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Certainty Model
Every point and segment in Tilde carries a solutions value that describes how well-determined it is. This drives the visual style.
The three states
one — uniquely determined
The vertex position follows logically from the constraints. There is exactly one valid placement.
Rendered as: crisp dot with a clean circle.
click to pan & zoom
infinite — underconstrained
The vertex has more freedom than the constraints remove. It could be anywhere on a line, circle, or plane — an infinite continuous family of solutions.
Rendered as: dot with a wavy circle; segments rendered as squiggly lines.
click to pan & zoom
Here c is constrained to be 4 units from b (bc = 4), but its angle around b is free — it could be anywhere on a circle of radius 4 centred at b.
multiple — finitely many discrete solutions
The vertex is fully constrained in terms of DOF, but the constraint equations are nonlinear (quadratic) and yield more than one isolated solution.
Rendered as: dot with a jagged circle in amber; segments as jagged lines. Each solution is numbered.
click to pan & zoom
Use pick b 1 or pick b 2 to select one.
Why this matters
A one result means your figure is fully determined — you can trust the coordinates. An infinite result means you haven't constrained the figure enough; add more constraints to pin it down. A multiple result means your constraints are sufficient but geometrically ambiguous — use pick to choose.
Inheritance
- A vertex constrained by distances to two placed neighbors inherits underconstrained status from those neighbors — if either was underconstrained, the result is too.
- A vertex on a segment is always underconstrained — its position along the segment is free.
- A vertex constrained by only one distance (not two) is always underconstrained — its angular position is free.