Performance Benchmarks

Pythagorean Snapping vs MLP

Test: Constraint satisfaction speed for snapping coordinates to geometric constraints.

Constraint Theory: Uses geometric constraints (Pythagorean theorem) for deterministic snapping.

Traditional: Uses Multi-Layer Perceptron (MLP) neural network for pattern matching.

Expected: Constraint theory is ~100x faster due to direct geometric calculation.

KD-Tree vs Linear Search

Test: Spatial query performance for finding nearest neighbors.

Constraint Theory: Uses KD-tree with O(log n) query complexity.

Traditional: Uses linear search with O(n) complexity.

Expected: KD-tree scales logarithmically, especially beneficial for large datasets.

Geometric Constraint vs Force-Based

Test: Physics simulation step time for constrained systems.

Constraint Theory: Uses geometric constraint solving (Lagrange multipliers).

Traditional: Uses force-based integration with penalty methods.

Expected: Geometric constraints are more stable and faster for stiff systems.

Deterministic vs Stochastic

Test: Output variance measured over multiple runs.

Constraint Theory: Deterministic output guarantee - same input always produces same output.

Traditional: Stochastic methods have inherent randomness.

Expected: Constraint theory has zero variance (0.0) vs traditional (0.1-1.0).