PleochromaSurface finish, silk and play-of-color
A real stone is not a flawless, perfectly polished crystal. Pleochroma can draw the polish of its facets, the silk and needles inside it, and the flashes of color of opal and labradorite, and it keeps the refractive index of each ray of a birefringent crystal on its own curve.
These effects are new. Every one is off until you switch it on: a design that uses none of them renders, is scored and is saved exactly as it always was. The one visible change for existing designs is a frosted facet, which is now a ground surface (section 2).
1The idea
The renderer already follows light through the stone with polarization, dispersion and birefringence. What it did not have was the stone’s texture: how well a facet is polished, what is inside the stone, and the structure that makes opal flash. Each new effect is a choice of the design, saved with it as one undo step, drawn by the path tracer on the processor and on the graphics card, and by a remote worker.
- Surface finish
- How well a tier, or one facet, is polished, or how coarsely it is ground, and which way the polishing scratches point on your machine.
- Inclusions
- Needles and plates inside the stone that all point one way: the silk of a sapphire, growth tubes, the fibres of a cat’s-eye, the sheen of a moonstone.
- Play-of-color and schiller
- The spectral flashes of a precious opal and the single sheet of color of a labradorite, which come from a fine internal structure and move as you tilt the stone.
- A curve for each ray
- A birefringent crystal has a refractive index for each ray, and each changes with wavelength in its own way. For the stones where published curves exist, Pleochroma uses them.
2Surface finish
A polished facet is never a perfect mirror. A good polish keeps the sharp reflection and sends a small share of the light, the total integrated scatter, into a soft halo around it. The share depends on the roughness of the surface (its RMS height, Rq, in nanometres) and grows with the square of the roughness, and it is larger for short wavelengths, so a poor polish hazes blue. The scratches of the lap are grooves in one direction, so the halo is stretched across them: the streaked highlight cutters know from a facet polished in one direction.
A Surface Finish submenu in the tier table and a section in the tier inspector set the grade for a whole tier. A single facet can override it.
| Grade | Typical lap | Roughness | Halo at normal incidence, 550 nm |
|---|---|---|---|
| Ideal | none | 0 | none (the default) |
| Mirror | 50k to 100k diamond or alumina | Rq 1 nm | about 0.05 % |
| Fine | 14k diamond | Rq 2.5 nm | about 0.3 % |
| Commercial | 8k diamond | Rq 6 nm | about 2 % |
| Prepolish | 3k diamond | Rq 25 nm | about 28 % |
| Ground (Fine) | 1200 grit | roughness 0.30 | a frosted facet, fine grain |
| Ground (Coarse) | 600 grit | roughness 0.50 | a frosted facet, coarse grain |
| Custom | any | 0 to 100 nm and an anisotropy | your numbers |
The roughness values are typical figures, chosen to look right for each lap. They are starting points for you to tune, not measurements of a particular lap.
Your faceting machine decides the scratches
While you polish, the lap moves along the tangent of the circle through the spot where the stone touches it, so the scratches run along that tangent. On a machine whose dop arm points at the lap centre the scratches run parallel to the girdle. On a mast machine, with the mast standing to one side, the angle between the arm and the tangent changes as the stone moves in and out along the lap, so the scratches fan over a range of angles. And the stone does travel: the program models the sweep of the last polishing pass between an inner and an outer radius of the lap, and draws the true mix of directions, a softer, fan-shaped halo instead of one sharp streak.
So the direction is a setting of your machine, not of the design. The Faceting Machine section of the Preferences holds the arm (pointing at the lap centre, or the mast to the side, with an arm offset), the lap radius, the mast position and the sweep range (Narrow, Typical, Wide or your own radii), with a small picture of the lap from above. It is saved in your settings and never in a design, so the same design shows each cutter’s own scratches. A tier can instead fix the direction with Custom Angle, or switch the fan off with No Sweep.
Frosting, worn edges and a view aid
A frosted facet is now a ground surface: a rough dielectric that scatters light forward and back as frost does, with the energy a rough surface would otherwise lose put back, so a ground girdle glows softly instead of turning flat and dark. Abraded Edges in the Stone tab wears a narrow band along every facet edge (a width and a wear). Show Surface Finish tints each facet by its grade and draws ticks along its scratches in the Solid view; it is a view aid and is not saved.
3Inclusions and silk
A needle scatters light that crosses it and ignores light that travels along it, and it throws the scattered light onto a cone around its axis: the source of the star in a star sapphire and the eye in a cat’s-eye. A plate acts as a tiny mirror and flashes when it faces both the light and the eye. Very fine inclusions scatter short wavelengths more and look bluish-white, coarse ones look grey.
The Stone tab offers presets for the materials that have them, with Density, Sheen (the width of the cone), Silk Color (Grey, Slightly Blue, Blue) and Silk Turn. Show Silk Directions draws the needle directions over the stone.
| Material | Presets |
|---|---|
| Sapphire, Ruby | Fine Silk, Rutile Silk, Star Silk: three needle sets in the basal plane, 60° apart |
| Chrysoberyl (yellow), Alexandrite | Cat’s-Eye Silk: one needle set along the crystal’s c direction (needs the Second Axis) |
| Tourmaline | Growth Tubes |
| Emerald, Aquamarine, Morganite | Rain |
| Quartz | Rutilated: needles of every orientation |
| Moonstone | Adularescence: one broad set of plates |
The inclusions are placed in the crystal, so they follow the crystal axis: turn the axis and the silk turns with it. For a one-axis crystal the Silk Turn is the stored turn about the axis used only to orient the needles; the optics of the stone ignore it. A custom material can carry up to four inclusion families of its own, set in the Material Editor.
Honestly: a faceted stone shows silk as a soft sheen that turns with the stone, a velvety body and bright streaks where the cone reaches the eye through a facet. A faceted star sapphire shows fragments of the star. A true star or eye needs a curved dome, and the program builds stones from flat facets and subtractive tools, so a smooth star or eye awaits a dome shape in a later version.
4Play-of-color and schiller
These colors are not absorption. They come from an orderly internal structure that reflects one narrow band of wavelengths, according to the spacing of its layers and the angle of the light, so they are pure and they shift as you tilt the stone. Precious opal is a close-packed array of silica spheres 150 to 300 nm across: about 200 nm reflects blue and about 270 nm red, in patches that each point their own way. Labradorite has fine lamellae of one orientation fixed in the crystal, so the whole face flashes at once from one direction, and the flash follows the crystal axis.
New built-in materials carry the host optics: Precious Opal (White), Precious Opal (Black), Labradorite and Moonstone. The Stone tab has a Play-of-Color group (Schiller for labradorite) with a Pattern (Pinfire, Harlequin, Broad Flash), a patch size, a color range, Purity, Coverage and a Reseed button that draws a new arrangement of the patches. The seed is saved with the design, so a design always shows the same patches. A custom material can imitate an opal or a labradorite.
5A curve for each ray
The refractive index of each ray of a birefringent crystal changes with wavelength. Where a published curve exists, Pleochroma now uses it for the ray, on the processor and on the graphics card alike:
- the extraordinary ray of sapphire and ruby (Malitson and Dodge, 1972) and of synthetic moissanite (Wang, 2013), joining quartz and rutile;
- the alpha and gamma rays of alexandrite and chrysoberyl (yellow) (Walling, 1980), whose total birefringence is therefore 0.0076 where it was 0.0090;
- a separate Cauchy curve for each ray of benitoite.
The doubled images of a birefringent stone also separate a little by color, because the direction in which the extraordinary ray is displaced follows its index at each wavelength. The Material Editor lets a custom material have its own extraordinary-ray curve, or alpha and gamma curves for a two-axis crystal. Materials without a published curve keep a constant offset, as before.
6Where they show
- The path-traced view (with or without the solid's edges), exports, render jobs, remote workers and the command-line tool draw the effects, and so does the graphics card.
- The web app reads the design’s choices and draws them on the processor.
- The Ray-Traced view ignores them, and says so next to each group.
- The optical figures (brilliance, windowing, extinction, fire, scintillation), the Verdict, Compare, the optimizer, the sweeps and Tune describe a clear, perfectly polished stone. When an effect is on, the Checks tooltip, the Verdict and the Compare header add “Figures ignore …”, naming what is on.
- The Android app does not carry these effects in its remote renders yet.
7Limits
- The polish grades, the silk amounts and the patch sizes of play-of-color are looks chosen to be plausible, with the grain, the amounts and the colors for you to tune. The correlation length of a lap and the size of the patches of opal are not published.
- The scratch direction comes from a model of the machine. Check it against a real facet and adjust the arm offset and the sweep.
- A faceted stone shows fragments of a star, not a star; a dome shape is planned.
- Cubic materials (star garnet, star spinel) have no inclusion presets yet.
- Thin-film colors (the rainbow of a crack), the glitter of sunstone and chips knocked out of an edge are not modeled.
- Silk and play-of-color may take longer to converge than a plain stone; the cost has not been measured yet. The graphics card and a remote worker are there for final renders.
The manual describes each control: Surface Finish, Inclusions and Silk and Play-of-Color and Schiller. The physics page explains the optics underneath and the materials page lists the materials.
Six short tutorials in the program (Help, Tutorials, section Materials and Color) walk through the effects: Polish Quality and Haze, Scratch Direction, Silk in a Sapphire, Opal Play-of-Color, Labradorite Flash, and Ordinary and Extraordinary Curves.
Ray-Traced and Path-Traced
Ray-Traced is a deterministic approximation: one d-line index, or three fixed indices with Fire, RGB absorption tint and 1/4/8/16 AA taps. It finishes at the tap count without denoising. It omits polarization, birefringent doubling, scattering, oriented inclusions, surface finish, play-of-color, zoning and edge rounding. Path-Traced retains the spectral model. Optical metrics, tilt sweeps and diagnostics keep their separate analytic tracer.