operation is needed:

angles  = derive_angle(face_coords, shifted_face_coords)

if quads:
    shifted_face_coords = torch.cat((face_coords[:, :, -2:], face_coords[:, :, :-2]), dim=2)

I am here assuming that the vertices in the quad have a CCW ordering (or CW).

[lucidrains]

@sbriseid hey Sverre! thanks for raising this; quads have been an experimental feature (was not in the paper)

could you let me know if this change lines up with your expectation?

[sbriseid]

Not quite. That fixes the issue with the area, and was my first pick (except I didn't use a roll since I'm a tensor newbie). But then I realized that such a solution would mess up the calculation of the angles, which relies on the single shift. Hence I used an additional shift operation for the quad case, applied after calculating the angles.

I am very impressed by the work you and Marcus have done! The autoencoder is already very good, with the transformer improving on an almost daily basis it seems.

[lucidrains]

@sbriseid oh got it, should be good now :pray:

and yes, thankfully had Marcus stress testing it

this repository wouldn't have made it without all his feedback!

[lucidrains]

and of course, thank you for reviewing the computed quad features!

[sbriseid]

Now it should be correct!

I haven't tested the quad feature, this was after reading through the code to understand the data flow. Being a mathematician I am able to follow most of the mathematics in the code, unless it is hidden inside some wizardry tensor operations :)

[lucidrains]

@sbriseid math is where it is at

if only i knew what i would be doing today, i would have studied it more