Fill a solid corner topologically correct

Question

When constructing technical objects I often come to a point where I want to add something into a corner. I haven't found an easy way to do so in a topologically correct way.

As a simple example this would be the situation with the corner to be filled

And this is the target to be achieved:

Given how easy it is to extrude such a block, I wonder if there is no easy way here as well.

Solutions I've tried so far:

• extrude one of the two adjacent faces -> this gives a topologically incorrect model which causes problems later on
• add a cube of the desired size, and make a boolean union -> (almost) impossible to avoid creating small steps and quite cumbersome
• extrude one edge and fill the three faces manually afterwards. -> this is topologically correct, but still a bit cumbersome
• isn't there an easier way???

Answer 1

If you have F2 addon enabled, here is a very magical trick.

Pressing F when F2 is enabled, several things will happen:

1. If 1 vertex is selected, it will create a face from the 2 edges connected with the vertex in the direction/position of the mouse cursor.
2. If 2 vertices or an edge is selected, it will try to created a quad face with the adjacent edges/vertices. And the result doesn't need merging or 'remove double'.
3. If 3 or more edges are selected, it will simply create a face with selected edges. Result can be an N-gon.

Answer 2

I've tried some methods with Bridge Edge Loops, Grid Fill and such, but I think that the fastest way would be this one:

1. Remove corner Edge.
2. Select Edges around one corner wall.
3. Turn on Snapping to Vertex.
4. Extrude along needed axis - E > X in this example.
5. Create Face - F.
6. Select all (A) and W > Remove Doubles.