Oblate Spheroid Redux
:
( skip the boring technical stuff )
The original Master Bedroom recessed ceiling was the
hemisphere of an
oblate spheroid
(think plain M&M cut through its greatest circumference).
This gave an
impression of infinite height.
Reduced roof height
in the redesign makes an oblate spheroid impractical.
And it was quite expensive,
using large amounts of
labor,
generating
waste material
to make trusses and requiring expensive plaster work to
accommodate curves.
Gary developed a scheme to get benefits of an elliptical
reflective surface
using 2' less roof height and avoiding much expense.
The key ideas are to make a rectangular
(rather than oval)
opening and limit the elliptical curves to the outer border
of the recess –
think of it as filet of
Chiclet.
This would be similar to the halved solid of a
superellipse,
a favorite architectural element of
Piet Hein.
In the
accompanying drawing,
one can imagine that a strip of lights is mounted along the
6" shelf.
Light will reflect off the elliptical surface above and
hopefully give an effect similar to the original ceiling.
Simpler curves mean standard wall board can be used.
Doing only the border means we can use material that would
be wasted anyhow and requires less height to make steep
reflective surfaces near the light source.
This steepness is augmented by a short vertical section
between the shelf and the start of the elliptical truss.
We are saving a bit more by making the ¼
ellipse trusses ourselves.
The disadvantage of the scheme is that the elliptical
borders will come together in seams at the corners of the
opening,
which will be noticeable and interfere with the visual
effect.
There are also problems figuring out how the elliptical
trusses intersect at these corners.
The solution turns out to be simple,
but is a bit complicated to describe;
we may wind up creating a model for the carpenters to work
from.
