It is important to note that
this analysis has three limitations:
- It assumes that pavilion and bezel slopes are constant:
This is essentially true for brilliant cuts, but not for
- It assumes that opposite facets have a common normal plane:
This is true for round, square, and rectangular girdle shapes,
but not for oval, pear, marquise, etc.
- It assumes that rays are in a plane through the gem axis:
This is only a small part of all rays, but these are the
only ones which can be analyzed simply.
The first two assumptions are
also inherent in the design slopes recommended by various
references; such data were developed by trial-and-error on
round brilliant cuts but may be used as approximate guides
for other cuts.
It is most significant, however,
that the theoretical results show good correlation with those
proven by trial-and-error, despite the third limitation described
above. This indicates the validity of the method.
The key to this study was the
effect of the viewer`s head, which can be observed by close
study of reflections in a cut gem. Other criteria which may
have been overlooked will be added in later articles. Several
sequels are already in process which probe specific aspects
of the problem in more detail.
As it stands, this is believed
to be one of the better faceting guides to date. Comments
from readers will be welcomed and reviewed toward making it