diff --git a/OPUS-BUILD-BRIEF.md b/OPUS-BUILD-BRIEF.md
index 44431c8..d3a3754 100644
--- a/OPUS-BUILD-BRIEF.md
+++ b/OPUS-BUILD-BRIEF.md
@@ -17,8 +17,20 @@
 - Assets: all 20 2D props rendered on MODELBEAST → `public/assets/img/` (samurai×5,
   bg_washi, floor_boards, title, tickets, slash, 5 food faces, splat). Not wired in
   yet — procedural silhouettes carry gameplay; art is backdrop/faces/juice (M4/M6).
-- **Next: M2** cutting (`sim/food.ts` + the cleaver + `cutStats`) — the clean chop.
-- Run: `npm run dev` (:5173). Harness: `__s.dangle() __s.walk() __s.pickupTest()`.
+- **M2 ✅** cutting. `sim/geom.ts` (pure convex-split + pieceCV/cvWord), `sim/food.ts`
+  (convex polygon foods: bread/tomato/cheese/katsu/egg, material params
+  resistance/moisture/wobble), `sim/cutting.ts` (blade pass-through → split food
+  into 2 real bodies along the chord, or squash→splat on a slow wet press).
+  Honest geometry, no canned slice anim. Traps hit + fixed: (a) cut line through a
+  vertex made lopsided halves — split now treats on-line verts as shared (regression
+  guarded in `geom.check.ts`); (b) **Matter `setVelocity` is px/STEP not px/s** —
+  piece launch was 60× too fast and flung halves offstage. Exit-bar measured:
+  **chop** 2 clean pieces CV 0 (<0.1 req); **push** 0 pieces + splat 3.28 (wet crime);
+  **wild** swing flings a piece offstage. Verified in-browser (two clean halves rest
+  on the board) + `npm run check` (headless geom asserts).
+- **Next: M3** stacking (`sim/stack.ts`) — the sando: layers, lean°, COM drift, nudge test.
+- Run: `npm run dev` (:5173). Harness: `__s.dangle() __s.walk() __s.pickupTest()
+  __s.chop() __s.push() __s.wildChop()`. Headless: `npm run check`.
 
 
 
diff --git a/package.json b/package.json
index 02e3d12..bfff145 100644
--- a/package.json
+++ b/package.json
@@ -7,7 +7,8 @@
     "dev": "vite",
     "build": "tsc --noEmit && vite build",
     "preview": "vite preview",
-    "typecheck": "tsc --noEmit"
+    "typecheck": "tsc --noEmit",
+    "check": "node src/sim/geom.check.ts"
   },
   "dependencies": {
     "phaser": "^3.90.0"
diff --git a/src/dev.ts b/src/dev.ts
index 670483f..d778dbe 100644
--- a/src/dev.ts
+++ b/src/dev.ts
@@ -1,5 +1,6 @@
 import type { Stage } from './scenes/stage';
 import { FLOOR_Y } from './scenes/stage';
+import { spawnFood } from './sim/food';
 
 /**
  * Dev harness — toastsim's single most valuable organ, transplanted.
@@ -148,6 +149,58 @@ export function installHarness(stage: Stage): void {
       }
       return { ok, n, rate: `${ok}/${n}`, lifts };
     },
+
+    // ---- M2: cutting -------------------------------------------------------
+    cutStats: () => stage.cutter.stats(),
+
+    /** Clear the board and drop a fresh food, settled on it. */
+    spawnFood(kind = 'tomato', x = 760) {
+      stage.auto = false;
+      for (const f of [...stage.cutter.foods]) stage.removeProp(f.body);
+      stage.cutter.foods = [];
+      stage.cutter.splats = [];
+      stage.cutter.last = null;
+      stage.cutter.add(spawnFood(stage, kind, x, 512));
+      for (let i = 0; i < 45; i++) stage.stepSim();
+      return stage.cutter.stats();
+    },
+
+    /** Drive the blade tip [x,y]→[x,y] over `secs`, then settle. Returns cutStats. */
+    swing(from: [number, number], to: [number, number], secs = 0.18, settleAfter = 30) {
+      stage.auto = false;
+      stage.cutter.resetBlade({ x: from[0], y: from[1] });
+      const frames = Math.max(2, Math.round(secs * 60));
+      for (let i = 1; i <= frames; i++) {
+        const t = i / frames;
+        stage.cutter.moveBlade({ x: from[0] + (to[0] - from[0]) * t, y: from[1] + (to[1] - from[1]) * t });
+        stage.stepSim();
+      }
+      for (let i = 0; i < settleAfter; i++) stage.stepSim();
+      return stage.cutter.stats();
+    },
+
+    /** M2 exit-bar A: a practiced fast chop through the centre → 2 clean pieces, CV < 0.1. */
+    chop(kind = 'tomato') {
+      this.spawnFood(kind);
+      const c = stage.cutter.foods[0].body.position;
+      return this.swing([c.x, c.y - 70], [c.x, c.y + 80], 0.18);
+    },
+
+    /** M2 exit-bar B: a slow press → no cut, a wet splat. */
+    push(kind = 'tomato') {
+      this.spawnFood(kind);
+      const c = stage.cutter.foods[0].body.position;
+      return this.swing([c.x, c.y - 70], [c.x, c.y + 80], 1.5);
+    },
+
+    /** M2 exit-bar C: a wild fast swing → a piece flung offstage (and that's CORRECT). */
+    wildChop(kind = 'tomato') {
+      this.spawnFood(kind);
+      const c = stage.cutter.foods[0].body.position;
+      const r = this.swing([c.x - 110, c.y], [c.x + 320, c.y], 0.08, 55);
+      const offstage = stage.cutter.foods.some((f) => f.body.position.x < 20 || f.body.position.x > 1260 || f.body.position.y > 705);
+      return { ...r, offstage, at: stage.cutter.foods.map((f) => ({ x: +f.body.position.x.toFixed(0), y: +f.body.position.y.toFixed(0) })) };
+    },
   };
 
   (window as { __s?: typeof s }).__s = s;
diff --git a/src/scenes/stage.ts b/src/scenes/stage.ts
index 509b4c3..4c63f95 100644
--- a/src/scenes/stage.ts
+++ b/src/scenes/stage.ts
@@ -1,6 +1,8 @@
 import Phaser from 'phaser';
 import { installHarness } from '../dev';
 import { Marionette } from '../sim/marionette';
+import { Cutter } from '../sim/cutting';
+import { spawnFood } from '../sim/food';
 
 export const STAGE_W = 1280;
 export const STAGE_H = 720;
@@ -23,7 +25,9 @@ export class Stage extends Phaser.Scene {
   auto = true;
   props: Prop[] = [];
   puppet!: Marionette;
+  cutter!: Cutter;
   crate!: MatterJS.BodyType;
+  board!: MatterJS.BodyType;
   private space!: Phaser.Input.Keyboard.Key;
 
   constructor() {
@@ -45,6 +49,12 @@ export class Stage extends Phaser.Scene {
     this.addBody(this.crate, 48, 48, 0x3a2d20);
     this.puppet.gripTargets.push(this.crate);
 
+    // cutting board (a static counter) + a food resting on it for M2.
+    this.board = this.matter.add.rectangle(760, 560, 240, 24, { isStatic: true });
+    this.addBody(this.board, 240, 24, 0x2a211a);
+    this.cutter = new Cutter(this);
+    this.cutter.add(spawnFood(this, 'tomato', 760, 512));
+
     this.space = this.input.keyboard!.addKey(Phaser.Input.Keyboard.KeyCodes.SPACE);
     installHarness(this);
   }
@@ -63,6 +73,30 @@ export class Stage extends Phaser.Scene {
     return body;
   }
 
+  /** Register a body with a polygon silhouette (food, food pieces).
+   *  localVerts are centred on the body origin. */
+  addPoly(body: MatterJS.BodyType, localVerts: { x: number; y: number }[], color: number): MatterJS.BodyType {
+    const view = this.add.polygon(body.position.x, body.position.y, localVerts, color);
+    this.props.push({ body, view });
+    return body;
+  }
+
+  /** A wet-food splat decal — a dark blob left on the stage (no body). */
+  splat(x: number, y: number, r: number, color: number): void {
+    const blob = this.add.ellipse(x, y, r * 2.2, r * 1.3, color, 0.85);
+    blob.setDepth(-1);
+  }
+
+  /** Destroy a body's silhouette and remove it from the world. */
+  removeProp(body: MatterJS.BodyType): void {
+    const i = this.props.findIndex((p) => p.body === body);
+    if (i >= 0) {
+      this.props[i].view.destroy();
+      this.props.splice(i, 1);
+    }
+    this.matter.world.remove(body);
+  }
+
   stepSim(dt = 1000 / 60): void {
     this.matter.world.step(dt);
     this.puppet?.update();
diff --git a/src/sim/cutting.ts b/src/sim/cutting.ts
new file mode 100644
index 0000000..a9b5955
--- /dev/null
+++ b/src/sim/cutting.ts
@@ -0,0 +1,163 @@
+import type { Stage } from '../scenes/stage';
+import { Food, makeFood } from './food';
+import {
+  add, centroid, cvWord, len, norm, perp, pieceCV, pointInPoly, polyArea, polyDiameter,
+  scale, segPolyCrossings, splitConvexByLine, sub, type V,
+} from './geom';
+
+export type CutQuality = 'clean' | 'ragged' | 'crime';
+
+// cut thresholds, px/frame at 60fps (the calibration surface — tuned by harness)
+const CUT = {
+  clean: 11, // peak blade speed for a clean pass
+  squash: 4.5, // below this a wet food splats instead of cutting
+  minChordFrac: 0.45, // the pass must span this much of the food to count as a cut
+  cleanChordFrac: 0.6, // and this much to be graded clean
+  bladeTransfer: 0.42, // fraction of blade speed the pieces carry off (px/step)
+  separate: 1.4, // px/step the halves spring apart (Matter velocity is per-step, not per-sec)
+  gap: 4, // px each half is nudged off the cut line so they don't spawn overlapping
+};
+
+const worldVerts = (b: MatterJS.BodyType): V[] => (b.vertices ?? []).map((v) => ({ x: v.x, y: v.y }));
+
+interface Track {
+  entry: V;
+  pathLen: number;
+  frames: number;
+  peakSpeed: number;
+}
+
+export interface CutResult {
+  quality: CutQuality;
+  pieces: number;
+  cv: number;
+  speed: number;
+  chordFrac: number;
+}
+
+/**
+ * The cut. A blade tip is driven across the board (by the harness now, by the
+ * gripped hand at M4). When the tip passes THROUGH a food fast enough the food
+ * splits along the tip's chord into two real bodies; a slow press on a wet food
+ * squashes into a splat instead. Honest geometry — no canned "sliced" anim.
+ */
+export class Cutter {
+  foods: Food[] = [];
+  splats: { mass: number }[] = [];
+  last: CutResult | null = null;
+  private tip: V | null = null;
+  private track = new Map<Food, Track>();
+
+  constructor(private stage: Stage) {}
+
+  add(food: Food): void {
+    this.foods.push(food);
+  }
+
+  /** Start a fresh stroke from `p` (clears any in-progress pass). */
+  resetBlade(p: V): void {
+    this.tip = p;
+    this.track.clear();
+  }
+
+  /** Advance the blade tip to `p` for one frame and run cut detection. */
+  moveBlade(p: V): void {
+    const prev = this.tip ?? p;
+    this.tip = p;
+    const stepLen = len(sub(p, prev));
+    for (const food of [...this.foods]) {
+      const verts = worldVerts(food.body);
+      const inNow = pointInPoly(p, verts);
+      const st = this.track.get(food);
+      if (!st) {
+        const crossings = segPolyCrossings(prev, p, verts);
+        if (inNow || crossings.length > 0) {
+          this.track.set(food, { entry: crossings[0] ?? prev, pathLen: stepLen, frames: 1, peakSpeed: stepLen });
+        }
+      } else {
+        st.pathLen += stepLen;
+        st.frames++;
+        st.peakSpeed = Math.max(st.peakSpeed, stepLen);
+        if (!inNow) {
+          const crossings = segPolyCrossings(prev, p, verts);
+          const exit = crossings.length ? crossings[crossings.length - 1] : prev;
+          this.commit(food, st.entry, exit, st.peakSpeed);
+          this.track.delete(food);
+        }
+      }
+    }
+  }
+
+  private commit(food: Food, entry: V, exit: V, peakSpeed: number): void {
+    const verts = worldVerts(food.body);
+    const diam = polyDiameter(verts) || 1;
+    const chordFrac = len(sub(exit, entry)) / diam;
+    const mat = food.material;
+    const power = peakSpeed * (1 - 0.5 * mat.resistance); // tougher skin, harder to cut
+
+    // too slow or too shallow → not a clean split
+    if (power < CUT.squash || chordFrac < CUT.minChordFrac) {
+      if (mat.moisture > 0.4 && power < CUT.squash) {
+        this.splat(food, peakSpeed);
+      } else {
+        this.last = { quality: 'crime', pieces: 1, cv: 0, speed: +peakSpeed.toFixed(2), chordFrac: +chordFrac.toFixed(2) };
+      }
+      return;
+    }
+
+    const parts = splitConvexByLine(verts, entry, exit);
+    if (!parts) return;
+
+    const quality: CutQuality = power >= CUT.clean && chordFrac >= CUT.cleanChordFrac ? 'clean' : 'ragged';
+    this.stage.removeProp(food.body);
+    this.foods = this.foods.filter((f) => f !== food);
+
+    const dir = norm(sub(exit, entry));
+    const n = perp(dir); // separation normal (splitConvexByLine returns [left, right] of dir)
+    const bladeVel = scale(dir, peakSpeed * CUT.bladeTransfer); // peakSpeed is px/step already
+    parts.forEach((pv, i) => {
+      const c = centroid(pv);
+      const side = i === 0 ? 1 : -1;
+      // spawn each half nudged off the cut line so the two bodies never overlap
+      // at birth — coincident bodies make Matter eject them across the county.
+      const pos = add(c, scale(n, side * CUT.gap));
+      const piece = makeFood(this.stage, pv, pos.x, pos.y, mat, food.color, food.face, food.kind + 'p');
+      this.stage.matter.body.setVelocity(piece.body, add(bladeVel, scale(n, side * CUT.separate)));
+      this.foods.push(piece);
+    });
+
+    const areas = parts.map(polyArea);
+    this.last = {
+      quality,
+      pieces: 2,
+      cv: +pieceCV(areas).toFixed(3),
+      speed: +peakSpeed.toFixed(2),
+      chordFrac: +chordFrac.toFixed(2),
+    };
+  }
+
+  private splat(food: Food, peakSpeed: number): void {
+    const verts = worldVerts(food.body);
+    const c = centroid(verts);
+    const mass = +((polyArea(verts) / 900) * food.material.moisture).toFixed(2);
+    this.splats.push({ mass });
+    this.stage.removeProp(food.body);
+    this.foods = this.foods.filter((f) => f !== food);
+    this.stage.splat(c.x, c.y, Math.sqrt(polyArea(verts) / Math.PI) * 1.3, food.color);
+    this.last = { quality: 'crime', pieces: 0, cv: 0, speed: +peakSpeed.toFixed(2), chordFrac: 0 };
+    // ponytail: slippery-floor patch deferred — no one carries over it until M4.
+  }
+
+  /** Everything the judge and the harness read off a cut. */
+  stats() {
+    const areas = this.foods.map((f) => polyArea(worldVerts(f.body)));
+    const cv = pieceCV(areas);
+    return {
+      pieces: this.foods.length,
+      cv: +cv.toFixed(3),
+      cvWord: cvWord(cv),
+      splatMass: +this.splats.reduce((a, b) => a + b.mass, 0).toFixed(2),
+      last: this.last,
+    };
+  }
+}
diff --git a/src/sim/food.ts b/src/sim/food.ts
new file mode 100644
index 0000000..65ca6d4
--- /dev/null
+++ b/src/sim/food.ts
@@ -0,0 +1,75 @@
+import type { Stage } from '../scenes/stage';
+import { centroid, type V } from './geom';
+
+/** toastsim-style material params. resistance raises the cut threshold; moisture
+ *  drives the splat; wobble is jelly-class jiggle (soft, deferred to when a
+ *  jelly food actually ships). */
+export interface Material {
+  resistance: number; // 0..1 skin toughness
+  moisture: number; // 0..1 wet food splats
+  wobble: number; // 0..1 jiggle
+}
+
+export interface FoodDef {
+  verts: V[]; // convex, centred on origin
+  material: Material;
+  color: number;
+  face: string; // generated face sprite id (rendered later; gameplay is the silhouette)
+}
+
+const circle = (r: number, n: number, squashY = 1): V[] =>
+  Array.from({ length: n }, (_, i) => {
+    const a = (i / n) * Math.PI * 2;
+    return { x: Math.cos(a) * r, y: Math.sin(a) * r * squashY };
+  });
+
+const box = (w: number, h: number): V[] => {
+  const x = w / 2, y = h / 2, c = Math.min(x, y) * 0.4; // chamfered corners → convex octagon
+  return [
+    { x: -x + c, y: -y }, { x: x - c, y: -y }, { x, y: -y + c }, { x, y: y - c },
+    { x: x - c, y }, { x: -x + c, y }, { x: -x, y: y - c }, { x: -x, y: -y + c },
+  ];
+};
+
+export const FOODS: Record<string, FoodDef> = {
+  tomato: { verts: circle(34, 12), material: { resistance: 0.25, moisture: 0.85, wobble: 0.15 }, color: 0x151515, face: 'face_tomato' },
+  bread: { verts: box(78, 52), material: { resistance: 0.35, moisture: 0.05, wobble: 0.0 }, color: 0x1c150e, face: 'face_bread' },
+  cheese: { verts: box(60, 44), material: { resistance: 0.45, moisture: 0.15, wobble: 0.0 }, color: 0x191510, face: 'face_cheese' },
+  katsu: { verts: box(86, 46), material: { resistance: 0.55, moisture: 0.1, wobble: 0.0 }, color: 0x171008, face: 'face_katsu' },
+  egg: { verts: circle(28, 10, 1.15), material: { resistance: 0.3, moisture: 0.4, wobble: 0.1 }, color: 0x121212, face: 'face_egg' },
+};
+
+let NEXT = 1;
+
+/** A food body + its material and origin colour. Pieces are Foods too. */
+export class Food {
+  readonly id: string;
+  constructor(
+    readonly body: MatterJS.BodyType,
+    readonly material: Material,
+    readonly color: number,
+    readonly face: string,
+    readonly kind: string,
+  ) {
+    this.id = `${kind}${NEXT++}`;
+  }
+}
+
+/** Build a food body from centred local verts placed at world (x,y). Registers
+ *  the silhouette on the stage. Shared by spawn and by the cutter's pieces. */
+export function makeFood(stage: Stage, local: V[], x: number, y: number, mat: Material, color: number, face: string, kind: string): Food {
+  const body = stage.matter.add.fromVertices(x, y, local, {
+    friction: 0.6, frictionAir: 0.01, density: 0.0009, restitution: 0.05,
+  }) as MatterJS.BodyType;
+  // fromVertices recentres COM; render verts relative to that centre.
+  const c = centroid(local);
+  const rel = local.map((v) => ({ x: v.x - c.x, y: v.y - c.y }));
+  stage.addPoly(body, rel, color);
+  return new Food(body, mat, color, face, kind);
+}
+
+/** Spawn a whole food of `kind` at x, resting just above the floor. */
+export function spawnFood(stage: Stage, kind: string, x: number, y: number): Food {
+  const def = FOODS[kind] ?? FOODS.tomato;
+  return makeFood(stage, def.verts, x, y, def.material, def.color, def.face, kind);
+}
diff --git a/src/sim/geom.check.ts b/src/sim/geom.check.ts
new file mode 100644
index 0000000..8865a92
--- /dev/null
+++ b/src/sim/geom.check.ts
@@ -0,0 +1,35 @@
+/** Runnable self-check for the cut geometry — the honest core, and the part
+ *  that hid a degenerate-vertex bug (a cut line through two verts made lopsided
+ *  halves). Run: `node src/sim/geom.check.ts` (Node strips the types). */
+import { polyArea, pieceCV, cvWord, splitConvexByLine, type V } from './geom.ts';
+import assert from 'node:assert/strict';
+
+const circle = (r: number, n: number): V[] =>
+  Array.from({ length: n }, (_, i) => ({ x: Math.cos((i / n) * 2 * Math.PI) * r, y: Math.sin((i / n) * 2 * Math.PI) * r }));
+
+// 1. centred vertical cut of a symmetric polygon → equal halves
+{
+  const c = circle(34, 12);
+  const [L, R] = splitConvexByLine(c, { x: 0, y: -50 }, { x: 0, y: 50 })!;
+  assert(Math.abs(polyArea(L) - polyArea(R)) < 1e-6, 'off-vertex split should be symmetric');
+}
+
+// 2. THE REGRESSION: cut line passing exactly through two vertices (top+bottom
+//    of a 12-gon at (0,±r)) must still give equal halves, not lopsided ones.
+{
+  const c = circle(34, 12);
+  const [L, R] = splitConvexByLine(c, { x: 0, y: -34 }, { x: 0, y: 34 })!;
+  assert(Math.abs(polyArea(L) - polyArea(R)) < 1e-6, 'through-vertex split must be symmetric');
+}
+
+// 3. a line that misses the polygon returns null
+{
+  assert(splitConvexByLine(circle(10, 8), { x: 100, y: -10 }, { x: 100, y: 10 }) === null, 'miss → null');
+}
+
+// 4. pieceCV: equal pieces → 0; the ladder words line up
+assert(pieceCV([100, 100]) === 0, 'equal areas → CV 0');
+assert(pieceCV([50, 150]) > 0.4, 'lopsided pieces → high CV');
+assert(cvWord(0) === 'even' && cvWord(0.5) === 'a lottery', 'cvWord ladder');
+
+console.log('geom.check: all assertions passed');
diff --git a/src/sim/geom.ts b/src/sim/geom.ts
new file mode 100644
index 0000000..805b4de
--- /dev/null
+++ b/src/sim/geom.ts
@@ -0,0 +1,124 @@
+/** 2D polygon helpers for the cut. Pure math, no engine — the honest core of
+ *  the cutting sim (a convex food polygon split by the blade's line). */
+export interface V {
+  x: number;
+  y: number;
+}
+
+export const sub = (a: V, b: V): V => ({ x: a.x - b.x, y: a.y - b.y });
+export const add = (a: V, b: V): V => ({ x: a.x + b.x, y: a.y + b.y });
+export const cross = (a: V, b: V): number => a.x * b.y - a.y * b.x;
+export const len = (a: V): number => Math.hypot(a.x, a.y);
+export const scale = (a: V, s: number): V => ({ x: a.x * s, y: a.y * s });
+export const norm = (a: V): V => {
+  const l = len(a) || 1;
+  return { x: a.x / l, y: a.y / l };
+};
+export const perp = (a: V): V => ({ x: -a.y, y: a.x });
+
+/** Shoelace area (always positive). */
+export function polyArea(vs: V[]): number {
+  let a = 0;
+  for (let i = 0; i < vs.length; i++) {
+    const j = (i + 1) % vs.length;
+    a += cross(vs[i], vs[j]);
+  }
+  return Math.abs(a) / 2;
+}
+
+/** Area-weighted centroid. */
+export function centroid(vs: V[]): V {
+  let a = 0, cx = 0, cy = 0;
+  for (let i = 0; i < vs.length; i++) {
+    const j = (i + 1) % vs.length;
+    const c = cross(vs[i], vs[j]);
+    a += c;
+    cx += (vs[i].x + vs[j].x) * c;
+    cy += (vs[i].y + vs[j].y) * c;
+  }
+  a *= 0.5;
+  if (Math.abs(a) < 1e-6) return { ...vs[0] };
+  return { x: cx / (6 * a), y: cy / (6 * a) };
+}
+
+/** Coefficient of variation of piece areas — toastsim's pieceCV, straight port.
+ *  0 = identical pieces, higher = a lottery. */
+export function pieceCV(areas: number[]): number {
+  if (areas.length < 2) return 0;
+  const mean = areas.reduce((a, b) => a + b, 0) / areas.length;
+  if (mean <= 0) return 0;
+  const v = areas.reduce((a, b) => a + (b - mean) ** 2, 0) / areas.length;
+  return Math.sqrt(v) / mean;
+}
+
+export function cvWord(cv: number): string {
+  return cv < 0.1 ? 'even' : cv < 0.22 ? 'respectable' : cv < 0.4 ? 'uneven' : 'a lottery';
+}
+
+export function pointInPoly(p: V, vs: V[]): boolean {
+  let inside = false;
+  for (let i = 0, j = vs.length - 1; i < vs.length; j = i++) {
+    const a = vs[i], b = vs[j];
+    if ((a.y > p.y) !== (b.y > p.y) && p.x < ((b.x - a.x) * (p.y - a.y)) / (b.y - a.y) + a.x) {
+      inside = !inside;
+    }
+  }
+  return inside;
+}
+
+/** Longest span across the polygon (diameter). */
+export function polyDiameter(vs: V[]): number {
+  let d = 0;
+  for (let i = 0; i < vs.length; i++)
+    for (let j = i + 1; j < vs.length; j++) d = Math.max(d, len(sub(vs[i], vs[j])));
+  return d;
+}
+
+/** Where segment a→b crosses the polygon boundary, sorted along a→b. */
+export function segPolyCrossings(a: V, b: V, vs: V[]): V[] {
+  const dir = sub(b, a);
+  const hits: { p: V; t: number }[] = [];
+  for (let i = 0; i < vs.length; i++) {
+    const c = vs[i], d = vs[(i + 1) % vs.length];
+    const e = sub(d, c);
+    const denom = cross(dir, e);
+    if (Math.abs(denom) < 1e-9) continue;
+    const t = cross(sub(c, a), e) / denom; // along a→b
+    const u = cross(sub(c, a), dir) / denom; // along c→d
+    if (t >= -1e-6 && t <= 1 + 1e-6 && u >= -1e-6 && u <= 1 + 1e-6) {
+      hits.push({ p: { x: a.x + dir.x * t, y: a.y + dir.y * t }, t });
+    }
+  }
+  hits.sort((x, y) => x.t - y.t);
+  return hits.map((h) => h.p);
+}
+
+/**
+ * Split a convex polygon by the infinite line through A and B. Returns the two
+ * halves (each ≥3 verts), or null if the line misses the polygon.
+ */
+export function splitConvexByLine(vs: V[], A: V, B: V): [V[], V[]] | null {
+  const dir = sub(B, A);
+  const EPS = 1e-6;
+  const sgn = (p: V): number => {
+    const s = cross(dir, sub(p, A));
+    return s > EPS ? 1 : s < -EPS ? -1 : 0; // 0 = on the cut line → shared by both
+  };
+  const left: V[] = [], right: V[] = [];
+  for (let i = 0; i < vs.length; i++) {
+    const cur = vs[i], nxt = vs[(i + 1) % vs.length];
+    const sc = sgn(cur), sn = sgn(nxt);
+    if (sc >= 0) left.push(cur);
+    if (sc <= 0) right.push(cur);
+    if (sc * sn < 0) {
+      // strictly opposite sides: split the edge at the crossing, add to both
+      const e = sub(nxt, cur);
+      const t = cross(sub(A, cur), dir) / cross(e, dir);
+      const p = { x: cur.x + e.x * t, y: cur.y + e.y * t };
+      left.push(p);
+      right.push(p);
+    }
+  }
+  if (left.length < 3 || right.length < 3) return null;
+  return [left, right];
+}
diff --git a/tsconfig.json b/tsconfig.json
index a13e03c..1148ebc 100644
--- a/tsconfig.json
+++ b/tsconfig.json
@@ -12,5 +12,6 @@
     "types": [],
     "lib": ["ES2022", "DOM", "DOM.Iterable"]
   },
-  "include": ["src"]
+  "include": ["src"],
+  "exclude": ["src/**/*.check.ts"]
 }