Frenet Frame — Cartesian ↔ (s, d)

The point travels along the line at constant speed — the exact same motion, yet the velocity looks different depending on the coordinate frame. Left Cartesian decomposes it into v_x·v_y → keeps changing. Right Frenet decomposes it into v_s·v_d → v_s constant, v_d=0.

Cartesian — regular square grid (x, y)

Frenet — curvilinear grid (s, d)

reference line (racing line) query point s (arc length) d (lateral offset)