Arch aperture (from a vert)

main page
34). Keeping the extruded face selected I also selected the underside of the 'wall' (now having 15 verts)
35). Apply Face | Bridge and Wings creates an aperture thro' the wall in the shape required and automatically produces the edges on the underside.
Basic aperture has now been formed.
36). Select all the faces around the inside of the aperture - I selected an edge, pressed G, then F
37). Apply Face | Extrude Region -> Normal and drag (a little) until you achieve something similar to that shown. Do not drag too much, or the corner details will 'cross over' - this result is to be avoided.
38). Further edges are needed to maintain the shape during smoothing.
Select all (short) edges thro' the thickness of the wall (select one, press G) then apply Edge | Connect to produce the result shown.
39). Apply Edge | Bevel and drag the 2 new edgeloops apart until they're quite close to the corners of the 'aperture' - approx. a similar distance from the corner as those produced earlier (see (37) )
There is now sufficient detail (with these 'mechanical bevels') for the shape to be maintained during smoothing.
40). All that remains is to connect the 'floating' verts up to existing (or newly-created) verts - as you desire - usually with a view to maintaining quads?

An alternative to the first 12 steps would be to align the 4 edges around the chosen vert (using flatten) - so that bevel produced a square. I used the described option because I thought the 'making a quad square' routine might be of more general use as well.
Steps 15 - 24 can be done in various (other) ways to achieve a similar result. What's described above isn't the gospel.
Eg: Scale all 141.42%, deselect TOP 2 verts and run scale (rmb) again with shift D - 141.42% to get the 2 lower verts into the correct positions for forming the lower 2 corners of the window. (this is better, in some ways - than what I describe in the text, because all you have to do is press shift D to repeat the whole op - no dragging)
(All these figures are based on sq root 2)

Whatever you do, don't cut 2 the edges forming the curved arch portion at the wrong time - because when you come to use Inflate to get it semi-circular, those edges will be of significantly different lengths.

The distance between the 'control' edgeloops of the mechanical bevel and the corner itself will affect the radius / sharpness of that geom during smoothing. I didn't put figures in because it's a 'suck it and see' sort of thing, which also depends on sizes of objects - mess around and see what happens :)

Even more edges will be required if you're going for a 'frame' or whatever that stands proud of the wall surface - but use a similar approach to 'hold' the shape during smoothing.
Depending on circumstances, there are many ways of making an arch-shaped 'hole' in something - many situations will allow much simpler methods than what follows to be used.
What follows is an approach for making an arched aperture (window / door etc) from a vert - maybe you've already done most of a model, but forgotten one :)

I've also decided to start with a 'worst-case' scenario - the (4) edges emanating from the chosen vert are not aligned or orthogonal, because it allows for the description of a sequence which might be of use for other things.

If edges are aligned / ortho, then you can go straight to step 13 (from 1) and ignore those in between.

Most images are viewed along the Y axis, with Z axis going up/down (X left / right)
(Blue is my vector display colour)
1). I've tweaked the top surface of a scaled cube (0.4thick) to provide these 6 polys as the basic 'canvas' for where an aperture is to be formed.
Select the vertex where you want to start forming the aperture.
2). Apply Vert | Bevel to suit - you can always scale the whole 'window' later, if what's produced now isn't exactly the size you want :)
Note that the quad formed is nothing like a square - as it would be if the edges had been aligned.
The next stages are associated with 'truing up' this quad.
3). Select a pair of verts - it doesn't matter which pair you start with.
4). The pair chosen are going to be flattened along the Z axis, so -
Apply Vert | Flatten (RMB option) and select one of the other verts (shown in blue) as the first stage of the 'anchor point' procedure.
5). Select the other (lower) vert - and you will see that the blue dot has now moved to the mid-point between the verts chosen in (4) + (5).
This blue dot denotes the position along the Z axis that the verts being flattened will be aligned with, once the command is complete.
6). Situation after executing Vert | Flatten - note how the 2 verts are aligned with the blue 'vector' spot in (5)
7, 8, 9). Repeat the same procedure as just carried out - but use Vert | Flatten (RMB option) this time on the other 2 verts (shown selected in (7) )
After this op. (9) - you will have a rhombus - all sides of equal length, diagonals crossing at 90deg, but also, diagonals of different lengths - I want a square :)
(Am now going to use Vert | Inflate (RMB option) to get it square, as this adjusts all selected verts to lie on the surface of a sphere - or - if all verts lie on a 2D plane, as here, then they will end up forming a circle (or part of))
10). Since it doesn't matter which pair of (opposite) verts are going to be adjusted to form a square, I'm going to use those already shown selected in (9)
Apply Vert | Deform -> Inflate (RMB option) -> 100%
Select the (rhombus) face to define the centre of the circle (shown in blue)
11). Define the radius required by selecting either (but not both!) of the other 2 verts (also shown in blue) and start the Inflate op.
Apply 100% (eyeball info, top left) and constrain to 100% by holding shift. The 2 verts will now move a little.
12). Situation after Inflate - we now have a square :) (check the lengths of sides / diagonals by using the measure facility if you want - Wings displays distance between 2 verts (or length of single edge) in info, top left)
Am now going to start on the arch 'proper'
13). Select all 4 sides of the square.
14). Edge | Cut -> 2 (press 2)
15). Vert | Scale Uniform (RMB option) - select square to define the centre of the scale op (shown in blue)
16). Apply scale -> 200% - result shown. (whilst this has given the base of the window, the top 2 verts will need re-adjusting)
17). Deselect the lower 2 verts.
18). Re-apply Scale (press D) to 70.71% (70% will probably do, but it has implications associated with 'arch' elements being of equal length - see comments at end)
19). Select the 4 edges shown.
20). Apply Edge | Cut ->2 (press 2)
21). Re-select the 2 verts shown in (18) and apply Vert | Deform -> Inflate (RMB option)
22). Select the 2 verts (shown in red) at either end of the 'diameter' of the semicircle. Doing this defines the centre of the (semi) circle as a point midway between the 2 (red) verts - centre shown in blue.
23). Select (again) one of these verts to define the radius of the semicircle. (shown in blue)
24). Drag Inflate -> 100% (hold shift to constrain) and accept. All verts around the top of the arch will now lie on a semi-circle.
(If you want to modify the 'shape' of the arch - then now, as it's in its simplest form, might be a good time)
The next few steps are associated with providing details to maintain the sharpness of the 2 corners during smoothing and can be achieved in many ways - not just as shown here.
25) Select the edge shown and apply Edge | Bevel
26). Drag so that the 2 new edges are quite close to the lower 2 corners of the shape.
27). A close-up view of final position.
28). Select the 2 edges shown
29). Edge | Cut 2
30). Vert | Move -> Z (downwards here) so that these new verts are approx. the same distance away from the corner verts as those produced by the previous bevel op.
There is now sufficient information to describe the basic (finished) shape - all that remains is to actually cut the aperture thro' the 'wall' - and provide additional geometry to ensure the shape is not lost when smoothed.
31). Face | Bridge is going to be used to create the 'hole'. For this to work correctly (see Bridge/weld page), both faces MUST have the same number of verts - this currently isn't the case.
To check how many verts the 'arch' shape has, one way is to select the 'arch' face and press V - info readout, top left will then display the vert count. (15 here)
The underside face of this block only had 4 (corner) verts originally - I used Cut -> 4 on the longer edges and top (shown here) and Cut -> 3 (shown in 32) to create all the necessary extra elements.
The vert counts now match - 15 on the two relevant faces.
33). We now need to extrude the arch shape into the thickness of the wall until it lies on the same plane as the rear of the wall.
You can either eyeball this (view X or Z, wireframe, ortho) or measure the thickness of the wall (measuring mentioned earlier) and note / remember this dimension - in this ex. 0.4 units.
I chose the latter option and applied Face | Extrude Normal -> 0.4