Naive Doric Shaft

Let’s start simple and do ‘naively’ the modeling of the base column! We will improve it later in the next post! Let’s first review what we need to model before diving into Houdini.

The doric order is the one on the left (credits: Khan Academy)

As you can see the doric one is the most simple one and managing to do the shaft seems to be the easiest task so let’s start with that! Let’s first note that for the Greek Doric columns (which is not the case for the Roman Doric order!!), the column does not have a base, which means the shaft touches the stylobate (approximately the floor of the temple) directly.

The Parthenon in Athens with typical Doric columns (credits: Steve Swayne flickr)

The Doric column has merely the shape of a cylinder but as you can notice on the pictures, it is not smooth: the column is carved in what is called flutes. The reason of the fluting is not clear: from what I read, the main hypothesis are that it brings dynamic since it contrasts with the roundess of the column, or simply that it comes from the fact that previous columns were carved in the wood and then presenting this kind of ornaments.

The particularity of the Doric fluting is that it is sharp: there’s only one edge between each flute in contrast with Ionic flutes which present planes. Plus, Doric classicaly presents 20 flutes, when the other orders present 24. Strangely, it was extremely hard to find documentation on how the flutes were carved but I showed some obstinacy and found this picture:

Top cut of a doric column (Credits: De re ædificatoria (On the art of building, book III), Alberti, Leon Battista, 1485)

That’s small but that was enough for me to understand how I could do:

  • Create a circle of the desired radius (a)
  • Found the centers of the squares (as shown in the pic ^) (b)
  • Substract the circles with these centers as origin from the original circle (c)
  • Extrude (d)

So let’s do it now 😀 First let’s create an empty geometry and let’s dive into it.

(a) Create a circle of the desired radius

Obviously the easiest step. Just create a circle and create a Null node where we will stock our variables for user control:

(b) Found the centers of the squares

For this task I will use an Attribute Wrangle. An Attribute Wrangle is a node in which you can write some VEX code to do whatever you want. To understand how I could use the Attribute Wrangle I mainly used this blog page. If you’re not already familiar with coding, maybe Rohan Dalvi’s videos on Youtube can be a better choice.

Ok, so we’re gonna code, but what? I don’t like coding so I spend as much time as possible preparing what I want to do before coding it (so that I spend as little time coding).

Our goal is to find the centers of the squares as shown in the picture from earlier.

First step will be to find the coordinates of the orange dots (see figure below)

The orange dots are uniformly sampled along the circle (which means the angle between two dots is always the same and equals to \theta = 2\pi / N radians -or 360/N degrees – with N the number of desired flutes). If you remember your trigonometry, the next step is fairly simple:

Then, finding the center of the square is straightforward (or if you forgot your math, just believe me):

In the end, here is the VEX code that does the trick (feel free to copy it):

The result: the points seem to be at the right place

(c) Substract the circles with these centers as origin from the original circle

In order to do that, we will use a Houdini node called ‘Copy to Points’. Basically we will give him a Circle and our Points from the Wrangle and he will create a circle on each of those points:

Of course, that’s not what we want, we want to substract those circles from the original circle. In order to do so, we will: convert those circles into meshes then use a boolean operator to perform a substraction:

(d) Extrude

As the title says, we just extrude by adding a PolyExtrude node and TADAM we have what we wanted:

Houdini’s PolyExtrude node comes with interesting possibilities: we can create some Twist and Shrink (and creating global variables in our Null item to control it). Twist is more fun than useful but Shrink will be really helpful in next steps.

In the end we managed to create a column with the flutes that we wanted. In your Null object, we also have some nice variables to easily adapt our shaft:

So we’re done with our basic Naive Doric Column. In the next post, I will speak about entasis or why this is not satisfying yet! Follow the link 😀

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