Projecting does not work

I have a raster of lines that represent the window frames (in yellow). The glass surface is the blue one in the image.
Before actually extruding the frames, I want all lines projected on the glass surface. But it doesn’t work. Nor does Pullback.The surface is gently curved at the beginning and clearly away from the raster plan at the end.
What is there wrong?
Thank you,

Hi Bogdan- Project uses the current CPlane Z direction- so in this case, Project from the front view… any luck?


Correct. That is the key. Thank you