How do you derive the UV coordinate/coordinates for each vertex?

[meijie0401]

When I run the run_reconstruction.py for pascal cars, I notice the dimension of vertices is 962x3, but the dimension of UV coordinate is 1054x2. So the mapping between vertices and UV coordinate is not one-to-one.

1. Which formula do you use to calculate UV coordinates for each vertex so that the mapping is not one-to-one?
2. Which line of code can tell us the mapping between vertices and UV coordinate/coordinates?

[meijie0401]

I know why the dimension is 962 and 1054 respectively: north pole and south pole, have 32 corresponded UV points respectively, and each of 30 boundary vertices has two corresponded UV points. So the total UV points are 962 + 31*2 + 30 = 1054.
For the second question, I also figured it out, topo_map is the one-to-one mapping between vertices and UV coordinates (but using averaged UV points for north pole, south pole, and 30 boundary vertices)

The remaining question is the first one.

[dariopavllo]

Your observation about the boundary vertices is correct!

Regarding the mapping: you can find it in the .obj file of the mesh template. There is no formula, this is simply what Blender exports when you generate a UV sphere. Of course, it is also possible to derive such mapping programmatically: for the u coordinate, you quantize the angle uniformly between 0° and 360° (where 0° is 0 and 360° is 1), and v is the height. But this is unnecessary.