math2ggb

# Math → GeoGebra (.ggb) For **each figure** in the problem, produce **three** files, all built from the SAME dependency-constrained construction. **In all three the base visible content equals the printed figure — exactly the same points, segments, and angle marks: no more, no less** (only the 动态理解图 adds aids, and only on a toggle that defaults off). 1. **静态复刻图** (static faithful) — the printed figure reproduced exactly: only the original's points, segments, and its own angle ticks; no axes/grid, no extra labels or auxiliary lines. The clean, print-matching reference still. 2. **干净可交互图** (clean interactive) — **visually identical to the original** (same marks; no text, no annotations, no visible auxiliary / locus / hidden circle), but the full interactive construction: helper constraint objects (e.g. the circumcircle a point rides on) are **kept but hidden**, so dragging a driver point keeps every condition satisfied. For hands-on exploration of the original figure itself. 3. **动态理解图** (dynamic teaching) — the SAME construction PLUS teaching aids (the revealed hidden circle, the fold, medians, a locus, annotations, live `Angle`/`Distance` readouts) on a **single toggleable layer** (a `显示辅助` checkbox). Unchecking it returns the view to the exact original. Relationship: 1 and 2 show the identical clean content (= the print) — 静态复刻图 is the faithful still, 干净可交互图 is the same figure meant to be dragged; 3 = the 干净可交互图 plus the toggle-gated teaching layer. Suggested filenames per figure: `<fig>_static.ggb`, `<fig>_clean.ggb`, `<fig>_dynamic.ggb`. ## Hard rules 1. **Never hand-write `geogebra.xml`.** Drive the real GeoGebra engine in a browser (its JS API) and export with `getBase64()` — the only way to guarantee a valid file. (Hand XML breaks on internal command names, path parameters, perspectives.) 2. **Encode the problem's conditions as real dependencies — in all three files.** A figure is NOT a pile of free points. Only the genuine degrees of freedom are draggable (**driver points**); every other point is **derived** by a construction that enforces a condition (concyclic, on-line, intersection, reflection/fold, midpoint, perpendicular, given angle/length, locus…). Dragging any driver point must move the whole figure while every condition stays satisfied. This includes the 静态复刻图 — it is a *clean render of the constrained construction*, not free dots. 3. **Match the original exactly by measuring it — never eyeball coordinates.** Point coordinates, segment lengths, and angle ratios must equal the printed figure. Crop + zoom each subfigure, read precise pixel coordinates of every labeled point, convert to a clean coordinate frame, and verify lengths/angles before AND after building. Driver points take the measured coordinates, so the constrained construction reproduces the drawing. *Exception:* when a figure is a 示意图 (explicitly not to scale) yet the problem gives exact metric values (e.g. `∠BAC=90°`, `BC=8`), honor the given values (they define the true figure) and use measurement for orientation/layout and for the positions of genuinely-free points. 4. **Final content = the original, no more no less — verify, then delete the scaffolding.** You MAY temporarily add measurement objects (extra `Angle`/ `Distance`, ratio checks) to confirm coordinates, segment lengths, and angle ratios match the image; once confirmed you MUST `Delete(...)` every such **verification object before export** (delete, NOT hide — a hidden object still lives in the file). Keep three object categories straight: *original marks* → shown · *construction helpers* that enforce conditions → kept but hidden · *verification scaffolding* → deleted. Teaching aids exist only in the 动态理解图, gated behind the `显示辅助` toggle. See recipes §4c–§4d. ## Requirements - A **browser tool**: navigate, evaluate JavaScript (CDP `Runtime.evaluate`), screenshot. - **Internet** (generator page loads GeoGebra from geogebra.org's CDN). - `python3` (helper server + measuring the image). ## Stage checklist ``` - [ ] A. Understand + measure: solve; write the CONDITION LIST; MEASURE the image (crop+zoom, read pixel coords of every labeled point); convert to clean coords; verify lengths/angles. - [ ] B. Model as a constraint graph: split driver (free) vs derived points; map each condition to a construction; plan the three renders (静态复刻=faithful still, 干净可交互=clean+draggable, 动态理解=+toggle aids). Only true DOF draggable. - [ ] C. Generate via the GeoGebra engine (server + browser); export all three .ggb per figure. - [ ] D. Validate: compare coords/lengths/angles vs the image; DRAG-TEST every condition holds; confirm no leftover aids/verification marks; round-trip re-open. - [ ] E. Deliver: list files (three per figure) + the sandbox-safe way to open them. ``` --- ## A. Understand & measure the original 1. **Solve** the geometry (exact positions, invariants, answer). Verify with a quick `python3` script when there is real computation (loci, minima, lengths). 2. **Write the condition list** — every relationship the problem states or implies. Example: `∠ADB=∠ACB ⇒ A,B,C,D concyclic`; `E = AD ∩ BC`; `fold ⇒ F = reflection of D over BC`; `H = midpoint AC`; `△BEK∼△AEH`; `∠BAC=90°, ∠ACB=30°, BC=8`. This list drives Stage B. 3. **Measure the image (mandatory — no eyeballing).** For each subfigure: crop it and upscale ≥4×; read the pixel coordinates of every labeled point; convert to a clean frame (flip y, anchor one point at the origin, choose a scale so a key length is round); record all coordinates. Then verify the measured coords reproduce the drawn shape (segment-length ratios, angles) and fit the condition list. See recipes §4a. ## B. Model as a constraint graph (per figure) 1. **Classify points** using the condition list: - **Driver (free) points** — the minimal set with genuine freedom (often the triangle's vertices, plus one point constrained to a circle/line, e.g. `D=Point(c)`). Place drivers at the **measured** coordinates. - **Derived points** — everything a condition determines (`Intersect`, `Reflect`, `Midpoint`, spiral similarity, `Locus`…). Lock them to the conditions; never leave them free. - Map each condition → a construction (recipes §4b table). 2. **Three renders from the SAME graph:** - **静态复刻图**: hide helper-only objects (a circle used only to constrain a point, helper lines used only for `Intersect`); show ONLY the original's points + segments + its own angle ticks; axes/grid off; no annotations. The faithful print-matching still. - **干净可交互图**: the same clean content as the 静态复刻图 (helpers hidden; only the original's marks; no text, no aids, no visible auxiliary/locus/hidden circle), delivered as the full interactive construction — dragging a driver keeps all conditions. In practice: the 动态理解图 with its teaching layer removed (no `显示辅助` checkbox, all aids hidden), or the 静态复刻图 explicitly presented for dragging. - **动态理解图**: build the teaching aids (revealed hidden circle, fold, medians, locus, descriptive `Text`, live `Angle`/`Distance`) and gate them all on one `显示辅助` checkbox (`SetConditionToShowObject` — recipes §4d), so the view collapses to the exact original when unchecked. Color by role. - For all three, **delete all verification scaffolding before export** (rule 4, recipes §4c). 3. Only true degrees of freedom are movable; derived points must not be free. Pick a clean view (axes off; ~1.34 aspect — recipes §3). ## C. Generate the .ggb (reliable, verified path) 1. **Start the server** (serves the generator page, receives exports): ```bash python3 scripts/ggb_server.py <OUTPUT_DIR> 8777 ``` Run it in the background; it prints the URL and save location. 2. **Open** `http://localhost:8777/generator.html`; evaluate the "wait until ready" snippet (recipes §1). 3. **Build → verify → clean → frame → export**, once per render (three per figure). Evaluate a `(function(){var g=window.ggbApplet; … })()` that resets, runs the `evalCommand` list, and styles. Then: - **Verify (scaffolding):** optionally add temp `Angle`/`Distance` objects and read them (`getValue`) to confirm lengths/angles match the measured image. - **Clean per render:** `Delete(...)` every verification object (recipes §4c). · 静态复刻图 & 干净可交互图 → hide all helper/auxiliary objects (`setVisible(false)`), show only the original's marks, add NO text/aids/toggle. · 动态理解图 → gate teaching aids on the `显示辅助` checkbox (recipes §4d). - `setAxesVisible(false,false)`, `setGridVisible(false)`, `setCoordSystem(...)`, return a status. **Screenshot** — it must show only the original's marks (for the 动态理解图, also screenshot with hints OFF to confirm it equals the original). Then **save**: ```js fetch('/save?name=<figure>_<static|clean|dynamic>.ggb',{method:'POST',body:window.ggbApplet.getBase64()}).then(r=>r.text()) ``` `references/example-hidden-circle.md` has complete, verified build blocks (静态复刻图 + 干净可交互图 + 动态理解图, with verify→delete and the toggle) to adapt. ## D. Validate - **Compare to the image**: screenshot each figure and check point arrangement, segment lengths/ratios, and angle marks against the original crop. Fix until it matches. - **Marks = original, no more no less**: every final file must show exactly the original's points/segments/angle ticks — **no leftover verification objects, no visible auxiliary/locus/hidden circle, no stray marks**. The 静态复刻图 and the 干净可交互图 show only the original's marks; for the 动态理解图, toggling `显示辅助` OFF must reproduce the original exactly. - **Drag-test the conditions** (esp. the 干净可交互图 and 动态理解图): move each driver point and confirm the whole figure follows and every condition still holds (e.g. `∠ADB` stays `=∠ACB`, `F` stays the reflection, `K` stays on its locus). If moving a "point" leaves the rest still, it was wrongly left free — turn it into a derived object. - **Round-trip** the most complex file (recipes §1); `unzip -l file.ggb` shows `geogebra.xml`. ## E. Deliver - List each figure's three `.ggb`: 静态复刻图 / 干净可交互图 / 动态理解图, and what's draggable. - **How to open (macOS):** the App Store GeoGebra Classic 6 is sandboxed and shows a **blank** window if a file is double-clicked or passed on the command line ("Cannot open file"). Open via **☰ menu → Open (打开) → From this device → pick the file**, or **drag the .ggb onto the GeoGebra window**. The web app (geogebra.org/classic) and non-sandboxed desktop builds open files normally. (Details: recipes §5.6.) --- ## Key gotchas (full list in `references/geogebra-recipes.md` §5) - Use the **'AG'** applet, never graphics-only 'G' — 'G' exports a broken perspective that opens **blank** on desktop. - **Export via the POST server**; don't return base64 to yourself. - `Reflect`, `Rotate`, `Dilate`, `Locus`, `Point(circle)`, `Intersect`, `Midpoint` all work via `evalCommand` input syntax. - Spiral similarity: `K=Rotate(Dilate(H,Distance(E,B)/Distance(E,A),E), Angle(Vector(E,B))-Angle(Vector(E,A)), E)`, then `Locus(K,D)`. - **Hidden ≠ removed**: helper/auxiliary objects a construction depends on (the path circle, `Locus`) must be **hidden** (`setVisible false`) in the 静态复刻图 / 干净可交互图, never deleted; only verification scaffolding is deleted. - Set **axes off before export** so a fresh open stays clean. ## Resources - `references/geogebra-recipes.md` — commands, JS API, image-measuring recipe, condition→constraint table, gotchas. - `references/example-hidden-circle.md` — a complete verified example (静态复刻图 + 干净可交互图 + 动态理解图, for 2 figures). - `scripts/ggb_server.py` — serve generator + receive exported `.ggb`. - `templates/generator.html` — loads the real GeoGebra engine (AG layout).