Constraint-based CAD systems — SolidWorks, Fusion 360, CATIA — use iterative solvers to resolve geometric constraints. This approach works well for design applications. For CNC machining workflows, it introduces seven documented failure modes.

How Constraint Solvers Work

A constraint solver maintains a set of geometric entities (points, lines, circles) and a set of constraints (dimensions, tangencies, parallelism). When a constraint is added or modified, the solver iterates to find a configuration that satisfies all constraints simultaneously.

The solver starts from the current geometry state and applies corrections until all constraints are satisfied within a specified tolerance. The result depends on the starting state — and the starting state depends on the history of operations.

The Seven Failure Modes

FM 1 — Solution Flip

A dimension change causes a tangent arc to flip to the wrong side of the profile. The solver, starting from a slightly different state, converges to the other valid solution.

XyzPilot: The direction selector is permanently recorded. The solution cannot flip.

FM 2 — Under-Constrained Drift

A bolt-hole pattern rotates by an unpredictable amount when the file is opened on a different machine. The under-constrained degree of freedom drifts to a different value.

XyzPilot: Explicit start angle required. No free degrees of freedom.

FM 3 — Constraint Conflict

A new dimension silently overrides an existing constraint. The solver resolves the conflict by modifying geometry the programmer did not intend to change.

XyzPilot: No constraint network. Each operation is independent.

FM 4 — Solver State Dependency

Two programmers get different geometry from the same file. The solver converges to different solutions depending on the history of operations on each machine.

XyzPilot: Geometry is fully determined by the operator sequence. Always identical.

FM 5 — Tolerance Accumulation

A 40-entity profile is not mathematically closed. The solver satisfies each constraint within tolerance, but the accumulated errors leave a gap at the profile closure.

XyzPilot: All results are exact. Profile closure is exact by construction.

FM 6 — Regeneration Failure

A sketch enters a dangling reference state after a 3D model change. The geometry cannot be used for CAM until the references are manually repaired.

XyzPilot: 2D scope eliminates this entirely. No 3D face references.

FM 7 — Version Non-Determinism

Geometry changes silently when the file is opened in a new software version. The solver algorithm has been updated, and it now converges to a different solution.

XyzPilot: Fixed analytic formulas never change between versions.

The Common Root Cause

All seven failure modes share a common root cause: the solver produces different results from the same inputs, depending on the starting state, the solver version, or the constraint history.

This is not a bug in any specific CAD system. It is an inherent property of iterative constraint solving. The solver is doing exactly what it is designed to do — finding a valid solution from the current state. The problem is that "valid" is not the same as "correct".

The Analytic Solution

Analytic geometry eliminates all seven failure modes by eliminating the solver. Every geometric operation executes a fixed mathematical formula. The result is exact, reproducible, and independent of history.

The direction selector — which constraint-based systems handle implicitly through solver state — is made explicit. The programmer specifies which solution they want. That choice is recorded permanently.

This is the architectural foundation of XyzPilot.