Add robert_engine: calculate_elasticity_breathing and calculate_drape_wave

[Copilot]

Implements the two fabric-physics simulation functions specified in robert-engine.test.ts: sinusoidal elastic "breathing" oscillation and per-point hem drape wave offsets.

New: api/robert_engine.py

Four module-level constants replace magic numbers:

Constant	Value	Role
BREATHING_FREQUENCY	0.0015	Human-rhythm oscillation (rad/ms)
ELASTICITY_AMPLITUDE_FACTOR	0.0005	elasticityPct → amplitude scaling
MAX_DRAPE_AMPLITUDE_PX	6.0	Max hem displacement (px)
DRAPE_WAVE_FREQUENCY	0.002	Drape wave frequency (rad/ms)

# Scale factor oscillating around 1.0 at breathing rhythm
calculate_elasticity_breathing({"elasticityPct": 80.0, ...}, timestamp=1000.0)
# → 1.0 + sin(1000 * 0.0015) * (80 * 0.0005)

# 8 hem wave offsets, each with independent phase, bounded by drapeCoefficient * 6 px
calculate_drape_wave({"drapeCoefficient": 0.5, ...}, timestamp=200.0, garment_w=300.0)
# → [sin(200*0.002 + i*(π/8)) * 3.0  for i in range(8)]

New: tests/test_robert_engine.py

11 unittest cases covering: identity at t=0, oscillation polarity, amplitude scaling, zero-coefficient boundary, phase distinctness, per-point amplitude bounds, and exact formula values against the exported constants.

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Project	Deployment	Actions	Updated (UTC)
tryonyou-pilot	Error		Apr 7, 2026 1:38pm