E01 · F01 · EN-003 — Turning angle at a contour vertex

Compute, at each vertex of a cyclic contour, the turning angle between the incoming and the outgoing edge (DERIV-local-radius-clamp, notation τᵢ), for the fillet computations.

Acceptance criteria

• Given the clockwise rectangle of US-001, when the turning angles are computed, then each one is a quarter turn in absolute value.
• Given three aligned vertices, when the angle at the middle one is computed, then it is 0.
• Given the first vertex of a contour, when its angle is computed, then the incoming edge is the last edge (cyclic contour, Q11).

Tasks

One task = one commit, referenced as EN-003.Tn.

• T1 — Verify a source for the turning angle formula (atan2 of cross and dot products) and record it in docs/references.md; otherwise write a derivation (1 h) — DERIV-turning-angle, MathWorld and MDN verified
• T2 — Write the tests of the cases above (1 h)
• T3 — Implement vector subtraction, dot and cross products (math, one file each) (2 h) — subtract, dot, perpDot
• T4 — Implement the turning angle at a vertex (geometry) (1.5 h) — turningAngle, turningAngles, cyclicVertex