E01 · F01 · EN-006 — Rounded contour geometry: segments and arcs

Evaluate a contour with effective radii into a closed sequence of segments and circular arcs (ADR-0001, ADR-0005 stage 3).

Acceptance criteria

Sources: DERIV-fillet-arc (check table), EPSILON of Q10 introduced by EN-005 (SP-001).

Given a 100 × 100 square with effective radius 50 everywhere, when evaluated, then the result is 4 quarter arcs and no segment of positive length.
Given a 100 × 50 rectangle with effective radius 10, when evaluated, then it has 4 segments and 4 quarter arcs, with the tangent points and centers of the DERIV-fillet-arc table (e.g. corner (100, 0): from (90, 0) to (100, 10), center (90, 10), positive direction).
Given a concave corner at V = (10, 0) (u_in = (1, 0), u_out = (0, −1), r = 5), when evaluated, then its arc goes from (5, 0) to (10, −5) around (5, −5) in the negative direction.
Given radius 0 everywhere, when evaluated, then the result is the sharp contour.
Given a rectangle of size 0 × 50, when evaluated, then no NaN appears.

One task = one commit, referenced as EN-006.Tn.

T1 — Vector helpers add, scale, unit (zero vector → (0, 0)), quarterTurn (math; REF-MATHWORLD-VECTOR-ADDITION, REF-OPENSTAX-CALC3-VECTORS, REF-MATHWORLD-UNIT-VECTOR, REF-MATHWORLD-ROTATION-MATRIX) with tests and properties (1.5 h)
T2 — Segment and arc types (start, end, center, radius, direction) (0.5 h)
T3 — Fillet of a corner: tangent points, center, direction (geometry, DERIV-fillet-arc) with the check table (2 h)
T4 — Closed sequence of segments and arcs; segments shorter than EPSILON dropped (geometry) (1.5 h)
T5 — Audit findings: spike limit documented and raised as Q16; Arc radius contract; chaining within EPSILON and the drop rule stated in the derivation; citations of unit, add and the references aligned (0.5 h)