Parametric Modeling of Vaults for Notre Dame in Revit - Part 3 of 6

Part 3: Methods for Modeling Vaults and Modeling Surfaces of Vaults

In Part 2 of this series we separated all the arcs around the supports, by placing a circle at each corner and making the arcs begin at the intersection of circles with diagonals and edges. Here in Part 3, we will discuss whether we should use a generic or an adaptive template to complete the vault.

So far, we have this, a wire frame model of the basic geometry:


But this is just a wire frame. The question is, which kind of family template should we use to complete the vault? Generic or adaptive? Let's compare the two methods first. Then I will propose a third method.

This is a six-part series. Click the links below to continue working.
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6

Method 1: Generic Family with Solids and Voids

In the generic templates, we have these tools to create forms: Extrusion, Blend, Revolve, Swept, and Swept Blend, as solid or as voids.


To create a cross-vault with these tools it is necessary to use voids. The approach in this template is simply "solid minus void". One way to do it is this: create a cross by intersecting two solid extrusions of a closed shape that represents an arc with thickness (marked as "S" below), and then create another cross, by intersecting two void extrusions of a closed shape that is a pointed arc with a line at the base, almost like a triangle (marked as "V" below); then the voids will subtract their volume from the solids. The result would be like this:


The result shown above is a crossed vault; however, not the type of vault that is used in Notre Dame. These are the differences:

a) Notice that the ridges in this result are horizontal; in Notre Dame, ridges are curved.

b) Notice that the diagonals (ribs) in this result are the intersection of the two extrusions, and since extrusions follow a straight direction, all these ridges are flat and meet at the center at the same height. In Notre Dame the diagonals (ribs) are semicircles, which creates an apex point at the intersection, higher than the top of the arcs.


c) Notice that in this result, ribs, arches, and apex are different than in Notre Dame; therefore, the surfaces in between, the vaults, are different, too.

Advantages of Method 1

a) It gives the idea.

b) It is quick and easy (if you are doing just one square crossed vault).


a) The geometry is not correct!
b) This family will not adapt to irregular layout plans, at least not without great efforts (or more voids? which makes things worse). How would you adapt this to different radii, different heights, trapezoids, triangular plans, special conditions? The more these vaults deviate from the typical four-part square type, the more incapable this generic method becomes.

c) Voids slow down the performance of Revit models. One solid and one void = two elements to compute.

d) Adding voids means adding more reference planes and more parameters, if you need to keep the result parametric.

Method 2: Adaptive Family Based on Reference Points

In the Adaptive templates, we have these other tools to create forms:


The most important tool of this template is marked with a red arrow: the reference point. The presence of this tool allows us to think of any form as the result of this sequence: points -> lines -> surfaces -> volume.

Therefore, the first task is to locate all the points. First, points "on the ground". These points will host other points that are projected upwards. Then, if the points of the ground move, the points "on the air" will move along. And, since points drive lines, and lines drive surfaces, the whole vault will be adaptable to irregularities in plan, heights, widths, etc.

Below is an example of a vault created with Method 2:

method 2

In the illustration above, notice the points "on the ground" and the points "on the air". For every point on the air there is a point on the ground that is its host.

Advantages of Method 2

a) It creates the correct geometry.

b) It can produce shapes that are difficult or not possible with the generic template, such as: conoids, hyperbolic paraboloids, ruled surfaces, double curvature.

c) The same vault family can be used for rectangular or trapezoids plans, and parts of this family could be used for triangular plans.

c) Heights and widths of arcs can be adjusted easily by parameters.


a) The thickness of the vault will be done with individual elements in the project because each face needs to be materialized as roof by face or wall by face.

b) It can be difficult and time consuming to find the location of all points with precision.

Method 3: Adaptive Families with Adaptive Points and Nested Families

This method appeared as a response to the disadvantage "b" of Method 2, above. The idea is to "pre-build" the ribs and arcs in other families, instead of having to find points for all the geometry as in Method 2. Therefore, if you need a diagonal rib between two points, you load a family that takes care of that. You need a pointed arc between two points? Then you load a family that does just that. This image below shows the three families that create the wire frame:


Then, in the vault family, you insert these components, and eliminate that time-consuming part that was a disadvantage in Method 2.

The process would be like this:

In an adaptive family, we made a square of four reference points. Optionally these points can be converted into adaptive points. Then we connect these four points with reference lines:


Then we load a family that we have done with the adaptive family. This family is a semi-circle as a model line between two points. The semi-circle is made with 2 arcs (to allow for selection of left or right side). The two points are adaptive, so that we can create the diagonal by simply clicking on two points, as shown below.


Actually, we click a little bit away from those points, to allow some space for arches to coexist on top of capitals (as explained in Part 2). Notice the enlarged view of point D in this illustration, and notice the diagonal starting away from point D.

point d

Then we insert a second family, which is a pointed arc, as a model line, from two points, and with this family we create the four-pointed arcs around the square, clicking on two points. After inserting the pointed arc families, the result would be like this:


Now at the callout around point D, notice that we see one diagonal and two pointed arcs:


Then we insert a third family to create an intermediate "broken arc", which is necessary to create the correct surfaces and curves. This family creates a pointed arc by clicking on 3 points. In plan view, this broken arc looks like a triangle. The projection of the 3 points A, q, D, creates the broken arc that is highlighted below. In this image all the four broken arcs have been created).


Now we have the three arcs that we need to create a surface correctly. Using the Tab and Ctrl keys of the keyboard we select one half of each of these three arc families together, and then do Create Form > Surface. The result would be like this:


Then, we repeat the process to create the other surfaces. The instances of the nested families are set to be not visible. The result would be like this:


Advantages of Method 3

a) It creates the correct geometry.
b) It uses nested families, with the geometry and proportions already figured out, therefore the process of making the surfaces goes much faster than Method 2.
c) It is still adaptable to variations in layout, heights and widths


a) Probably only the same mentioned before, that the thickness of the vault will be done with individual elements in the project because each face needs to be materialized as roof by face or wall by face.

This is a six-part series. Click the links below to continue working.
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6

Alfredo Medina is a very experienced and knowledgeable BIM / Revit professional with a background on architecture, high skills in training, troubleshooting, technical support, parametric modeling, extraction of quantities, definition of standards and best practices, clash detection, and coordination of large BIM projects. Alfredo has several years of experience and a reputation as an expert due to his participation in forums and international conferences.

Companion Class

In this class, you’ll create an adaptive parametric Revit family that represents one of the types of crossed vaults used in the ground-floor ceiling of the Notre-Dame cathedral in Paris, France. This class is a result of Alfredo Medina’s collaboration in Andrew Milburn’s initiative about creating a Revit model of Notre-Dame, a work motivated by the love of using Revit software as a "BIM pencil" (Mr. Milburn’s words) to study historical buildings. Mr. Milburn started the model in April 2019, soon...

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