3D Gemstone Simulator

The trace

Each pixel is ray-traced on the graphics card. The camera is a pinhole about five stone widths away. At the entry facet, a Fresnel fraction F reflects off the crown and the rest refracts in. Inside, the ray bounces up to 14 times. At each facet where it can escape, the transmitted fraction leaves and the reflected fraction carries on, so one branch is followed and the energy is split, not sampled. The path stops when less than 0.3% of its energy remains.

While the stone is still, the image refines over up to 64 samples per pixel, placed by the R2 low-discrepancy sequence. There is no random noise.

The room is a function of direction that turns with the camera: soft ambient light, a six-segment ring, lamps above and below, and small spot lights, in ten scenes from studio to candlelight. A head shadow blacks out the light within 6° of the line of sight and fades in by 10.5°. Colour temperature follows Tanner Helland’s fit, with 22% of the shift applied, because the eye adapts.

Fresnel and dispersion

Reflectance is the full unpolarised Fresnel equation, the mean of the two polarisations at each surface:

Fire comes from refracting the ray out three times, once per colour channel:

where D is the published B to G dispersion. Red and blue display primaries sit about 0.6 of that interval apart. A channel that reflects totally contributes nothing on that exit. Dispersion is applied at the exit facet only; inside the stone the three channels share one path.

Colour, clarity and fluorescence

Body colour is Beer–Lambert absorption per channel along each internal segment of length ℓ:

For the D to Z scale, σ grows as (grade/22)^1.25, from zero at D. Path lengths are in model units, so colour depth does not change with the carat weight you choose. Clarity grades place a fixed set of crystals, pinpoints and feathers, sized per grade, from a seed tied to the cut. Crystals and pinpoints end a path; feathers reflect part of it. Fluorescence adds a glow proportional to path length (up to 3 model units), under the UV scene only.

Polish is applied after the trace, as a loss of contrast and saturation. It does not scatter rays. Symmetry grades tilt each crown and pavilion facet by up to 0.25°, 0.6°, 1.2° or 2.0° in a seeded direction; the table and culet stay put.

Light Return

The Light Return map is traced face up and orthographic, with no Fresnel, no dispersion and no absorption, so it depends on the geometry alone. Each ray is classed by the direction its light came from, measured as elevation above the girdle plane:

Contrast (blue)

75° and above: within 15° of the line of sight, where your head is

Direct (red)

45° to 75°

Indirect (green)

below 45°

Leakage (black)

out through the pavilion, below the horizon, or still inside after 18 bounces

The four shares are the share of face-up pixels in each class, from a 160 × 160 render with one ray per pixel, rounded to whole per cent.

Cut grade

The simulator’s cut grade shows how a worse make of the same design looks. Each grade moves the design by a fixed schedule, and the weight is held constant by rescaling the stone:

Crown and pavilion facets turn about their girdle edges. The table and culet are rebuilt until their size, as the square root of the area ratio, meets the target. Volume is integrated over 512 horizontal slices by the trapezoid rule. The grade describes the make; it is not a measure of light return. House cuts, the heart and the Platonic solids are shown as designed.

Size

Measurements are the model’s reference dimensions multiplied by the scale factor k from Volume and weight, for the gemstone and carat weight you choose.

The simulator renders a stone the way a camera would see it, in a lit room. It is for seeing, not scoring: the only figures it reports are the Light Return shares, the cut grade proportions and the size.