#EggsAndDarts is a common classical design motif with endless variations, two of which are shown here β€” 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.

Previousβ€” https://pixelfed.social/p/Splines/795361973789834465
Splines (@[email protected])

This sweeping shape is a timeless design that first appeared in the scrolls of the #IonicCapital as the most distinctive part of the #IonicOrder in classical Greco-Roman architecture more than 2500 years ago. Shown here with a zebra pattern on the wireframe of a CAD model to accentuate its features and attest to the smoothness of its 3-dimensional surface, the design has been refined many times since the original version over the last two millennia. The two most remarkable things about this design are that: β€” It can be recreated with modern CAD tools by drawing simple 2-dimensional straight lines and circular arcs exclusively. The end result is truly breathtaking and makes one wonder how architects visualized the result and put theory into practice. In the CAD model, the ultimate surface is a #NURBS surface that uses #BSplines extensively, but none of the B-splines or surfaces need to be created "by hand." One only has to draw straight lines and circular arcs with accurate measurements snapped to grids. β€” For a design that has survived the ages, it is lamentable how few authoritative sources that accurately describe fine details and exact reconstruction methodology remain accessible to the general public in the age of Internet. The most comprehensive is the 10-volume tome that Marcus #Vitruvius Pollio, a Roman architect and engineer, wrote for #JuliusCaesar and his successor Emperor #CaesarAugustus. [https://www.gutenberg.org/files/20239/20239-h/20239-h.htm] I frequently use two more authoritative sources: β€” "Regola delli cinque ordini d' architettura," or simply #RegolaArchitettura by Giacomo Barozzi da #Vignola [https://archive.org/details/gri_33125008229458/page/n3/mode/2up], and β€” "A Course in Theoretical and Practical Architecture," or simply #PracticalArchitecture by Francisco Salvatore #Scarlata (#Bordonaro), which documents #VignolaProportions in tabular form [https://babel.hathitrust.org/cgi/pt?id=mdp.39015031201190&view=1up&seq=5]

Pixelfed
Classic variation of the #IonicEntablature. Left side shows the macro-level plan. Right side shows the detailed plan for the #moldings.

All moldings should be familiar from the #IonicPedestal, except the #fascia β€” flat bands, of which there are 3, at the bottom of the #Architrave. The fascias grow progressively taller, starting at 36 units at the bottom, to 48 in the middle, and 60 at the top, with each successive one offset horizontally by 6 units from the previous one.

Above the fascia, we have a #cymaReversa which is 24 units tall and 20 units wide. Here we are using half turn of a helix with a vertical axis. Either helix or elliptical arcs are acceptable, but the choice must be consistent across the entire order. You cannot use ellipses in the pedestal and helices in the entablature, for example.

If you do use a helix, remember that it is a 3D shape like a round coil. To use it as a #profileCurve, it must be flattened to a 2D shape by #projecting it to the #constructionPlane. I will describe this technique in detail later.

The #frieze is a flat surface with no moldings. It is meant as a blank space on which to put custom decorative 3D #ReliefCarvings or sculptures.

There are no new moldings in the #cornice. Note that the order of #cymaRecta and cyma reversa are reversed from that of the #pedestal, with cyma recta at the top and cyma reversa at the bottom. The only difference between the two is that the recta has a horizontal axis and reversa has a vertical axis. Rotating either one 90Β° yields the other.

So, the bottom of the cornice starts with a cyma reversa 32 units tall and 34 wide. This is followed by a fascia 56 units tall on which the #dentils will appear later on. The 36 unit horizontal offset for the 4-unit thick fillet above it is to leave room for the dentils.

This is followed by a #reed (8 units), #ovolo (32 units), #corona (48 units), cyma reversa (16 x 12 units), fillet (4 units), cyma recta (40 x 44 units), and fillet 12 units