SplinesMar 13, 2025
#Milestone9 - #ArcadeIntercolumniation #Keystone and #Modillion

#Arch without Pedestal https://pixelfed.social/p/Splines/803615973439041638

#Arch with #Pedestal and Keystone https://pixelfed.social/p/Splines/804537414363507454

#Keystone and #Dentil Details https://pixelfed.social/p/Splines/804548474524642209

#Modillion Details https://pixelfed.social/p/Splines/805587292338863257

#ModernEntablature with Detail https://pixelfed.social/p/Splines/805607059171193759

#Milestone8 - #SimpleIntercolumniation https://pixelfed.social/p/Splines/803106316515798367

#Milestone7 - Complete #IonicOrder https://pixelfed.social/p/Splines/800050647761776920

#Milestone6 — #Braids #3StrandBraids https://pixelfed.social/p/Splines/799602946527813102

#Milestone5 — #EggsAndDarts https://pixelfed.social/p/Splines/797069447808333887

#Milestone4 — #IonicScroll https://pixelfed.social/p/Splines/795361973789834465

#Milestone3 — #IonicColumn https://pixelfed.social/p/Splines/792803978865652429

#Milestone2 — Classic #IonicEntablature https://pixelfed.social/p/Splines/791021871062069787

#Milestone1 — #IonicPedestal https://pixelfed.social/p/Splines/790752092700055739
Splines (@[email protected])

#Arcade #Intercolumniation without #Pedestal In https://pixelfed.social/p/Splines/803089629244302486, we saw #simpleIntercolumniation, also known as #Architravato. Roman architects combined columns with walls thick enough to bury half of the column width inside the walls and added arches to them for better load distribution. An arcade (multiple arches) can be run in series along a single wall, or in parallel to form a walkway. They can also be combined in both series and parallel configurations, perhaps the most famous of which is the #Colosseum in Rome. In the Colosseum, the outer walls follow an elliptical curve (even though it looks circular from the outside), and it has multiple tiers of arches in series. The interior has arches in concentric passageways in the lower tiers giving it a lattice-like design. Because arches distribute the load from above, they allow for wider intercolumniation. The rules for #ArcadeIntercolumniation differ depending on whether the columns have pedestals or not. Besides the arch itself, which is part of the wall, the figure shows some new architectural elements. The narrow part of the wall immediately behind a column is known as a #pier. The visible face of a pier between a column and the opening under the arch is known as #alette. The base of the pier has a molding, the flat part of which has the same height as the column base (µ) while the rest follows the #fillet and #cavetto or #conge of the #shaft. As we move up the pier, there is a horizontal molding known as #impost just below where the arc of the arch starts. The impost wraps around on the sides of the pier. Around the arc is a circular molding known as #archivolt, the bottom portion of which has a #fascia that is aligned with the face of the wall. The wall itself extends all the way to the top of the #entablature. It is worth noting that the entablature is repeated on the wall. It doesn't end at the columns and has two "outside" corners and one "inside" corner.

Pixelfed
SplinesMar 13, 2025
#ModernIonicEntablature with #modillions and #dentils adapted for #arcadeIntercolumnation.

This image shows modillions across the top of the entablature, including modillions visible on the side wall. The dentils are below the modillions and are a bit shorter than in the classic variant.

As with dentils, a #modillion must be centered on a column axis. In the front, there are two modillions directly above the two columns and eight other modillions equally spaced between them. The number is always 10. So the spacing is different for an #arch with no #pedestals.

This image also shows a skinnier #keystone. Its thickness is half that of the one shown in https://pixelfed.social/p/Splines/804548474524642209 but all other measurements remain the same. There is never a modillion directly above the keystone.

The #cymaReversa and #fillet above the keystone have #profileCurves identical to those in the #capital but the top is a square that is only µ x µ units. The top slab is centered front to back on the face of the arch.

In this image, the modern entablature is shown with the classic capital, but it goes really well with the #modernIonicCapital. As I mentioned in https://pixelfed.social/p/Splines/791065657488081419, the classic variant of the column capital has parallel flat #volute slabs only visible from the front and back, but not from the sides. Because of its lack of radial symmetry, the capital does not look as satisfying when viewed from the side, especially in a #colonnade, as seen in https://pixelfed.social/p/Splines/803089629244302486.

The modern variant has curved volute faces on all four sides with pointed ends at all corners and optimized for use in a corner column, but not limited to that. The modern #IonicCapital is the last remaining piece in our systematic look at the complete #IonicOrder.

This concludes our look at the entablature, both classic and modern, and both for #simpleIntercolumniation, or #Architravato, and #arcadeIntercolumniation.
Splines (@[email protected])

#Arch with #Ionic #Entablature and #Keystone Detail The #dentils arrangement we saw in https://pixelfed.social/p/Splines/791013152244518907 goes well with the classic entablature #profile we saw in https://pixelfed.social/p/Splines/790888454384861893, and they both go well with #simpleIntercolumniation, also known as #architravato. However, with arches, the entablature profile has to be adjusted a bit so that the dentils arrangement is as shown here. The shape, size, and gap between individual dentils remains the same, but a crucial difference is that the dentils at the #outer corners touch each other. As I mentioned in https://pixelfed.social/p/Splines/803615973439041638, in #arcadeIntercolumniation, the entablature is repeated on the wall behind the half-column. It doesn't end at the columns and has two "outside" corners and one "inside" corner. While the dentils at the outer corners touch each other, there is a single dentil in the inside corner that is shared by both walls. A bedrock principle of dentils (like that with #flutes and with eggs in the #EggsAndDarts motif) is that when viewed directly from the front or the sides, a dentil must be centered on the column axis. It is this principle that forces us to adjust the profile of the entablature in arcade intercolumniation giving us the arrangement shown here. The image also shows the detail of the decoration in front of the #keystone. The most easily recognizable component of that is the large #volute, which is the exact same size as the ones on the #capital. The smaller volute is exactly half the size of the larger one. It is mirrored, rotated and put within a bounding rectangle whose height is exactly 2µ (288 units). The channels of both volutes are bridged with #sinusoids derived from half turn of #helix curves that have been flattened. This motif in the keystone, where volutes of different sizes are combined with sinusoids is very common. It will be seen in the #modillions of the #modernEntablature.

Pixelfed
SplinesMar 6, 2025
#Milestone8 - #SimpleIntercolumniation

Floor Plan of archetypal Greek Temple https://pixelfed.social/p/Splines/803021258359555093

Front and back #intercolumniation https://pixelfed.social/p/Splines/803076419096100108

Side intercolumniation https://pixelfed.social/p/Splines/803089629244302486

#Milestone7 - Complete #IonicOrder https://pixelfed.social/p/Splines/800050647761776920

#Milestone6 — #Braids #3StrandBraids https://pixelfed.social/p/Splines/799602946527813102

#Milestone5 — #EggsAndDarts https://pixelfed.social/p/Splines/797069447808333887

#Milestone4 — #IonicScroll https://pixelfed.social/p/Splines/795361973789834465

#Milestone3 — #IonicColumn https://pixelfed.social/p/Splines/792803978865652429

#Milestone2 — Classic #IonicEntablature https://pixelfed.social/p/Splines/791021871062069787

#Milestone1 — #IonicPedestal https://pixelfed.social/p/Splines/790752092700055739
Splines (@[email protected])

Floor Plan of https://pixelfed.social/p/Splines/802974815166948953 showing #intercolumniation. Greek architects classified temples and public buildings based on number of columns in front, number of columns in both front and rear, as well as interior columns. The simplest buildings are those with walls on three sides, and partial walls called #antae (singular #antis) in front, flanked by just two columns. Buildings with 2 columns in front are #distyle, 4 columns are #tetrastyle, 6 are #sexastyle, 8 #octastyle, 10 #decastyle, and those with 12 columns would be #dodecastyle. The classifications are refined further. Those with 2 columns flanked by antae are called #inAntis. These never have any columns in the back or sides. Tetrastyle buildings with 4 columns only in the front are #prostyle, and those with 4 columns in both front and back are #amphiProstyle. Sexastyle buildings like those in the previous post are called #peripteral. Octastyle buildings with densely arranged internal rows are called #dipteral, and when some internal columns are removed, the sparse structure is called #pseudoDipteral. Decastyle buildings are also called #hypaethral. With 10 columns in front and rear, these are noteworthy for their width. In fact, they are so wide that they don't have a roof in the middle, which is open to the sky. Only the four sides have roofs supported by columns. In addition to the number columns, there is a further classification based on #intercolumniation. #Vitruvius described five classes of temples, designated as follows: "#pycnostyle, with the columns close together; #systyle, with the intercolumniations a little wider; #diastyle, more open still; #araeostyle, farther apart than they ought to be; #eustyle, with the intervals apportioned just right." The building in my previous post (shown without walls) has 6 columns in front and back — so, it is sexastyle. It is also known as a "Peripteral Eustyle," with column "intervals apportioned just right."

Pixelfed
SplinesFeb 26, 2025
We have now looked at every nook and cranny of the complete #IonicOrder in microscopic detail.

Here is one more look at the underside of the #ovolo to revel in the splendor before we move on to the macro level, the first step of which is arranging columns in a row to create a #colonnade according to spacing rules known as #intercolumniation.

Colonnades need not be straight and can follow arcs or other (preferably loose) sweeping curves.

As mentioned in https://pixelfed.social/p/Splines/790357912719769731, a #pedestal is always optional.

Greek designers designed the Ionic Order with full columns. The Romans introduced half columns on surfaces of walls, with or without arches. Multiple columns with arches, whether in series or in parallel, are called #arcades.

The rules for #arcade intercolumniation are different from those for simple intercolumniation, varying even by whether pedestals are present or not.
Splines (@[email protected])

This is a sketch of the complete #IonicOrder, excluding #intercolumniation and #arches, which came later. Different people have different abilities and different levels of mathematical knowledge. I make few assumptions about the minimum knowledge one must possess to follow my posts. At a minimum, one must understand ratio, proportion, similar, congruent triangles, Pythagoras, and basic properties of circles, including radius, diameter, circumference, tangents, secants, and chords. No trigonometry or calculus is assumed, but people who have a knowledge of differentiable continuity, maxima, minima, and inflection points will have increased appreciation of the nuances of some designs featuring smooth curves and surfaces. I start with first principles, even if it might be a little boring for people with advanced skills. The most basic requirement is that one must be able to mark points on a 3D grid, draw a straight line between two points, and draw a circle or arc from the center. The CAD tools should help with the rest, for example, to find a point of tangency, draw a circle through three arbitrary points, or tangential to three curves (if possible). There are three components in the #Ionic order. Starting at the bottom is the #pedestal (which is optional), the #column, and the #entablature. Each of these three components has three subcomponents: — Pedestal has #basement, #dado, and #cap. — Column has #base, #shaft, and #capital. — Entablature has #architrave, #frieze, and #cornice. The pedestal, column, and entablature are always in 4:12:3 ratio. If all components are present, the total order height is divisible by 19. If there's no pedestal, the total height is divisible by 15. The entire order is parameterized by a SINGLE parameter — the radius of the column at its base. #Vitruvius called the radius a "module" (µ) — an abstract unit of measure independent of physical units. Components of Ionic column and entablature also have classic and modern variations.

Pixelfed
SplinesFeb 25, 2025
#Milestone7 - Complete #IonicOrder with fluted and unadorned #IonicColumn with details of #decorativeElements

#Milestone6 — #Braids #3StrandBraids https://pixelfed.social/p/Splines/799602946527813102

#Milestone5 — #EggsAndDarts https://pixelfed.social/p/Splines/797069447808333887

#Milestone4 — #IonicScroll https://pixelfed.social/p/Splines/795361973789834465

#Milestone3 — #IonicColumn https://pixelfed.social/p/Splines/792803978865652429

#Milestone2 — Classic #IonicEntablature https://pixelfed.social/p/Splines/791021871062069787

#Milestone1 — #IonicPedestal https://pixelfed.social/p/Splines/790752092700055739
Splines (@[email protected])

#Milestone 6 — #Braids #3StrandBraids #Sinusoid from #Helix https://pixelfed.social/p/Splines/797893262102038801 Braid Geometry https://pixelfed.social/p/Splines/797916882329430160 Braid Strand https://pixelfed.social/p/Splines/798252244743520392 Braid Assembly https://pixelfed.social/p/Splines/799340150182400358 Braid #FlowOnSurface https://pixelfed.social/p/Splines/799514176049543252 #Milestone 5 — #EggsAndDarts https://pixelfed.social/p/Splines/797069447808333887 #Milestone 4 — #IonicScroll https://pixelfed.social/p/Splines/795361973789834465 #Milestone 3 — #IonicColumn https://pixelfed.social/p/Splines/792803978865652429 Milestone 2 — Classic #IonicEntablature https://pixelfed.social/p/Splines/791021871062069787 Milestone 1 — #IonicPedestal https://pixelfed.social/p/Splines/790752092700055739

Pixelfed
SplinesFeb 25, 2025
#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.
Splines (@[email protected])

#IonicColumn #Flutes This diagram shows the 2D geometry of an #Ionic #flute. The larger blue circle shows the flute outline near the #base of the #column. The smaller blue circle shows the flute outline near the #neck of the #shaft. Both subtend a 12° angle at the center of the column. Like an egg in the #EggsAndDarts motif, a flute must be centered on the column axis when viewed directly from the front, back, or the sides. This is why the 12° are split into 6° on either side of the X axis. The center of the larger circle is µ = 144 units from the origin on the X axis. The center of the smaller circle is 5/6 of µ, or 120 units from the origin. In https://pixelfed.social/p/Splines/799340150182400358, I mentioned working at sub-micron precision, and you might wonder where that came from when we have been using abstract units like µ without specifying any physical units. My apologies for not making it clear that I had assumed 1 unit was equal to 1 mm. If that assumption holds, then µ = 144 mm gives a total order height of 4104 mm, that is 13.46 ft. At smaller scales, the precision is even higher than 1/10 of a micron. With that said, here the radius of the larger circle is 15.0728 units and that of the smaller circle is 12.5606 units, with sub-micron precision if 1 unit = 1 mm. Refer to https://pixelfed.social/p/Splines/791399680747885646 and place the center of the smaller circle exactly at point J on the neck line. Later we will draw a sphere at the same location with the same radius. If you want a flat bottom for flutes, place the center of the larger circle at exactly 28 units (12 for the #fillet and 16 for the #cavetto or #conge) above point A in that figure. If you want a round bottom, then further move the larger circle up by the size of its radius. Nobody would quibble if you used a radius of 15 units instead of 15.0728 units, but it would make it easier to switch from flat to round bottom or vice-versa by simply moving the circle up or down 15 units.

Pixelfed
SplinesFeb 24, 2025
#IonicColumn

#Flutes have a different configuration in the #IonicOrder than they do in the #DoricOrder. In #Doric, the flutes run right next to each other, dividing the circumference of the column into 24 equal sectors, or 15° each.

In #Ionic, there is a small gap between the flutes. This gap used to vary, but over time, Ionic designers seemed to have settled and standardized the measurements by splitting 15° in 4:1 ratio, giving 12° to a flute and 3° to the gap between flutes.

Because of this standardization, there would seem to be little room for variants, but there is. In his #RegolaArchitettura [see https://archive.org/details/gri_33125008229458/page/n37/mode/2up], #Vignola documented flutes with hemispherical tops but flat bottoms, as shown in the image here.

However, it is acceptable to have hemispheres at both top and bottom as long as they are consistently used within a #colonnade or #arcade.

Flute geometry is interesting. Just like the #IonicColumn #shaft, a flute also gradually tapers as it rises from bottom to top. Additionally, it bends along the shaft surface due to #entasis [see https://pixelfed.social/p/Splines/791794072490907090]. In other words, flutes hug the column shaft.

Unlike other decorative elements like #eggsAndDarts and #3StrandBraids, flutes are #subtractive, not #additive to the rest of the design. In other words, we have to carve the flutes out instead of adding them to the design.
Regola delli cinque ordini d' architettura : Vignola, 1507-1573 : Free Download, Borrow, and Streaming : Internet Archive

48 leaves : 44 cm (fol.)

Internet Archive
SplinesFeb 24, 2025
#3StrandBraids #FlowOnSurface

In the top-left, the highlighted magenta portion shows the interface between the #braids assembly and the #IonicScroll from https://pixelfed.social/p/Splines/795276076797088402.

Extract the #profileCurve shown as ABC in the top-right where the interface meets the scroll.

In https://pixelfed.social/p/Splines/794199123072358090, we rebuilt curves from 2nd-degree arcs to 3rd-degree NURBS for smoothness and swept the scroll surface one set of arcs at a time.

Now we have to flow braids on a single surface in one operation. So we need to combine the separate segments into a single NURBS curve. To do that, #explode the profile curve into individual segments, discard the straight portion, and join the curved portions.

Curves and surfaces have a #direction that you can change in the #CAD tool. Check that the direction of the joined curve is A to C, not C to A, and flip it if necessary. Then divide the curve at 120 units starting at A. This is marked by point B. Split the curve AC at B so that AB is 120 units long.

At this point AB is still made up of 5 segments, and exploding it would again decompose the curve into separate segments. So #rebuild AB as a single NURBS curve with 32 sections.

#Extrude AB to get a 48 units wide surface shown in magenta in the top-right. Point D is at the midpoint of AE and lies on the XZ plane.

Slice the channel assembly so that it is 8 units tall, 6 of which will be above the #tectonicSurface for the braid and 2 below. The tectonic surface is shown in the bottom-left as the flat magenta surface on the channel and the curved magenta surface for the scroll neck.

Flow the entire braid and channel assembly along the curved surface lining up points A, D, and E. For the vertical part on the side of the capital, just use the 33 unit tall block from https://pixelfed.social/p/Splines/799340150182400358 and bury 1 unit inside the #ovolo.

This concludes 3-strand braids. Only the non-essential #column #flutes remain.
Splines (@[email protected])

After ensuring that the object in https://pixelfed.social/p/Splines/795271266191779399 is #airtight, extrude the front and rear planar surfaces by 1 part (8 units) on each end. At the end of this step, you should have a solid #scroll object with a smooth surface except for the flat parts that will butt against the head of the unadorned #capital. We have now concluded the #tectonic portions of the entire #IonicOrder. All that remains are decorative #eggsAndDarts that go on the #ovolo of the capital and the #3StrandBraid that goes on the scroll.

Pixelfed
SplinesFeb 18, 2025
#3StrandBraids

#Braids are the last of the #decorative elements on the #IonicScroll, but like #EggsAndDarts, they are not specific to the #IonicOrder.

Braids are a popular design motif that find wide currency in modern #hairstyle, #fashion, and fashion accessories like #belts and #bracelets.

Braids come in infinite varieties with varying number of strands, thickness of strands, roundness or flatness of strands, and how tightly or loosely they are wound together. Here, I focus on the 3-strand variant mentioned in #Vignola's book and previewed in https://pixelfed.social/p/Splines/792015485979791089. The image here is brightly colored to draw attention to the 3 strands.

The geometry of braid strands is not at all obvious despite how familiar they look. Also, a braid strand is the only feature in the entire iconic order whose geometry cannot be captured with straight lines and circular arcs. Instead, a strand geometry must be defined in a series of steps starting with a basic #sinusoidal curve.

A sinusoidal curve or #sinusoid is a wave form whose function belongs to a family of functions known as #transcendentalFunctions that also include #logarithmic and #exponential functions. I mentioned #logarithmicSpirals in https://pixelfed.social/p/Splines/792499765146596723, and in a future post I will show how to construct one and compare it with the #spiral used in our implementation of #IonicVolute.

They are called transcendental functions because they transcend the math of finite algebraic polynomials and go beyond geometry into trigonometry. Fortunately, we don't have to go there.

Few #CAD tools have a direct primitive for a sinusoid, but almost all have a primitive for a 3-dimensional round coil shape called a #helix which we can use to create the sinusoids we need for a braid strand. To create a sinusoid, all we need to do is #project a helix on a flat surface to convert it into a 2D waveform.
Splines (@[email protected])

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.

Pixelfed
SplinesFeb 13, 2025
#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
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: — 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]

Pixelfed