Projected texture trouble

I’m trying to project a texture onto a slightly curved surface. But try as I might, I can’t get the texture to fill in the surface completely. In order to create the surface in the first place, I had to draw numerous lines across the shape; i couldn’t get a lofting program to fill it in for me. Any thoughts about why projected textures isn’t working in this case?
chinese armchair.skp (3.4 MB)

Select all the faces and apply the projected texture


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Many thanks. I should have thought of that myself.