SplinesThis 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
Splines (@Splines@pixelfed.social)
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: — 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. — 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: — "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 — "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]