E01 · F02 · EN-008 — Unit regular polygon with a flat base

The n vertices of a regular polygon on the unit circle, with a horizontal bottom edge, in the SVG frame (DERIV-regular-polygon-fit steps 1–2, with the y flip of step 5 already applied; sources from SP-002).

Acceptance criteria

• Given n = 4, when the unit polygon is built, then its vertices are those of a square with horizontal edges (not a diamond), within EPSILON.
• Given n = 3, when the unit polygon is built, then it is a triangle pointing up, its base horizontal.
• Given any n ≥ 3, when the unit polygon is built, then it has n vertices on the unit circle, equally spaced, listed clockwise on screen from the topmost vertex, the leftmost on a tie (Q11, Q18): the j-th at angle βⱼ = −π/2 + (2⌊n/2⌋ + 1 − 2j) π / n (DERIV-regular-polygon-fit step 2).

Tasks

One task = one commit, referenced as EN-008.Tn.

• T1 — The geometry function, its TSDoc (@see DERIV-regular-polygon-fit) and its hand-computed cases n = 3, 4, 6, signed zero (1.5 h)
• T2 — Properties for any n (n vertices on the unit circle, equal chords, clockwise, starting vertex, flat base) and mutation checks (1.5 h)