Constraint Model

Before the solver loop can run, every statement in the program gets walked once to build the constraint model — a graph of vertices and the relationships between them. This is the data structure the placement loop works from.

What gets built

The model holds:

Structure	What it stores
points	Every declared vertex, initially unplaced (dof = 2, coordinates null)
segments	The set of all declared edges, as canonical pairs
lengths	A length value for each segment that has one, or null
lines	Named lines, stored as (a, b, c) where any coefficient may be null for partial/bare declarations
onLine	Which vertex is constrained to which named line(s)
onSegment	Which vertex is constrained to lie on which segment
solutionPicks	Which solution index was chosen for each ambiguous vertex

How shapes become vertices and edges

The solver never sees a triangle. triangle t with a b c reaches it as three points and the three segments between them; no positions are assigned yet — that's the placement loop's job.

triangle t with a b c

This registers vertices a, b, c and three edges: a–b, b–c, c–a.

segment a b

Registers one edge: a–b.

How constraints layer on top

Each constraint a program states adds information to what is already registered. A distance sets a length on an edge (adding the edge if it is new). An on-line or on-circle constraint records that a vertex must lie on a specific line or circle.

The model also has room for on-segment constraints, angles and chosen solutions (onSegment, angles, solutionPicks); nothing in the language reaches them since the classic syntax went — see the roadmap.

What the model captures

The model does assign coordinates to explicitly placed vertices — point a at 3 4 resolves immediately to dof = 0. Every other vertex enters the loop as an unplaced working point: both coordinates null, dof = 2. The constraint model is purely relational for those: it says what exists and what constraints apply, not where anything is.