(2024-01-16, 22:01)Travis Cobbs Wrote: I'm not sure if you are referring to cylindrical or spherical mapping here. If the former, the UV coordinates are essentially undefined anywhere on the axis of the cylinder. (I think they have a valid V value, but their U value is effectively "all of the above".) If the latter, then I think the same thing happens at the north and south poles. When texture UV mapping is performed in advance, the U value can be calculated based on the U values of the other two vertices in the triangle that touches the pole. But for projected textures, I don't think this is possible.
I was thinking of the cylindrical coordinates. Yes, you are right. The U coordinate is undefined at the north pole (and would be at the south pole if we had one on our hemisphere). Taking the angle between one vector and a zero length vector isn't defined. However I've defined the angle as zero, since that's how the calculations fall out anyway. It helps the look of the model to give the vertex some UV coordinate (rather than be untextured?), and 0.5 is as good a U as any. An "average" of the UVs of nearby points if you like. As you say, at least the V coordinate is defined ok.