Columns with sunset lighting

[Helmut]

It is all 𝚪𝛄𝛒𝛆𝛆𝛋 to me...
* The really tricky bit seems to be the composition of the capitel . Abacus and echinus are trivial meshes, but the volutes are a bit complex.
* This is just a first brain storm (actually more of a mild breeze).
* As above, I stuck to parametric objects and tools from the C3D toolbox. There needs to be further editing and fine-tuning plus customising options. If I get somewhere useful, I will publish a zipped .jas template.

* The early Ionic volutes were “simplish” parallel scrolls with a pinch in the middle, but that meant that front view and side were quite differerent. So the architects / stonemasons flared out the left- / rightmost peripheral parts of the volutes and duplicated these to achieve an identical reading of the capitel on each facade.

Starship Enterprise, I(r)onic Prototype by Archimedes of Syracuse

 

[Chris Heath]

It is all 𝚪𝛄𝛒𝛆𝛆𝛋 to me...
* The really tricky bit seems to be the composition of the capitel . Abacus and echinus are trivial meshes, but the volutes are a bit complex.
* This is just a first brain storm (actually more of a mild breeze).
* As above, I stuck to parametric objects and tools from the C3D toolbox. There needs to be further editing and fine-tuning plus customising options. If I get somewhere useful, I will publish a zipped .jas template.

* The early Ionic volutes were “simplish” parallel scrolls with a pinch in the middle, but that meant that front view and side were quite differerent. So the architects / stonemasons flared out the left- / rightmost peripheral parts of the volutes and duplicated these to achieve an identical reading of the capitel on each facade.

Here is a link to how the volute is constructed geometrically (two methods)...

Delle differenti maniere di descrivere la voluta Ionica e particolarmente della regola ritrovata da Giuseppe Porta detto Salviati : con alcune riflessioni sul capitello Ionico : dissertazione : Selva, Giovanni Antonio, 1753-1819 : Free Download, Borr

Includes bibliographical references

archive.org

You may need to zoom in for a clear image.

 

[Helmut]

Thank you, Chris, for the reference!
Interesting to note that many of these analyses (Vitruvius, Vignola, Palladio, etc) go back centuries.
Some poking in the internet implies that volutes may not be any known mathematical spirals. Early Ionic volutes seem to follow an unknown algorithm, later curves are described as Cornu / Euler polynomial spirals aka clothoids. Much of this is way beyond my education (and possibly my intellect).

I remember ZooHead writing, many years ago, that he was not exactly a mathematical genius, so that makes - at least - two of us.

 

[Helmut]

FWIW, I am trying to provide a simple template for interested C3D users. The volute currently is a simple helix “out of the box”. If a precise clothoid for a specific volute in a specific temple is required, this can be replaced in the object hierarchy by a customised spline. That´s why I prefer to stick to parametric meshes and tools in prototyping.

Fine-tuning the parametric helix:
* reduce sections to obtain a square helix
* make editable and switch to Bezier
* activate soft interpolation to reestablish a helix proper
* tidy up the controlling points to achieve orthogonal tangents via scale box
* tweak the handles to achieve proper curvature
* snapping and a suitable grid size may help

If you are working with a blueprint (there are dozens of images in the internet) this will give you a precise rig for the volutes spline. A bit laborious, but a bit faster than the Hellenic stonemasons.

NB: For visibility, I show the helical spline as a sweep in red

 

[Helmut]

Ionic Template #2:
This shows the later Scamozzi version of the volutes. Still needs some work and fine tuning, but all the basics work nicely in C3D. I will use an edited / customised helix in the hierarchy, so, this gets more complicated.

 

[Helmut]

Ionic Capitel (simplified)
* Most components are parametric to allow editing.
* If you need precise volutes to show a specific temple, replace the helices in the model with customised splines, as suggested in the link of Chris Heath or in posting #24.
* For parallel Volutes, hide the sidereal volutes and show the funnel objects.

 

[ZooHead]

@Helmut Very nice work on those capitals. I've been avoiding
those Ionic versions because they always looked too difficult.

I may attempt it after I take a closer look at your file.

The latest model I've been working on is a recreation of the Tempietto del Bramante.
Luckily there are a many pictures and videos to study. I'm curious about the history
of maintenance. How much is original/replaced? There must have been many
thousands people passing through it over the years. There is evidence of
long term wear on the threshold of the left hand doorway, but not the other two.
Also there are some very obvious "patches" on the main walkway.

Here's what I have so far.

 

[Helmut]

Hi ZooHead
* The only tricky object in the Ionic capitel are the volutes. Using flat helices (height = zero or minimal for a 3D rise in the centre) in combination with an L-shaped profile gives "reasonable" results. I am actually using a letter L out of the box in sample #26.
* This geometry definitely needs a bit of editing, resulting in a better and clean geometry. Intuitively, I think that merged lofts generating nested helicoids (sort of) should give a tidy topology. I will try that as it seems a nice challenge in geometry.

* No idea about maintenance, but the Gothic cathedral in the centre of Vienna has been (partly) hidden by scaffolding for some 30 years until the work was completed a couple of weeks ago. AFAIK, blocks of sandstone are continuously checked for static properties plus moisture plus internal cracks by some sort of X-ray (?) process. In sub-zero temperatures any freezing could fragment affected blocks. To the best of my knowledge, this maintenance is executed permanently and artisans / stonemasons are on site all year.
* Surprisingly, the medieval plans are largely extant, have been digitised and are (or, at least were) public.

After a bit of experimentation: This (ie, replacing sweeps with using lofts for volutes) seems to work quite nicely. 1) Copy helix, paste plus move and 2) copy, paste plus fiddle scales.
You get a superior result if all helices are collapsed into square Bezier splines when you want a proper fit. You will need 12 sections for a volute with 3 turns, as every 360° loop has 4 arcs, be these straight lines or 1/4 circles.

 

[Helmut]

Volute Geometries: Alternatives
1 polyplane plus loft
2 L-letter sweep
3 sweep plus sweep

* Getting s proper topology for ascending helices is a bit time consuming.

 

[Helmut]

Volute Geometries: More Alternatives
Simple method, without using a helix:
* a simple linear cuboid (like a long squarish L-profiled batten) can be transformed with the bend modifier; depending on the angles relative to the orthogonal axes this can also give an ascending volute. Note that the bend modifier will give a reasonable helical, but it is not a clothoid, neither can it easily be customised to fit a specific temple.
* It seems useful as the volute can be based on parametric objects out of the toolbox.

Ascending volutes are easily generated by:
* using the loft method in linear mode plus a shell modifier; fine-tune helices as per methods above in post #24 or by refs from Chris Heath, East of Down Under.
* the bend method (above) also can result in a helical mess rising in the centre.

 

[ZooHead]

I made some progress on the little temple. The column style is Tuscan,
which takes some cue's from the Doric order, except for the flutes.