Every kinetic sand table needs the same thing from a pattern file: an ordered list of positions for the ball. Two formats dominate, and they disagree about how to describe a position at all.
That disagreement is not arbitrary. It follows from how the machines are built, and it has real consequences for whether a pattern you made today still works after you buy a bigger table.
Theta-rho: describing a circle in its own terms
Circular tables — the Grounded Oasis models, the Sisyphus range — move a ball on a polar mechanism. One motor rotates an arm. Another moves a carriage along that arm. There is no such thing as "left" in the machine's own frame of reference; there is only rotate and extend.
Theta-rho matches that exactly. Each line is two numbers:
0.0000 0.0000
1.5708 0.5000
3.1416 1.0000
Theta is an angle in radians. Rho is a radius from 0 at the centre to 1 at the rim. Those three lines say: start at the centre, quarter-turn while extending halfway, another quarter-turn while extending to the edge.
The crucial detail is that rho is normalised. It is not a measurement — it is a fraction of whatever radius the table happens to have. That one decision gives the format a property G-code cannot have.
G-code: describing a rectangle in millimetres
Rectangular tables like the ZenXY use two perpendicular linear axes, which is mechanically a small CNC machine. So they speak the language CNC machines have spoken since the 1950s:
G21 ; millimetres
G90 ; absolute positioning
G0 X10 Y10 ; rapid move — reposition
G1 X90 Y40 ; linear move — draw
Only a handful of commands matter. G21 and G90 are declarations that appear
once. Then it is G0 and G1 all the way down.
The G0/G1 distinction is worth dwelling on, because on a CNC router it is
meaningful — G0 lifts the tool and moves fast. On a sand table, nothing
lifts. The ball ploughs its groove during a G0 exactly as it does during a
G1. The distinction survives in the file format but the physical difference
does not, which is why travel moves are visible in the finished pattern.
The portability difference
This is the practical consequence, and it catches people out.
Theta-rho files are portable between circular tables. Because rho is a fraction rather than a measurement, the same file draws correctly on a 165 mm Oasis Mini and a 622 mm Sisyphus Coffee Table. Upgrade your table and your entire pattern library still works.
G-code files are not portable. X90 Y40 means ninety millimetres and forty
millimetres. Load a file made for a 500 × 350 bed onto a 400 × 300 table and it
will drive into the wall. Change bed size, reconvert.
There is a caveat on the theta-rho side. Portable does not mean identical — fine detail that reads clearly at 622 mm can fall below the ball's resolution at 165 mm. The geometry survives the move; the legibility might not.
Two problems that only exist in polar
Converting Cartesian paths to theta-rho involves two subtleties that G-code never encounters.
Angle continuity. Theta is not confined to one revolution. A table's arm keeps rotating, so a pattern can legitimately wind through several turns. But naive Cartesian-to-polar conversion returns an angle in the range −π to π, and a path crossing that boundary produces a jump from +3.14 to −3.14. The machine faithfully executes that as a full rotation backwards, which is a spectacular and very visible defect. SandPath unwraps the angle across the boundary so the sequence stays continuous.
Density at the centre. Near rho = 0, a large change in theta moves the ball almost not at all; near rho = 1 the same change sweeps a long arc. Path detail is therefore not uniform across the table in polar coordinates the way it is in Cartesian ones — the centre gets crowded, the rim gets sparse.
The rim margin
All of SandPath's circular profiles cap rho at 0.95 rather than 1.0.
That 5% is not conservatism for its own sake. At the very edge of a sand bed the sand piles up, and the magnet's grip on the ball is at its weakest because the carriage is fully extended. Patterns that run right to the rim are where balls stall and lose the plot. Clipping to 0.95 leaves a working margin.
Rectangular profiles set the equivalent value to 1.0 because the concept does not apply — bounds are the bed dimensions, and clipping happens against those.
Which should you care about?
Mostly, you should not have to. Choose your table and SandPath emits the right format with the right constraints.
The one moment it matters is when you are buying. If a pattern library you care about matters to you, circular tables and theta-rho give you a collection that survives an upgrade. That is a genuine, if minor, point in their favour — and one nobody mentions in a product listing.
Ready to convert something? Open the converter, or see which tables are supported.