How can I "grid fill" this edge loop WITH the three interior edge loops smoothly integrated in the mesh surface? The idea is that the latter afterwards are not visible as edges (i.e. smooth). The interior edge loops have exactly the same number of vertices as the side edge loops, so that shouldn't give any problems.
Using grid fill
- Start by selecting two pairs of edge loops and the connecting edges, as shown in the picture below.
- Press space and search for "grid f" and choose "Grid Fill".
Repeat that for each pair of ledge loops, and you will have a full mesh.
Using the bridge tool
Start by selecting all the loops except for the edges on the top and bottom.
Now simply press W and choose "Bridge Edge Loops". Change the number of cuts to match the number of vertices in between each selected edge loop (in your and my example mesh it is 3). You can find that in the operator half of the tool shelf.
Now you just have to fill the top and bottom parts. You can quickly do that with the F2 addon (that fastest way), or by any combination of bridging, and grid fill.