To unwrap a genus-0 mesh such as a sphere, I can make a full sphere from an unwrapped half sphere applied with mirror modifier. the amount of uvs equal the amount of vertices. But the two verts selected in image below have two different uvs with the same value.(by checking in the exported .obj)
Or I can make a seam then 'Unwrap'. This way the number of uvs is larger than the amount of vertices. Each uv coord is unique, no repeated values.
I wonder how to unwrap a genus-0 mesh so each vert has one and only unique uv? Unique means there're no repeated uv coord values, it's not unique if the ith
vt and jth
vt have the same coord values.