"Quadrature" refers to a special category of trompe l'oeil painting.
There were churches which had a slightly concave roof, not a real dome.
However, parishoners of these churches wanted the cachet of having great
works of art painted on their church dome. This could be catered to by
using trompe l'oeil "dome" paintings which made their relatively flat
domed churches appear to have deep vaulted domes. Thus the rectangular
(quadratured) flat roof could be made to appear like the Sistine Chapel.
Several paintings that use quadrature have a occulus that opens to the
sky, as is the case above. Indeed, the painted roof above is in fact
almost a Euclidean flat surface!
Illusionist quadrature paintings have also been used outside of churches,
for example, to give a feeling of a very much exaggerated estate size.
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