Parametric Modeling of Vaults for Notre Dame (part 5)

(Part 5 of Handout for Autodesk University 2019 class)

At the end of Part 4 of this handout, we had already put vaults on columns, at their full size, and modeled the diagonal (ribs) of the vaults, like this:

In this Part 5 of the handout, we are going to model the arches that go on the four sides of the vault. These arches can have different profiles. Let's say "A" ,"B", and "C". If an arch is in between two vaults of the same kind, it uses a profile "A"; if the arch is exposed as a "facade" of the arcade, it uses a profile "B"; if the arch is adjacent to a space that has a vault of a different height (as in the chapels), the arch uses a profile "C". In this image from Leica's True View Cloud, I have marked these three types of profiles. You can explore this by yourself at: https://notredame.truview-cloud.com/scan/99c5a977-eb9e-4c39-afc5-3e21dd74fa4d

Note: I think that the profile of the arch adjacent to the chapels ("C") is different than the profile that faces the nave ("B"). But for this exercise, to simplify things, we are going to use profile "B" for the arches marked as "C" in these images.

In our reflected ceiling plan, I have marked in red the arches that use profile "A"; in blue those that use profile "B", and in green those that use profile "C".

Profile "A"

In this illustration, taken from Viollet Le-Duc's dictionary, he talks about the geometry of the stones used for the arches, not for Notre Dame in particular, but in general. Highlighted in yellow, is a section of a stone for an arch that goes in between two vaults, which is what we need for profile "A".

It is basically an enlarged version of the profile of the ribs, but instead of being 1 foot wide (approx. 300 mm), this profile is approx. 500 mm wide (approx. 1'-8"), based on Leica's panoramic images and measurement tools. Therefore, I have scaled the profile of the rib, and saved as my profile "A", like this:

We load this profile "A" family into the vault family. Then we place a reference point, using "draw on face", on one of the arcs. Then we use the Set tool to set one of the work planes of a reference point as the current work plane, the plane that is perpendicular to the arc on the left or the arc on the right side of the vault, like this (profiles highlighted in yellow).

Then we select one arc and one profile, and do Create Form. Then we do the same on the opposite side. The result would be like this:

Even though the profiles are different depending on the position of the arch in the project, we could use the same profile "A" in all the arches to begin with, and then use an instance Family Type parameter to change the profile family as per the location of each arch. Therefore, let's put the same profile "A" in the other two arcs, front and back, like this:

Then, let's select profile families and arcs, and then do Create form, as explained above. The result would be like this:

If we turn on the surfaces, the vault family would look like this, below. I turned preview visibility on, to check that the profiles families are not going to be seen in the project.

Meanwhile, in the project, I have copied my group of columns and vaults to create the two isles, north and south, and part of the great nave in between, like this:

If we load now our vault to the project, without having changed all the profiles of the arches yet (all arches are using profile "A" so far), it would look like this:

But remember that the arches that face the nave need to have a different profile. Maybe for structural reasons because those arches not only carry their share of the vault but also their share of the weight of the walls and other elements that enclose the nave. According to Viollet Le-Duc's illustrations, that profile "B" is something like this (highlighted in yellow, below).

It's like an enlarged profile "A" (but with a width of 600 mm instead of 500), plus one additional stone below, to increase the depth of the arc. Something like this:

It's literally two stones, one on top of the other. However, for our vault family, we need to simplify the profile, erasing that line in between the two stones, to make one single closed shape, as if the two stones were merged into one, like this:

Then we load this family into the vault family. But we don't have to place it on any arc. Loading it is enough. Then, in the vault family, we select one of the instances of profile "A" (the one that corresponds to the "front" of the view cube), and create a new parameter, such as "Profile for Arch-Front", like this:

Then we select another instance of profile "A" on the right side, and create "Profile for Arch-Right" parameter, and so on, until we have something like this:

Now in the project, we can select a vault, and specify which profile, A or B is each arch going to use, depending on its position. Remember, all the arches facing the nave use profile B. In that case, in the project, we select each vault, and make sure that the arch facing the nave uses "profile-stone-arch-B" for one of its parameters. The words "front, back, left, right" don't need to match the orientation of the vault. It would be good, but that does not matter.

Once you assign profile B to all the arches facing the nave, you would have something like this, below. In this cutaway view, notice the profile B creating the arches that face the nave, and the profile A that creates the arches in between vaults. Also, notice that the capital of the columns facing the nave need to be different than the capitals of the columns in between arches. That is a different topic that we will address later.

This is enough for Part 5 of this handout. In Part 6 we will add thickness and material to the surface of the vaults. So far we have this, below. All arches on the exposed side of the vault are using profile "B".

Thank you for reading, and stay alert for Part 6 next week.