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Modelling Question, Project to double curved surface

Hi there. I'm working on some framing to the top of a building. It's a 4 sided shape with each face curving in two directions. I've defined each face as the centroid of my structure and now i need to project lines onto it to allow me to begin modelling the actual members. Each face will have a column on the corner and a column in the center.. my questiion is, how do i project a line onto the surface accurately at the center of the face?

Abny help would be greatly appreicated as my deadline is day after tommorow :/

Kind Regards,


Ps please find below an example of what i'm trying to accomplish.