#ModernIonicCapital #Volute Construction
As mentioned in https://pixelfed.social/p/Splines/807933255910367093, we mentally rotate the floor plan of the modern #IonicCapital 45° so that the volute #spiral curves lie flat on the XZ plane.
The top-left diagram shows the original volute spirals from https://pixelfed.social/p/Splines/800383518517869430. If you haven't already rebuilt them from disjointed arcs to seamless #NURBS curves as described in https://pixelfed.social/p/Splines/794199123072358090, do so now. Explode the whole spiral into constituent arcs, select all arcs for the outer spiral and join them separately, and repeat this step for the inner spiral. Then, rebuild both spirals with 256 segments each.
Volute spirals for the classic and modern variants are the exact same size, but the ones in the modern version appear smaller. That's an optical illusion because the spirals are rotated 90° in the modern version as shown in the bottom left diagram.
The bottom right diagram shows the placement of the volute spirals relative to the #profileCurves of the lower portion of the modern capital. The #voluteEye is slightly above and far to the right of the #astragal profile in the modern version compared to the classic version.
At this point, we make two copies of the volute spirals and trim them to the top of the #ovolo. In one copy we only trim away the outermost arms of the spirals while maintaining the inner spirals, as shown in the bottom right figure. In the other copy, we trim away the inner spirals as shown in the top right image.
The bottom right figure in https://babel.hathitrust.org/cgi/pt?id=mdp.39015031201190&view=1up&seq=142 shows the eye 6.5 parts (52 units) from column shaft. That's not an error, but poor documentation. See floor plan in https://pixelfed.social/p/Splines/807782440025967685 where x = 198 on the square is homologous to x = 250 on the circle. To reconcile, scale 52 by 250/198 = 65.656, or 66, and offset by 120 to get 186 units.
#Astragal
#ModernIonicCapital sketch
The modern #IonicCapital with curved faces and radial symmetry is a drop-in replacement for the classic Ionic capital with flat faces.
Unlike the classic variant, which has a rectangular footprint, the modern variant has a footprint that fits in a square. In the classic variant, the volutes and scrolls project out so that they are visible from the top. In the modern variant, there are no scrolls, the volutes have a curved face, and they are completely nestled under the top.
The sketch omits the #fillet at the bottom because we added that to the column #shaft in https://pixelfed.social/p/Splines/791794072490907090.
So, we start at the bottom with an #astragal which is exactly the same size as in the classic variant.
Next up from the bottom is the #ovolo which is shorter than in the classic variant. It still has a #tectonicSurface on which #decorativeElements rest, and a #virtualSurface that envelops the decorative elements. In this case, I chose a minimalist design with no #eggsAndDarts. Instead, I use another plain ovolo as a substitute that is offset from the tectonic surface by 1 part (or 8 units, when µ = 144).
Above the ovolo is the #channel, which in this case is a round slab whose surface matches the neck of the column with a radius equal to 5/6 of µ (120 units).
Above the channel is the #abacus which has a curved face that is repeated on all four sides. There is an abacus with flat sides in the classic variant as well, but it is not visible from the front because it is hidden behind the #volute slab. In fact, the vertical #braidsAssembly in the classic variant is attached to the abacus.
Above the abacus is a #reed, and above that, another small Ovolo that tops the modern capital.
The curved volutes follow the blue circular arcs at the bottom of the sketch. The volutes are shaped like a wedge, as can be seen more clearly in the corner facing the front. The portion of the wedge between the outer rims has a concave surface.
The modern #IonicCapital with curved faces and radial symmetry is a drop-in replacement for the classic Ionic capital with flat faces.
Unlike the classic variant, which has a rectangular footprint, the modern variant has a footprint that fits in a square. In the classic variant, the volutes and scrolls project out so that they are visible from the top. In the modern variant, there are no scrolls, the volutes have a curved face, and they are completely nestled under the top.
The sketch omits the #fillet at the bottom because we added that to the column #shaft in https://pixelfed.social/p/Splines/791794072490907090.
So, we start at the bottom with an #astragal which is exactly the same size as in the classic variant.
Next up from the bottom is the #ovolo which is shorter than in the classic variant. It still has a #tectonicSurface on which #decorativeElements rest, and a #virtualSurface that envelops the decorative elements. In this case, I chose a minimalist design with no #eggsAndDarts. Instead, I use another plain ovolo as a substitute that is offset from the tectonic surface by 1 part (or 8 units, when µ = 144).
Above the ovolo is the #channel, which in this case is a round slab whose surface matches the neck of the column with a radius equal to 5/6 of µ (120 units).
Above the channel is the #abacus which has a curved face that is repeated on all four sides. There is an abacus with flat sides in the classic variant as well, but it is not visible from the front because it is hidden behind the #volute slab. In fact, the vertical #braidsAssembly in the classic variant is attached to the abacus.
Above the abacus is a #reed, and above that, another small Ovolo that tops the modern capital.
The curved volutes follow the blue circular arcs at the bottom of the sketch. The volutes are shaped like a wedge, as can be seen more clearly in the corner facing the front. The portion of the wedge between the outer rims has a concave surface.
Classic #IonicCapital #Tectonic Surfaces Plan
We already made the 8 unit tall #fillet at the bottom of the #capital a part of the #shaft in https://pixelfed.social/p/Splines/791794072490907090. So, excluding that, the remainder of the capital is 14 parts or 112 units tall, for the bottom half of which we use the #revolve operation (like the #columnBase and #columnShaft), and for the top half we use the #extrude operation (like the #pedestal, #entablature, and #plinth).
Starting at the bottom, we have an #astragal that is 2 parts or 16 units tall and has the same profile as a #reed and #torus, falling in between the two in terms of size. The arc AD is shown in gray because it is an invisible #virtualSurface that envelops the decorations like #eggsAndDarts on the #ovolo. This is the measurement that is given in #Scarlata's #PracticalArchitecture, but it makes no mention of the #decorative and #tectonic surfaces. Arc BC with a radius of 4 parts or 32 units is the tectonic surface on which the Ovolo decorations rest. Such decorations have a variable or uneven surface which may not exceed 1 part or 8 units.
Points E and F mark the horizontal tangent or maxima of the second spiral and the first (outermost) spiral, respectively. The gap between them is exactly 4 parts or 32 units. GH is the profile for the vertical side surface on which part of the #ribbon and #braid lie flat, protruding exactly 6 units to coincide with the invisible virtual flat surface through EF.
The #cymaReversa is 2 parts or 16 units tall and 1.5 parts or 12 units wide. It starts 4 units to the right of F and stops 4 units short of the top fillet, which is one part or 8 units tall and 20 parts or 160 units from the #columnAxis.
Of the 4 parts or 32 units between G and H, the lower 3 parts or 24 units are part of the #voluteChannel groove and the top 1 part or 8 units is a fillet that follows the curve of the #volute and progressively gets narrower until it converges with the #eye of the volute.
We already made the 8 unit tall #fillet at the bottom of the #capital a part of the #shaft in https://pixelfed.social/p/Splines/791794072490907090. So, excluding that, the remainder of the capital is 14 parts or 112 units tall, for the bottom half of which we use the #revolve operation (like the #columnBase and #columnShaft), and for the top half we use the #extrude operation (like the #pedestal, #entablature, and #plinth).
Starting at the bottom, we have an #astragal that is 2 parts or 16 units tall and has the same profile as a #reed and #torus, falling in between the two in terms of size. The arc AD is shown in gray because it is an invisible #virtualSurface that envelops the decorations like #eggsAndDarts on the #ovolo. This is the measurement that is given in #Scarlata's #PracticalArchitecture, but it makes no mention of the #decorative and #tectonic surfaces. Arc BC with a radius of 4 parts or 32 units is the tectonic surface on which the Ovolo decorations rest. Such decorations have a variable or uneven surface which may not exceed 1 part or 8 units.
Points E and F mark the horizontal tangent or maxima of the second spiral and the first (outermost) spiral, respectively. The gap between them is exactly 4 parts or 32 units. GH is the profile for the vertical side surface on which part of the #ribbon and #braid lie flat, protruding exactly 6 units to coincide with the invisible virtual flat surface through EF.
The #cymaReversa is 2 parts or 16 units tall and 1.5 parts or 12 units wide. It starts 4 units to the right of F and stops 4 units short of the top fillet, which is one part or 8 units tall and 20 parts or 160 units from the #columnAxis.
Of the 4 parts or 32 units between G and H, the lower 3 parts or 24 units are part of the #voluteChannel groove and the top 1 part or 8 units is a fillet that follows the curve of the #volute and progressively gets narrower until it converges with the #eye of the volute.
The bottom 1/3 of the #columnShaft for an #IonicColumn is a perfect cylinder. So the line below point B is a straight line.
In https://pixelfed.social/p/Splines/791723063470910081, we blended the bottom end of the 60° arc and the top end of the long interpolated curve between points J and K. Now blend the bottom end of the interpolated curve and the top end of the straight line between points B and C to obtain the 3rd and final #NURBS segment for the #primaryProfileCurve of the shaft.
Just like there's a #cavetto and #fillet near the #neck of the shaft, there is a fillet and cavetto near the foot of the shaft. However, there is a subtle difference between the two. The cavetto near the neck is tangential to the blended #NURBS curve that is not a straight line. The profile curve for the cavetto near the foot is tangential to a straight line.
There is a special name for a cavetto that is tangential to a straight line or flat surface, like the two cavetto moldings in the #dado of the #pedestal. It's called a #conge. Another alternate name for the cavetto molding is #cove, which is evocative of "cave" because of its concave profile curve.
Above the neck is a fillet 8 units tall and an #astragal 16 units tall that #Scarlata puts in braces in the column shaft section within his tables of #VignolaProportions, with a note saying they are not counted as part of the shaft but are accounted for as part of the #capital.
I decided to include the top fillet as part of the shaft and keep the astragal with the capital. It does not change the design or alter the proportions in any way, but the inclusion of the fillet makes it more practical for #3DPrinting and #CNCMilling of the neck. This concludes the profile curve for the shaft with a height of 291 parts or 2328 units + 8 for fillet.
The column shaft is tapered in the upper 2/3 due to #entasis whose purpose is to make optical corrections to the shape of the column which, without correction, appeared concave near the top.
In https://pixelfed.social/p/Splines/791723063470910081, we blended the bottom end of the 60° arc and the top end of the long interpolated curve between points J and K. Now blend the bottom end of the interpolated curve and the top end of the straight line between points B and C to obtain the 3rd and final #NURBS segment for the #primaryProfileCurve of the shaft.
Just like there's a #cavetto and #fillet near the #neck of the shaft, there is a fillet and cavetto near the foot of the shaft. However, there is a subtle difference between the two. The cavetto near the neck is tangential to the blended #NURBS curve that is not a straight line. The profile curve for the cavetto near the foot is tangential to a straight line.
There is a special name for a cavetto that is tangential to a straight line or flat surface, like the two cavetto moldings in the #dado of the #pedestal. It's called a #conge. Another alternate name for the cavetto molding is #cove, which is evocative of "cave" because of its concave profile curve.
Above the neck is a fillet 8 units tall and an #astragal 16 units tall that #Scarlata puts in braces in the column shaft section within his tables of #VignolaProportions, with a note saying they are not counted as part of the shaft but are accounted for as part of the #capital.
I decided to include the top fillet as part of the shaft and keep the astragal with the capital. It does not change the design or alter the proportions in any way, but the inclusion of the fillet makes it more practical for #3DPrinting and #CNCMilling of the neck. This concludes the profile curve for the shaft with a height of 291 parts or 2328 units + 8 for fillet.
The column shaft is tapered in the upper 2/3 due to #entasis whose purpose is to make optical corrections to the shape of the column which, without correction, appeared concave near the top.
#IonicColumn #VignolaBase and #AtticBase #CAD Plans
Both #Vignola base and #Attic base have the same square footprint of 400 units x 400 units. The #plinth for both is 48 units (6 parts, or µ/3) tall, and the total height for both is 144 units (18 parts, or exactly µ). As such, they are easily interchangeable.
In the Vignola variant, we start at the plinth with a #fillet 2 units tall and a classic #scotia 18 units tall gouging out part of the fillet.
Then there is another fillet 2 units tall, followed by two #reeds, each 8 units tall, followed by another classic scotia as described above.
This is followed by yet another fillet 2 units tall and topped off with a #torus 40 units tall. A Torus is the same as a reed, except larger. When we reach the neck of the shaft, we will see another molding called #Astragal which has the same profile as reed and torus, but sits in the middle in size. Think of reed, astragal, and torus as small, medium, and large of the same profile.
The modern Attic variant is more elegant with fewer moldings. It also gives the impression of more heft for more stately columns. It starts at the plinth with a torus 36 units tall, followed by a fillet 4 units tall, followed by a modern scotia 24 units tall, followed by another fillet 4 units tall, and topped off with another torus 28 units tall.
As in the construction of #IonicEntablature [https://pixelfed.social/p/Splines/791013152244518907], split the construction of the #columnBase into two steps.
Just as we extruded #dentils separately, we extrude the plinth separately. First draw a square 400x400 in the top view. Then extrude the square 48 units in the front view.
For the rest of the base, we need a new 3D operation — #revolve around an axis. Instead of extruding the #primaryProfileCurve, we revolve it around the #columnAxis, and cap the #planarHoles on both ends before performing a #booleanUnion with the plinth. Finally check edges of the solid for #nakedEdges and #nonManifoldEdges.
Both #Vignola base and #Attic base have the same square footprint of 400 units x 400 units. The #plinth for both is 48 units (6 parts, or µ/3) tall, and the total height for both is 144 units (18 parts, or exactly µ). As such, they are easily interchangeable.
In the Vignola variant, we start at the plinth with a #fillet 2 units tall and a classic #scotia 18 units tall gouging out part of the fillet.
Then there is another fillet 2 units tall, followed by two #reeds, each 8 units tall, followed by another classic scotia as described above.
This is followed by yet another fillet 2 units tall and topped off with a #torus 40 units tall. A Torus is the same as a reed, except larger. When we reach the neck of the shaft, we will see another molding called #Astragal which has the same profile as reed and torus, but sits in the middle in size. Think of reed, astragal, and torus as small, medium, and large of the same profile.
The modern Attic variant is more elegant with fewer moldings. It also gives the impression of more heft for more stately columns. It starts at the plinth with a torus 36 units tall, followed by a fillet 4 units tall, followed by a modern scotia 24 units tall, followed by another fillet 4 units tall, and topped off with another torus 28 units tall.
As in the construction of #IonicEntablature [https://pixelfed.social/p/Splines/791013152244518907], split the construction of the #columnBase into two steps.
Just as we extruded #dentils separately, we extrude the plinth separately. First draw a square 400x400 in the top view. Then extrude the square 48 units in the front view.
For the rest of the base, we need a new 3D operation — #revolve around an axis. Instead of extruding the #primaryProfileCurve, we revolve it around the #columnAxis, and cap the #planarHoles on both ends before performing a #booleanUnion with the plinth. Finally check edges of the solid for #nakedEdges and #nonManifoldEdges.
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