There're two ways to unwrap a genus-0 mesh such as a sphere.
One is to make a full sphere from an unwrapped half sphere applied with mirror modifier. It will output similar uv layout as below image. By checking in the exported .obj, you'll find 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.
One is to make a seam then 'Unwrap', which will lead to the number of uvs is larger than the amount of vertices. Each uv coord is unique, no repeated values.
Is it possible 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. For example, can we unwrap the sphere and manually merge the uvs for the same vert on the seam in the uv map?