Using curves as boundaries

I’m trying to fill in a curve. In this picture, I want the entire top of the cube to be covered by a surface, the boundaries of which are formed by the curve. Is this possible? I tried using NURBS but modelling the curves was too hard.

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The simplest way might be to trace the profile (z and x axes) with a series of edges, both the bottom of the cube and the curve that you want for the upper surface. Then extrude these edges in the y direction to make the shape 3D. Start with a single vertex (add a plane and delete three corners) and ‘draw’ the profile with Ctrl LMB.

You can just build the whole thing with a Curve, and convert it to a Mesh later with Alt-C if you want.

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