The light census
Each cut is scaled to unit size in plan. For each gemstone, 3,200 rays from a fixed seed fall on the stone from above: their directions are cosine-weighted within 0.12 rad (6.9°) of vertical, and their starting points cover a disc larger than the stone. Rays that miss are not counted, and every ray that enters is fully transmitted: there is no Fresnel loss. Inside, a ray reflects totally or leaves through the first facet that lets it out, for up to 12 bounces. Each entering ray ends in one class:
- Useful
- out through the crown, after at least one pavilion reflection, within 64° of vertical
- Blink
- out through the crown without touching the pavilion
- Leak
- out through the pavilion, or through the crown heading down
- Grazing
- out through the girdle
- Lost
- out of the viewing cone, or still inside after 12 bounces
A useful ray also counts as fire when refracting it out at n − Δ and at n + Δ sends the two colours more than 0.6° apart. The census runs twice: face up, and tilted 20° about x (2,200 rays).
The eight axes
With N the rays that enter, f the cut’s active facets and depth in per cent:
- Brilliance and fire are traced. Fire is a share of the useful light, not of all light, so a dim stone can still score high on fire.
- Scintillation is not traced. It is a saturating function of the number of facets that reach the surface; buried planes do not count. It is the same in every gemstone.
- Tilt is retention: how much of its face-up light a cut keeps at 20°. It is capped at 100, so a dim cut cannot score well for having little to lose.
- Symmetry groups the pavilion facets into angle families, split wherever consecutive angles differ by more than 0.45°. σ is the size-weighted mean, over families, of the standard deviation of their angles plus 57.3 times the relative standard deviation of their distances from the centre, both in degrees. A multi-angle pavilion is a design, not an asymmetry.
- Spread is face-up size per carat against a 61.5% deep stone. Weight goes with the cube of the diameter, hence the cube root.
- Shape-norm compares brilliance with a ceiling for the cut’s family: 93 for round brilliants, 86 for fancy brilliants, 76 for step cuts and 64 for the rest.
Spread and Shape-norm are the only axes that can pass 100. The wheel draws them on the 100 ring and the list gives the true figure. Every other axis is an absolute figure, not scaled to any reference. The T73 round brilliant in the same gemstone is the comparison: the dashed outline on the wheel and the thin mark on each cut-page bar. In diamond it reads 93 brilliance, 78 fire and 80 scintillation.
House cuts
DG-M5 and DG-Rafaello use research plane sets that match our models to within 0.09°. DG-Miliano, DG-Elongated Hexagon and DG-Octagonal Kite are measured on our own models, placed as the census places every stone. Before those scores are accepted, six cuts with known figures are re-measured the same way, and each must land within 0.5 of its Global score. Three cuts are not measured: the heart, because it is concave, and DG-Cabochon and the Elongated Hexagonal Bipyramid, because they have no table for face-up light to enter.
Rankings
- Cut pages tag “Highest brilliance” and “Highest fire” on the gemstones with the highest rounded figure, and “Best overall” on the highest brilliance plus fire. Scintillation is left out there because it is the same in every gemstone. Ties tag every stone.
- Gemstone pages rank cuts by brilliance + fire + scintillation, rounded. Equal totals share a place (1, 2, 2, 4), and every cut placed tenth or better is shown, so a list can run to eleven. Brilliants and jewelry cuts are ranked separately.
The Cut Performance Wheel, the chart on every cut page and the top ten on every gemstone page share one set of scores, computed once by our face-up light census and stored unrounded. Pages round half up for display.