feat(syntax): axiom 4 — project a point onto a line #16

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toph merged 9 commits from feat/axiom4 into main 2026-06-30 10:05:20 +00:00

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toph commented 2026-06-30 09:44:46 +00:00

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Adds axiom 4 — map .p onto --l1 perp --l2 — the fold that projects point .p onto line --l1 with a crease perpendicular to --l2.

Classic Justin operation ④, which is Wikipedia/Huzita-Hatori O7 — not Wikipedia O4 (that numbering is the already-shipped axiom 3, perpendicular-through-a-point). Beloch tracks classic Justin numbering throughout; the spec and journal spell the clash out so it isn't re-conflated.

• Geom.project_crease — pure construction: line through .p parallel to --l2, meet --l1 at Q, perpendicular-bisect .p–Q. Stays in ℚ, no square roots — unlike axiom 5.
• At most one solution, so no toward selector. Errors when --l1 ∥ --l2; when .p already lies on --l1, the crease is the perpendicular to --l2 through .p.
• Spec §4.5a, example examples/project.bel (project a corner onto the diagonal, crease ⊥ an edge).

---

Worked example — examples/project.bel: fold corner .c onto a slanted line --l1 (slope ½), with the crease forced perpendicular to a second slanted line --l2 (slope 2). Neither line is a diagonal.

Crease pattern — the axiom 4 · project crease (orange) sits perpendicular to --l2:

Folded — .c lands on --l1; the V-tip of the flap is the projected corner:

Adds axiom 4 — `map .p onto --l1 perp --l2` — the fold that projects point `.p` onto line `--l1` with a crease perpendicular to `--l2`. Classic Justin operation ④, which is Wikipedia/Huzita-Hatori **O7** — not Wikipedia O4 (that numbering is the already-shipped axiom 3, perpendicular-through-a-point). Beloch tracks classic Justin numbering throughout; the spec and journal spell the clash out so it isn't re-conflated. - `Geom.project_crease` — pure construction: line through `.p` parallel to `--l2`, meet `--l1` at `Q`, perpendicular-bisect `.p`–`Q`. Stays in ℚ, no square roots — unlike axiom 5. - At most one solution, so no `toward` selector. Errors when `--l1 ∥ --l2`; when `.p` already lies on `--l1`, the crease is the perpendicular to `--l2` through `.p`. - Spec §4.5a, example `examples/project.bel` (project a corner onto the diagonal, crease ⊥ an edge). --- Worked example — `examples/project.bel`: fold corner `.c` onto a slanted line `--l1` (slope ½), with the crease forced perpendicular to a second slanted line `--l2` (slope 2). Neither line is a diagonal. **Crease pattern** — the `axiom 4 · project` crease (orange) sits perpendicular to `--l2`:  **Folded** — `.c` lands on `--l1`; the V-tip of the flap is the projected corner: 

project-axiom4.png

10 KiB

project-cp.png

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project-folded.png

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toph added 8 commits 2026-06-30 09:44:47 +00:00

docs: design for axiom 4 (project point onto line, crease ⊥ l2) 8e922f05b9

docs: implementation plan for axiom 4 53870c9ae0

feat(geom): project_crease — axiom 4 construction (project point onto line) 9da35eb568

feat(syntax): map .p onto --l1 perp --l2 — axiom 4 grammar + AST aeb29641af

feat(eval): axiom 4 handler — project point onto line via project_crease ffa15e6856

docs(spec): axiom 4 — project a point onto a line (v0.4-dev) b6f97c75d0

refactor: address final-review findings for axiom 4 (test assertion, AST order, docs) ... e415146ff7

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

docs(examples): project.bel — axiom 4 demo (project corner onto diagonal) 937e22ae17

toph added 1 commit 2026-06-30 09:58:53 +00:00

docs(examples): richer axiom-4 demo — fold a corner onto a slanted line + fold2svg axiom-4 colour 630ced25fc

toph merged commit f854bbdea4 into main 2026-06-30 10:05:20 +00:00

toph referenced this pull request from a commit 2026-06-30 10:05:21 +00:00

feat(syntax): axiom 4 — project a point onto a line (#16)

toph referenced this pull request 2026-06-30 10:54:32 +00:00

feat(syntax): axiom 6 — fold a point onto a line, crease through a fixed point #17

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