Creating a groin vault with a raised center


I,m trying to build a groin vault with a raised center. This is easy enough to do. See example. However, in raising the center, I need to maintain the exact half circles on the four vault sides. You can see in the example where the true half circle is shown in red. So, it’s close but still off. I,ve tried it a bunch of different ways to no avail. Maybe it’s not possible. Any thoughts? I’m using SketchUp Make (the latest) on a Mac.

Spherical triangle help

Create a circle. Draw a line across the ground from one side to the other, and delete the lower face and lower arc.

Push pull it proper distance.

Select just the end face, and click the ScaleTool. Stretch just in the vertical axis.

Delete the unneeded faces, and group the result.

Rotate copy as needed, then explode the groups so they intersect. Cleanup the unneeded surfaces from below (orbit so your looking up from below.)


A similar solution:


Round two adjacent edhes on rectangular rod (SU2014)

Yea that’s better, 1 quarter the cleanup.


Yet another method. The ones you propose have a straight length profile, Pzbloser seems to want it to be curved too.
I also made a quarter and then rotated copies.



The tunneled arch can be parameterized in terms of u and v (Ruby syntax):

x = 10.0 * Math.cos(u)
y = v
z = 10.0 * Math.sin(u) + 30.0 * Math.cos(Math.asin(v / 30.0)) - 25.965475

where 0 <= u <= PI and -15 <= v <= 15. This will produce an arch formed by 10-inch radius half-circles and follows a 30 inch radius arc (total tunnel length = 30 inches). I used a U-V surface generator to create the following:

Note: Using 0 <= v <= 15 will produce half the tunnel. making trimming and cleanup easier.

The model is here: groin_vault.skp (671.0 KB)

The plugin is uv_polygen.rb and can be downloaded from

[edit (added)] Completed Groin Vault:


Hello again. Apparently my screen snapshot didn’t go through so here’s a second try.


Thanks for this solution. I have a feeling it’s the very best one, but unfortunately it’s Greek to me. I don’t know anything about Ruby syntax, or even if it works on SketchUp Make. But I’m going to look into it, and put my feeble math skills to work!


Yet another way using the native tools. I started with a sphere because it was easy, but not necessary. Take advantage of components - edit one and all copes will change. In this example, the geometry inside a component was scaled and moved before intersecting to trim off unncessary geometry.

A copy of the component can be placed off to the side of the main model and edited. That would mainly be useful when it’s time to remove unnecessary geometry after an intersection.



Your vault would need a column in the middle to hold it up - the central intersection point curves downwards. It is a n intersection of four pendentive domes.

Geometry is interesting. I built a first version of my version of the vault with the assumption that the diagonal ribs, too, ought to have a semicircular profile, without realizing at first that the result was a pendentive dome, not a groin vault.



The central intersection doesn’t have to point downward. The model inside the component can be moved before finalizing the end model. It was getting late, and I wanted to finish the tutorial before retiring. I mainly wanted to emphasize the sketchy power of this program using the native tools - no math needed cluttering up the creative design process. Structural reality can come later - and the model adjusted in SU with the native tools too.

I also should remind the OP, the creative process of making the vault doesn’t require modeling anything to scale. After finishing the vault, make it a group. Then use the Measurement tool to size it correctly by measuring the distance between 2 known points.


hey @catamountain

your outlined method is a good one… however, in the case of OP’s spec, they stated the 4 openings of the fault need to be half-circles.

here’s a method using fredo’s Curviloft plugin:


Scale the results from my method to get the half circle. SU is very plastic. Modeling methods aren’t locked in stone.



I found when I used your method of constructing the groin vault that I couldn’t get the four sections to seam perfectly together no matter how many attempts I made. I retried your method, using full length frameworks crossed and then intersected. Cutting away material after was laborious, but the result is astonishing.

Thought you’d like to know.