Unit Resolution

Before any geometry is processed, the solver determines the active unit for the program. This is what gives a bare number like 5 its physical meaning — centimetres, inches, or nothing at all.

Why a single active unit?

Tilde doesn't track units per-length. There's one active unit for the whole program, and every length is interpreted in that unit. This keeps the constraint model simple and avoids the ambiguity of mixing units mid-program.

How the active unit is resolved

The three outcomes

Explicit unit — you declared set unit cm at the top of the program. Every bare number is in centimetres.

set unit cm
let triangle abc = 3, 4, 5

Inferred unit — no set unit, but a length carries a suffix. The solver reads the first suffixed length it encounters and uses that unit for everything.

let triangle abc = 3cm, 4cm, 5cm

No unit (abstract) — no set unit, no suffixed lengths. Numbers are dimensionless. This is fine for purely relational geometry where you only care about proportions.

let triangle abc = 3, 4, 5

Ordering constraint

set unit must appear before any geometry declaration in the program. Placing it after a shape, line, or constraint is an error:

let segment ab = 5  ← geometry
set unit cm         ← error: too late

This is enforced because the unit affects how every length is interpreted, so it must be known before any length is read.