The crystal axis

1The idea

A sapphire looked at along its special axis shows one color and one sharp image. Looked at across it, the same crystal shows another color, and a strongly birefringent stone shows its back facets twice. The direction of that axis in the finished stone is the Crystal Axis.

The axis is a line, described by two numbers with the table facing up: tilt, the angle to the table normal (0 to 90 degrees; 0 runs the axis straight through the table, 90 lays it flat), and azimuth, the direction it leans toward, counted clockwise as seen from above, from the first position of the index gear. The cutting sheet prints the azimuth as an index of the design’s gear as well, so the rough can be oriented on the machine.

For a biaxial crystal there are three principal directions. The Crystal Axis fixes one, and a Second Axis (0 to 180 degrees) turns the other two about it. In a trichroic stone such as tanzanite that turn decides which of the three colors faces up.

Colors named by what you see

Where color depends strongly on direction, the presets are named by the face-up color they give, with a swatch beside the name: Best Blue Face-Up and Violet Face-Up for tanzanite, Strongest Color Change for alexandrite, Best Green Face-Up for an andalusite that has a green direction (the built-in andalusite color shows none, so it offers no named preset). The geometry presets, Through the Table, In the Table Plane and Along the Width, work for every material that has an axis.

Silk follows the axis

Needles and plates inside a stone are placed in the crystal, so they turn with the axis. For a one-axis crystal the Silk Turn is the stored second turn, used only to orient them. The cat’s-eye preset needs the Second Axis. See inclusions and silk.

Doubling

A birefringent stone splits each light path into an ordinary and an extraordinary ray. The Doubling figure is how far apart, in arc-minutes, the two images fall when you look through the table. It is zero along the axis and grows as the axis leans away. The brilliance, fire and scintillation figures count both images.

2In the studio

The Stone tab has a Crystal Axis section: As Material keeps the material’s own axis, and Set for This Stone takes the tilt, azimuth and, for a biaxial material, the Second Axis, and saves them in the design. Each change is one undo step.

The Crystal Axis pill in the Solid viewport’s toolbar draws the axis over the stone, with a handle to drag. It also appears in the path-traced and ray-traced views and in the diagram’s profile panel. Dragging the handle turns the stone live and is one undo step; Escape puts it back. The metrics bar shows two more figures, Axis (the angle to the table normal) and Doubling, and the Verdict adds an informational note, never a score, saying how far the axis is from the usual orientation for the material.

The axis is used everywhere the stone is: live render, exports, render jobs, remote workers, catalogue thumbnails, tilt curves, Compare, the color pattern preview, the scoring behind Optimize, sweeps, Tune and Retarget, and the command-line tool. A zoned color pattern can Follow the Crystal Axis, so its zones turn with the stone.

3Materials

Each built-in material brings its own axis. A custom material gets the table normal unless the Material Editor’s Crystal Axis row gives it a default; for a biaxial material the row sets the axis of the largest index. The order of precedence is the design’s own setting, then the material’s default, then the built-in axis.

The rules below are the orientations the program proposes for the built-in materials. It never applies one silently.

4In the rough planner

The rough planner has a Crystal Axis panel for the rough. The axis is Unknown until you set it, and the planner then plans exactly as before. Set it by typing a tilt and an azimuth in the rough’s own frame, or with Align to Face, Align to Edge, Fit to Crystal Length (with a stated confidence) or From Color Zones, which takes the axis of a zone you accepted in the Rough Color wizard. The axis is drawn in the 3D view with a handle you can drag, and as a line over the photos.

As soon as the axis is set, the material’s rule is switched on, with a visible line such as “Stones are oriented to the crystal axis: Table Across (Sapphire default)”. A rule has a kind, a tolerance and a strength: Preferred lets a stone off the rule still count at a reduced value (0.5 % per degree beyond the tolerance by default), and Required lets no stone be off. A Preferred rule also gives alternative layouts, Best Orientation (Unrefined) and Balanced (Unrefined), so you can see what the rule costs in weight.

Overrides, with a Reason

You can differ from the planner for the whole plan (Ignore the Axis or a rule of your own), for one design, or for one stone (one of its four box poses, Re-Fit, or Free Orientation for a single exact stone). Each override has an optional Reason, is one undo step, is saved with the plan, shows as “overridden (reason)” in the stone’s row and is printed on the cutting sheet.

Lock

Lock keeps one stone and makes the next plan cut the rest of the rough around it. The locked stone is listed first and is cut first; the slabs below it are for the remaining rough. That is a real limit of the saw plan, and the results say so.

Open in Editor

The design gets the stone’s true orientation: the rough’s axis turned by the pose the stone actually has, never the rule’s target. The rule it was planned under goes with it.

5At the bench

When a stone’s axis is set, the cutting sheet has an Orientation block: the tilt and azimuth (with the azimuth as an index of the gear), the Second Axis turn for a biaxial stone, the sentence “Orient the rough so the crystal axis (c-axis) …”, whether the stone follows the rule of its material, any Reason, and two small drawings, from above (index 0 at the right) and from the side. The first step of Cutting Mode shows the same instruction and picture. A design without an axis prints the same sheet it always did.

6Mobile and web

The Android app has the same presets (including the color-named ones), As Material, the Second Axis, a Doubling readout and the orientation in Cutting Mode. The web app reads the linked design’s own axis, which wins over the per-user setting, and offers a Second Axis for biaxial materials; its tilt sweep keeps the axis.

7Limits

• Along the Width needs a solved design.
• A block of rough offers four poses per stone; Re-Fit and Free Orientation reach the others.
• Rules take effect at the next plan. A rule is never applied while the axis is Unknown.
• The alternative layouts of a Preferred rule are not refined like the plan’s own.
• A color pattern adopted from the Rough Color wizard keeps the frame it was measured in and does not follow the axis.
• The pictures on the cutting sheet and in Cutting Mode draw the Crystal Axis, not the Second Axis. The web app shows no Doubling figure.
• For a birefringent material the optimizer, sweeps and tilt curves do roughly twice the work per figure, because they follow both images of the light.

The manual chapter explains each control. Five short tutorials in the program walk through it: Orient a Sapphire, Tourmaline With the Axis in the Table, Best Blue Tanzanite, Set a Stone’s Crystal Axis and Override a Stone’s Orientation. The physics page describes the optics underneath, and the materials page lists the materials.

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, zoning and edge rounding. Path-Traced retains the spectral model. Optical metrics, tilt sweeps and diagnostics keep their separate analytic tracer.