Bingo! I'm so used to thinking of projections on a texture by texture basis that I forget about the projection options in the basic material tag all the time. I would have wasted a lot of time tracking that down.galleon27 wrote:Your uv mapping projection is set to spherical. Set it to uv map

Later... I was just thinking about this some more, and realized where my mental blind spot is: I don't generally think of the Material Tag as being different from the Material, when clearly it is. When I first looked at this scene, I saw that the material behaved as expected on other objects, and that deleting and re-applying the texture to the lashes geometry fixed the problem. That should have been a flag that told me to look at the Material Tag. A lesson learned, I hope.