feat(axiom5): Angle bisector (`bisect --l1 --l2 toward .p`) #3

Merged

toph merged 7 commits from v0.4-axiom5 into main

2026-06-29 11:32:15 +00:00

toph commented

2026-06-29 09:47:10 +00:00

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Adds classic axiom 5 — the fold placing one line onto another (the angle bisector) — as bisect --l1 --l2 toward .p. Two intersecting lines have two bisectors; the optional toward .p selector picks the one whose angular sector contains .p; two parallel lines give their single midline.

This is the first axiom to leave ℚ, so the geometry core is migrated from Q to the exact constructible reals (Num, v0.3) — axioms 1–4 stay rational on the fast-path (behaviour unchanged, regression-gated), and bisectors carry exact √ coordinates (e.g. slope √2−1).

Errors: identical lines; intersecting without toward; .p on a fold line. 52 tests green; version 0.3.0-dev. Spec §4.5; the Num decision is ADR 0010.

Examples this PR adds (rendered with tools/fold2svg.mjs):

bisect-a.bel vs bisect-b.bel — same two midlines (--v/--h), toward .p picks a different bisector:

bisect-parallel.bel — parallel inputs → their single midline (no toward):

bisect-intermediate.bel — toward .int (a constructed point at (1/4,0)) selects the side only; the a–c bisector does not pass through .int:

Adds classic axiom 5 — the fold placing one line onto another (the angle bisector) — as `bisect --l1 --l2 toward .p`. Two intersecting lines have two bisectors; the optional `toward .p` selector picks the one whose angular sector contains `.p`; two parallel lines give their single midline. This is the first axiom to leave ℚ, so the geometry core is migrated from `Q` to the exact constructible reals (`Num`, v0.3) — axioms 1–4 stay rational on the fast-path (behaviour unchanged, regression-gated), and bisectors carry exact `√` coordinates (e.g. slope `√2−1`). Errors: identical lines; intersecting without `toward`; `.p` on a fold line. 52 tests green; version `0.3.0-dev`. Spec §4.5; the `Num` decision is ADR 0010. --- **Examples this PR adds** (rendered with `tools/fold2svg.mjs`): `bisect-a.bel` vs `bisect-b.bel` — same two midlines (`--v`/`--h`), `toward .p` picks a different bisector: ![bisect-a](https://git.toph.so/attachments/ddde411a-4b0e-4ef4-ae47-cbd096bd5f78) ![bisect-b](https://git.toph.so/attachments/ee28b9ae-22ee-4558-848d-78dc64a761e0) `bisect-parallel.bel` — parallel inputs → their single midline (no `toward`): ![bisect-parallel](https://git.toph.so/attachments/bf6c62ef-71c3-4f3f-bdc4-c8e9375e9062) `bisect-intermediate.bel` — `toward .int` (a constructed point at (1/4,0)) selects the **side only**; the a–c bisector does not pass through `.int`: ![bisect-intermediate](https://git.toph.so/attachments/20e484a3-e987-4f53-b326-4a94f1e000b7)

bisect-a-pr.png

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bisect-b-pr.png

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bisect-parallel-pr.png

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bisect-intermediate-pr.png

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toph added 7 commits

2026-06-29 09:47:10 +00:00

docs(plan): v0.4 axiom 5 implementation plan (Q->Num migration + bisect) 452202856f

refactor(geom): migrate geometry core Q -> Num; harden Num.inv 55a0f973e8