project points on surface

Hello !

I´m trying to project a bunch of points onto a surface. That bunch of points comes from a rectangular grid. From this grid, half points are moving up, and half points are moving down, so they have a specific height. 

Now, I want to project those points on a curved surface, but keeping also the height information. If it´s not clear, there is an attached picture where it is shown my idea. 

Using project point component or pull point on a surface will just mapped the point on the surface. 

Is someone have an idea how i could achieve that result ?

thank you !