Thomas de Groot wrote:

> 
> I followed the Greek guideline that says that a column, to be appealing to 
> the eye, should not be a simple cone shape but bulge a tiny bit out at the 
> middle. I acchieved this by using a vertically very elongated sphere, cut at 
> the middle (i.e. the base of the column) and at the place where the top 
> should be. You have to experiment with the vertical elongation until you 
> have both bottom and top diameters correctly. An easy way to do this is to 
> first make a proxy model in Moray to get the measurements needed.

Yes, my approach too.  I saw somewhere on the web that Roman columns 
have more of a middle bulge but Greek have a curved taper but the base 
is the thickest.  No idea if they knew what they were talking about.
http://www.uen.org/Centennial/08BuildingsA.html



> 
> Once the shaft of the column is thus obtained, I used (again) vertically 
> very elongated toruses so that the curvature matched the curvature of the 
> shaft. Again, a proxy in Moray can help but is not strictly necessary. The 
> toruses have to be cut to the correct length of the flutes, provided with a 
> top end (a sphere) and a bottom end (an inclined section). Then, by boolean 
> substraction from the shaft, the flutes are successively modelled into the 
> column shaft.

Interestting.  So even though you are using mesh you used boolean 
subtraction of torii?  Again I have been trying exactly the same 
approach but with POV CSG.  The problem I had was getting the 
circumference of the torus to decrease at an rate appropriate to the 
diminishing circumference of the tapering shaft.

The other problem was how to position the spheres to difference out at 
the top of the flutes.  The solution I thought for the second issue was 
to begin with a sphere of radius square root two.  Then if I made the 
cap of the column at height one unit before scaling, the radius there 
would always be one unit no matter how I scaled it vertically, and using 
the supposed Greek model, the bottom radius would remain root two. So 
differencing spheres at both the top and bottoms of the column would be 
a known quantity.  (Actually with a little more calculation a narrower 
base could also be scaled down in the negative direction and have the 
radius remain known)

But what screwed this method up was the fact that the vertically scaled 
torii do not have a diminishing footprint on the diminishing 
circumference of the shaft.  By overscaling by 5/4 vertically, (ie if I 
wanted the top of the shaft to be at 20 units, I would scale the sphere 
and torii by 25 times vertically), I managed to get the relationship 
between the torii and the shaft circumference to look okay to the eye, 
at least, though the flutes are still narrower at the base than at the 
top.  But as soon as I did that I lost my ability to exactly position 
the spheres at the top.  If there is a mathematical relationship 
describing what the radius would be at the 4/5 point I couldn't find it. 
  I finally managed an 'eyeballed' solution for positioning the spheres 
but this feels as unsatisfying in so far as I doubt it would hold up for 
different ratios of height to radius.

The obvious advantage of mesh it is that the polys match the contour of 
the surface so that a vertical line of polys could be used to shape a 
flute which would diminish in size appropriately. So now I an curious as 
to why you used the boolean approach.


> 
> If you want to follow the classical rules, number and form of the flutes are 
> fixed, but that is another discussion entirely.

I would be intereseted if you have any references.  Right now I am using 
18 flutes, so a 20 degree rotation.


> 
> Once you have the shaft modelled to your satisfaction, you can model 
> separately the different elements that form the base of the column, and the 
> top. The top part is particularly challenging because of the distinctive 
> capitals. I have not attempted the Corynthian order!! The Ionian order is 
> already difficult enough. I used a background image as a proxy for modelling 
> that particular spiral shape.

Yeah, I'll give that a wait.  Actually for my purposes I can diverge 
from the strictly classical and indulge myself with my own caprices as 
well as any 19th century neoclassical architect


> 
> I won't speak now about corner columns!!! They have their own challenges in 
> the way to model the capitals.

Hasn't come since it is a circular collonade but will remember that when 
tempted to do the other.

> 
> The result is shown in this low resolution image when I finished building 
> the complete temple.

Very nice.  I am also impresses with the texture in 'Eavesdropping', 
which, if you are using mesh, must be a perturbed normal?

-Jim

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