Continued from https://pixelfed.social/p/Splines/808187718454868394

Explode the wedge on the top with curved faces and discard everything except the two faces.

Centered on the column axis marked with A, draw two concentric circles parallel to the XY plane — one with radius AB and another with radius AC. Split both circles with the two wedge faces.

Using the edges of the two wedge faces as #rails and using the two arcs BB and CC as #sweepingCurves, perform a #sweepTwoRails operation to generate a concave surface. Join this concave surface with the two faces.

The shape we just produced still has an open hole between the two arcs BB and CC. Cap this #planarHole to create an #airtight wedge shape with curved faces. As always, check for #nakedEdges and #nonManifoldEdges.

Align the wedge shape and the two 16 units thick spirals from the previous post. Then rotate both 45° about the column axis. Rotate and copy them again at 90° about the column axis until you have the curved volutes on all four corners.

#IonicColumn #Flutes

In https://pixelfed.social/p/Splines/799864068250003272 I mentioned rounding off the radius of the bottom circle, but you don't have to. #CAD tools are perfectly happy working with 15.0728 or even higher precision as they are with 15.

After placing the two circles as described in that post, use the full #primaryProfileCurve of the shaft from https://pixelfed.social/p/Splines/791794072490907090 as a #sweepingRail and the two circles for the flutes as the #sweepingCurves, and #sweepOneRail for the body of a single flute. Close #planarHoles on both ends to get an #airtight solid.

Then draw a sphere at the center of the top circle using the same radius as the circle, and perform a #booleanUnion between the sphere and the flute body.

If you want a round bottom for the flute, repeat the sphere at the center of the larger circle using the same radius (15.0 or 15.0728) and perform another boolean union to get one flute.

Switch to the top view and make 24 copies of the flute (including the original) centered at the column axis and #group the 24 flutes.

Finally, perform a #booleanDifference with the flutes group on a copy of the solid #unadornedShaft to get a fluted variant.

The result is a column shaft with flutes carved out. Save the flutes separately for future reuse.

This concludes the entire #IonicOrder, including all #decorativeElements.

Now we pause and reflect: The whole exercise seemed like one of #art and #sculpture. Where is the #architecture in all of this?

Without a ceiling or a roof, there is no building. Without additional columns or walls, there is no ceiling. So, while we have completed the Ionic Order itself, we only have the first #buildingBlock — a single column.

Next step is to repeat the columns to create a #colonnade, which together with supporting walls or additional colonnades can support a ceiling.

Just like with everything else in design, there are rules of proportion for #intercolumniation, or space between columns.

#EggsAndDarts is a common classical design motif with endless variations, two of which are shown here — the top-left variant has convex eggs and the bottom-left variant has concave eggs. The sketch on the right shows the bottom view of the concave variant.

This motif is neither specific to the #IonicOrder, nor limited to the #ovolo of the capital. It is common to find it laid on linear #moldings like #cymaRecta or #cymaReversa of a #cornice.

The egg shape, the dart shape, the degree of convexity or concavity, and so on, are infinitely variable from subtle to pronounced. Designers are not limited to convex or concave, and it is possible to combine both in a single design. Also, it is not necessary to use the eggs and dart motif at all. There are infinite possibilities. However, when the eggs and darts motif is used, it is almost invariably sliced off at the top, as the bottom view of concave variant on the right reveals.

The concave version here is quite subtle, but a more pronounced version can be really eye-popping. I will show how to construct one using just straight lines and circular/elliptical arcs exclusively as I originally promised in https://pixelfed.social/p/Splines/789956327130679640.

As usual, we start with a flat 2-dimensional plan with lines and ovals to use as #sweepingRails. Then, we add circles and arcs as #sweepingCurves to define the cross-sections. After sweeping the cross section curves on the rails, we create the eggs.

Simply #revolve an ellipse on its major axis to get the convex version of an egg. To get the concave version of an egg, simply create a flat slab and perform a #booleanDifference on that slab using a convex egg.

Once we have all of this preparatory work done, we have to transfer the 3-dimensional design from the flat surface it was originally created on to the #doublyCurved surface of the Ovolo. This requires some elementary calculations using circle geometry.

Previous— https://pixelfed.social/p/Splines/795361973789834465

With the #secondaryCurves derived from #primaryCurves in https://pixelfed.social/p/Splines/794105734853818690, we are almost ready to sweep the #scroll surface. I say "almost" because there is at least one more refinement needed before we can use any of these curves.

Look at the front view of three sections of the scroll surface labeled A, B, and C, and you will see a qualitative difference among them. Surface A appears crude and surface C appears refined, while surface B lies somewhere in between. While B and C are both acceptable, A is not.

The difference is due to two factors — the nature of the curves themselves and the degree of precision used.

Surface A is built using the circular arc sections for #volute #spiral (original and scaled) as #railCurves and the secondary curve sections as #sweepingCurves. The nature of the two sets of curves is different. Straight lines are 1st-degree curves, #circular or #conic sections (including ellipse) are 2nd-degree curves, but the projected sweeping curves (secondary curves) are 3rd-degree #NURBS curves.

Sweeping 3rd-degree NURBS curves along 2nd-degree arcs does not produce a salubrious effect. So we #rebuild the arcs into a 3rd-degree curve using the #CAD tool. When we do that, we are able to control how close the rebuilt curve should be to the original arcs in terms of precision.

I rebuilt each arc in the spirals using 16 subsections, and the effect is visible in surface C.

Look at surface A again. The cross-section arcs appear unevenly spaced compared to those of the other surface sections. To fix that, I also rebuilt the projected NURBS curves (secondary curves) to obtain what I call #tertiaryCurves.

For the frontmost sections, I rebuilt the sweeping curves using 64 subsections, and for the rear sections, I rebuilt them with 8 subsections.

Experiment with what produces pleasing results, but remember that higher precision curves require more processing time as well as more storage space.