From:  Michael Gibson
3689.2 In reply to 3689.1 
Hi Sharif, it looks like you're using the "closest point" mode for project?

That will drop the curve down to the nearest point that it can find on the surface.

So for example for this endpoint here:

The closest point to the surface from that point would be like this:

So that's why you get that kind of result.

You would need to make the endpoint stick down quite a ways further or possibly curve around somewhat similar to the surface in order for the closest point for the curves's endpoint to be the bottom edge of the surface.

Otherwise if you want to use just those lines that you already have instead of longer curves to project, it seems like you want projection in a single direction for each curve. For that you can use the other projection mode which lets you specify which direction to project, but since you want a separate direction for each curve you will have to do each one separately instead of all as one single batch.

I'm not entirely sure the result is supposed to be, but instead of projection you may want to build something like some vertical planes or extruded surfaces and then generate curves of intersection between those vertical pieces and your surface. That can be done by selecting the surfaces and running Construct > Curve > Isect - that will generate a curve in areas where the surfaces intersect each other.

- Michael