Revolutionary #Volutes

The two large blue circles at the bottom marked with A and B are from the floor plan for #ModernIonicCapital shown in https://pixelfed.social/p/Splines/807782440025967685. The larger one has a radius of 296 units, while the smaller one is 16 less, at 280. Both are centered at x = 416. Both are then rotated ±45° about the column axis to give us the four red circles. The small blue circle with radius 120 units is for the column neck.

The two red circles in the back are shown extruded vertically as cylinders. The other two haven't yet been extruded because we want to see the rest of the structure from the front.

The two tube or #torus-like structures are obtained by revolving the trimmed #spiral #volute outlines from https://pixelfed.social/p/Splines/808043616946914228 about the vertical axis located at x = 416. Only the bottom tube maintains the interior shape of the spiral.

With this setup, vertically extrude the two remaining red curves in the front so they are at least as high as the top of the upper tube.

Next, perform a #booleanDifference between the top tube and the two extrusions marked A. Keep the wedge shape of the top tube on the left side and discard the remaining portion of the tube from the right.

Then, perform a boolean difference between the bottom tube and the two extrusions marked B. With the wedge shape of the bottom tube on the left side, perform a further #booleanIntersection with the two extrusions marked A. This will produce two curved spirals that are 16 units thick. Discard the remaining portions of the bottom tube as well as all the red extrusions.

After these operations, we are left with one wedge shape with curved faces and two spirals that are 16 units thick, also with curved faces.

The next step is to convert the outer surface of the wedge shape from convex to concave.

#IonicVolutes are the sinews of #IonicScrolls. Without #volutes, there would be scrolls, but not #Ionic Scrolls. Each scroll starts with a volute in front and is modulated by as many as six volutes of different shapes and sizes as it reaches the back, with the scroll surface tightly hugging the volutes at each contact point in ALL 3 dimensions. This is a key point to remember before we start #reverseEngineering the first #primaryProfileCurves from old image scans.

This diagram shows the #scaffolding we will construct using straight lines and rectangles, first in 2 dimensions, then place them front-to-back in 3 dimensions using precise markers, and finally scale and superimpose the volutes on this scaffolding.

All of this will be done before we derive the primary profile curves from the image scans.

How did I know about this scaffolding? I didn't. It is not documented anywhere that I'm aware of. I developed this after years of striving to derive the correct shape, and I hope that there are people who can still "see" things I might have missed and help improve the design.

So, the actual process went like this: I drew outlines from 2D image scans in the top view, getting close to #Vignola's detailed sketches. Then, I did the same thing with image scans in the side view, and I found that the designs didn't line up.

After several iterations, I got the designs to line up in both views, and it was obvious that the bell shape of the scroll would follow the large volute in the front.

So, I used the large volute as a "rail" and tried to sweep the primary profile curves on one rail. Big mistake! The undulating shapes of the primary profile curves wobbled wildly on the single rail — The middle, 3/4, and back of the scroll were twisted out of shape!

Instead of trying to #sweepOneRail, I decided to clamp down wobbling with another operation called #sweepTwoRails, using volutes at both front and back ends as rails with less wobbling.

You will need a #CAD tool to practice.

The #Capital is the last essential component of the complete #IonicOrder. The column #flutes remain, but they are #decorativeElements, and I will cover them later when I cover the decorative elements of the capital like the #EggsAndDarts motif on the #ovolo and the #3StrandBraid on the ribbon or belt around the middle of the smooth #scrolls.

The Ionic capital is complex, but not unapproachable. We will systematically construct everything in this draft rendering using just straight lines and arcs as promised in https://pixelfed.social/p/Splines/789956327130679640, with the exception of the #cymaReversa near the top and the 3-strand braid on the ribbon.

In this rendering, the cyma reversa near the top is made using a flattened half-turn of a #helix, but it can also be constructed using elliptical arcs as I described in earlier posts.

The braid is a #periodic shape with infinite variety and is also based on a helix. You can vary the number of strands, their thickness, pitch, and so on, none of which are essential to the Ionic Order itself. They're only a jumping point for further exploration.

The eggs in the 'eggs and darts' motif can have different shapes. They can be convex like real eggs or concave as shown here, but the top is almost always sliced off. The total depth of the convex or concave shapes can vary, but only within a range of 1 part, or 8 units.

The #volutes in the front and back of the capital are based on #spiral shapes, of which there are many different kinds. Some have #continuous curvature changes, while some do it in #discrete steps, like #fibonacci spirals that can approximate #logarithmic spirals seen in nature, e.g., nautilus. When curvature changes are discrete, the spiral arms can diverge in #arithmetic, #geometric, or some other sequence.

We will construct all of these, and most notably the smooth, sweeping surface of the scrolls using just straight lines and arcs, and let the #CAD software deal with delicate #NURBS curves and surfaces.

This shows the detailed measurements of the top and bottom portions of the #IonicPedestal. For macro-level measurements, see https://pixelfed.social/p/Splines/790571135473463588

Each of the blue curve segments (lines and arcs) that are marked with a yellow bubble is the #profileCurve for a #molding whose name is inside the bubble.

Starting at the bottom, we have a #plinth, a #fillet, a #cymaRecta, and a #reed as part of the #basement of an Ionic pedestal.

Next up, we have a #fillet and a #cavetto at the bottom of the #dado, and another cavetto and fillet at the top of the dado.

Moving higher up, a reed, an #ovolo, a #corona, a #cymaReversa, and a final fillet top off the cap of the pedestal.

They are called profile curves because each is the outline or silhouette of a 3D molding as seen from one side or in a cross section. In the case of a pedestal, these curves can be used directly to recreate the 3D shape of the pedestal. For this reason and in this case, I call them #primaryProfileCurves.

This is not always the case. For more complex shapes, such as the #scroll surface of an #IonicCapital shown in https://pixelfed.social/p/Splines/789956327130679640, the profile curves recovered by #reverseEngineering the image scans in #Vignola's book cannot be used directly to sweep the scroll surface because the scroll shape is not cylindrical. Like the inside of a rose, the scroll surface follows the outlines of spiral #volutes in the front and back, neither of which are circular. So, additional steps are necessary to derive the curves that we can actually use to reconstruct the surface.

In the case of the scroll surface, the derivation of these curves is not trivial and not obvious, but it is not difficult to understand, and no math is involved. There are multiple sets of curves, and each successive set is derived from a previous set. I call them secondary, tertiary, and quaternary curves.

For now, we stick with the primary profile curves for the pedestal.

This is a sketch of the top of an #IonicColumn with #scrolls, #volutes, and other embellishments. Before I delve into my modern designs, I want to emphasize that most of them are rooted in classical designs of antiquity but still retain their timeless essence.

Different regions of the world have developed and refined distinct design patterns over thousands of years. Greeks, Romans, Ottomans, Arabs, Moghuls, Hindus, and others — all have something to contribute to what we call #art and #design in human civilization.

My initial focus is on Greco-Roman architecture and design which has five distinct orders: #Tuscan, #Doric, #Ionic, #Corinthian, and #Composite. Of these, the #IonicOrder is of medium complexity. The Doric and Tuscan are simpler, while Corinthian and Composite are more complex.

Because of its moderate complexity, I chose the Ionic Order for a complete and systematic look at its design methodology and proportions of its elements. I use concrete measurements to make concepts easier to understand. Once you understand the Ionic order, it's easy to step down to the Doric and Tuscan orders. It's more work to step up to the Corinthian and Composite orders, but if you follow my methodology with dedication, you will learn the skills necessary to tackle the more complex orders or branch out on your own.

In an earlier post, I mentioned the importance of sticking to proportions and measurements. I'll point out opportunities for variation as we progress systematically.

An additional, but very important point I want to emphasize is that this #digitalArt is not just #art, but #engineering design as well, because the end result is to realize physical artifacts from these designs, whether by #AdditiveManufacturing (#3DPrinting), #SubtractiveManufacturing (#CNC #Carving), #ReliefEngraving, #Printing, or any other physical realization.

You'll need a #CAD tool to practice, but you can also follow along as a reader initially, and come back when you're ready to practice