roman ogee geometry

Hi all,
Maybe I'm dense and everybody else on the planet already knows the answer to the following question.
Is it by definition that a roman ogee is self-complementary? I don't think that is true for all ogee's. Yes/no?
Consider the following. Cut an ogee on a piece of trim using a router. Let's say you need to fit another piece of trim perpendicular to the first. If the roman ogee is it's own complement than you can use the same bit, with the second piece upside down relative to the first and get an exact fit. No coping necessary.
hex -30-
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Of course you do, GOAT.
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On 28 Dec 2003 15:56:38 -0800, snipped-for-privacy@yahoo.com (hex) wrote:

Yes (I'm pretty sure) and definitely no.
An ogee is a moulding derived a cyma curve. Architectural and archaeological references may talk about cyma more than ogee. The cyma has an ancient historical tradition and they were widely used by both Greeks and Romans as the basis for an architectural frieze or cornice, then carved with a moulding; acanthus leaves, egg & dart etc..
As is widely known, you can cut a cyma either way up - cyma recta, or cyma reversa. The cyma recta (concave part above convex) on a cornice is more usual on the cymatium - the very top moulding, with nothing above it. Lower down in the architrave and often used to support the cornice, the cyma reversa has the convex part (the bulge) above the concave. This is thought of as visually more "supporting" than the cyma recta which looks "hollow" and "fragile" on its upper edge.
The ogee (strictly speaking) is a cyma reversa. When used in a freehand router on a table top, the typical "ogee" router cutter actually cuts the other sort, the cyma recta. Although this cutter in a table can cut either way, depending on how you feed the stock.
The Greek and Roman cyma curves are distinguished by the Greek being based on ellipses, the Roman on circular arcs. It's common for the Greek cyma to be asymmetric, usually a cyma recta with a smaller lower curve to give a larger area for a carved hollow moulding. As far as my refs can tell though, all the Roman cyma are symmetrical.
A good text on these styles is Carving Architectural Detail in Wood Frederick Wilbur <(Amazon.com product link shortened)>
It's a book of two parts. One is obviously a guide to the technical aspects of carving such details. Perhaps the more interesting though is a very accessible history of architectural details in the classic tradition of Greece, Rome and Palladio, through to Colonial America. It does assume a certain level of carving skill and is thankfully brief on the usual repetition of basic techniques. Any woodworker (or even a stonemason) looking to choose the mouldings to use on 18th century furniture, interiors fittings such as mantelpieces, or an exterior facade or portico will find this a very useful book.
-- Klein bottle for rent. Apply within.
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(hex)

<Much information snipped>
Andy, Thanks for the encyclical reply including references! -- much more interesting than the feeble attempt to drive the discussion far off topic and into the gutter. I didn't see your reply go by and had given up the thread as dead/useless.
hex -30-
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