Domed ceilings sound like fun.
The completed test map is going to look like this:

I started a new test map for this as the last one was
getting a little too busy with meshes.
So build a new box map. At some appropriate height above the floor build
another, smaller box out of common/caulk but without a brush on the bottom. This is going to be the
outside of the domed ceiling.
Once that's done build a new brush the size of the hole
in your box.
Then go to x-y view then turn it in to a cone. (Curve
menu then cone)
Notice the cone is taller that the caulked box that's
because we are going to shape it.
Now you could of made the dome first then after shaping
it make the box around it.
Looks like this.


Invert the mesh by hitting (crtl + I)
Now switch to x or y view.
And turn on vertex editing. (V key)
Should look something like this.

Now we are going shape it in to a dome.
First pull the middle control point down.
Like this:

Now we are going move the middle control points up and
in to make ceiling more round.
Like this:

Do this in both x and y views.
Now hit the V key then shift+S then set in
the x box type in 8, in the y leave it 4 then ok.
There, we're done with
the dome for now.
Now let's build some corner walls for the dome and some beveled
corners (these are known as pendentives) to match up with our dome.


Ah yes, pendentives - these are the transitional pieces between a
dome and a flat wall.
You will notice the brushes that I have built for the
walls have openings in them. These are going to be
doorways (more about that on the next page).
If you don't want doorways in the wall then you will
have to build your pendentives so they have straight
sides on them that match up with your brush work on the
wall to avoid z fighting and t-junction errors.
This will make more sense later in this page.
Ok let's build a pendentive. They start out as simple
bevels that are 1/4 the size of the dome and positioned at its base.
Looks like this from the x-y top view.

And like this in side or front views.

Move the bottom corner control points to the center. In the
pic above move 1 to the control point numbered 2. Do
this in both side views.
Now your pendentive should look like pic below this is
how we are going to leave it for now. It will change on
the next page when we add a square cylinder trim around
the doorway.

Now I'm going to get a little side tracked. What if you want a
pendentive to be straight at the sides like a wedge?
Make your brushes behind it the same shape a triangle.
However, you'll still have a problem with the side of the
mesh not being aligned.
What to do? Try to shape the brush behind to the mesh
good luck you will still get z-fighting at the edge.
I use a trim brush that is wider than the edge gap - problem fixed.
But I still like how it turns out in the next page.

Patch mesh page 9
The following short cut keys will come in handy while working
with meshes:
ctrl-G
Snap to grid (I use this one a lot)
ctrl-
I
Invert texture
shift-control-N Cycles cap textures patch
V
key
Turns on vertices so you can drag them.
control-N
Naturalize patch texture
Control-P
Toggle show patches
shift-C
Cap selected curve
shift-S
Patch Inspector (I use this one a lot)