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Schluffe
2026-07-30 22:06:28 +02:00
parent 7262752e16
commit ec9f2e2a2d
13 changed files with 873 additions and 68 deletions
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@@ -52,29 +52,29 @@
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@@ -286,9 +286,9 @@
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engine/system/physics.ts
+37 -18
View File
@@ -154,26 +154,45 @@ function sweptAABB(
const vx = velocityA.x * delta; // scale x by delta for collider a const vx = velocityA.x * delta; // scale x by delta for collider a
const vy = velocityA.y * delta; // scale y by delta for collider a const vy = velocityA.y * delta; // scale y by delta for collider a
let txNear = (inflAABB.x - ax) / vx; // setup interval for x
let txFar = (inflAABB.x + inflAABB.width - ax) / vx; const minX = inflAABB.x;
const maxX = inflAABB.x + inflAABB.width;
const inRangeX = minX <= ax && ax <= maxX;
let txNear = inRangeX ? -Infinity : null;
let txFar = inRangeX ? Infinity : null;
let tyNear = (inflAABB.y - ay) / vy; if (vx !== 0) {
let tyFar = (inflAABB.y + inflAABB.height - ay) / vy; // setup the span for x
txNear = (minX - ax) / vx;
if (txNear > txFar) { txFar = (maxX - ax) / vx;
[txNear, txFar] = [txFar, txNear]; if (txNear > txFar) {
} [txNear, txFar] = [txFar, txNear];
if (tyNear > tyFar) { }
[tyNear, tyFar] = [tyFar, tyNear];
} }
// no collision at all // setup interval for y
if (txNear > tyFar || tyNear > txFar) { const minY = inflAABB.y;
const maxY = inflAABB.y + inflAABB.height;
const inRangeY = minY <= ay && ay <= maxY;
let tyNear = inRangeY ? -Infinity : null;
let tyFar = inRangeY ? Infinity : null;
if (vy !== 0) {
// setup the span for y
tyNear = (minY - ay) / vy;
tyFar = (maxY - ay) / vy;
if (tyNear > tyFar) {
[tyNear, tyFar] = [tyFar, tyNear];
}
}
// no collision possible
if (!inRangeX || !inRangeY) {
return null; return null;
} }
const thNear = Math.max(txNear, tyNear); const thNear = Math.max(txNear!, tyNear!);
const thFar = Math.min(txFar, tyFar); const thFar = Math.min(txFar!, tyFar!);
// thFar < 0, collision is behind a frame // thFar < 0, collision is behind a frame
// thNear > 1, collision is ahead a frame // thNear > 1, collision is ahead a frame
@@ -183,13 +202,12 @@ function sweptAABB(
collision.normal.x = 0; collision.normal.x = 0;
collision.normal.y = 0; collision.normal.y = 0;
if (txNear > tyNear) { if (txNear! > tyNear!) {
collision.normal.x = vx > 0 ? -1 : 1; collision.normal.x = vx > 0 ? -1 : 1;
} else { } else {
collision.normal.y = vy > 0 ? -1 : 1; collision.normal.y = vy > 0 ? -1 : 1;
} }
// thNear == -Infinity if velocity is 0
const time = Math.max(0, thNear); const time = Math.max(0, thNear);
collision.time = time; collision.time = time;
@@ -524,7 +542,7 @@ export function moveAndSlide(
let i = 0; let i = 0;
while (i++ < 4 && timeLeft > 0) { while (i++ < 4 && timeLeft > 0) {
const deltaLeft = delta * timeLeft; const deltaLeft = delta * timeLeft;
const collisions = moveAndCollide(id, velocity, delta); const collisions = moveAndCollide(id, velocity, deltaLeft);
if (collisions.length < 1) { if (collisions.length < 1) {
position.x += velocity.x * deltaLeft; position.x += velocity.x * deltaLeft;
position.y += velocity.y * deltaLeft; position.y += velocity.y * deltaLeft;
@@ -540,7 +558,8 @@ export function moveAndSlide(
} }
const time = closest.time; const time = closest.time;
const scalar = Math.max(0, time - EPSILON) * deltaLeft; // const scalar = Math.max(0, time - EPSILON) * deltaLeft;
const scalar = Math.max(0, time - EPSILON) * timeLeft;
position.x += velocity.x * scalar; position.x += velocity.x * scalar;
position.y += velocity.y * scalar; position.y += velocity.y * scalar;
package.json
+3 -3
View File
@@ -8,13 +8,13 @@
"check": "biome check --write" "check": "biome check --write"
}, },
"dependencies": { "dependencies": {
"@biomejs/biome": "2.5.3", "@biomejs/biome": "2.5.6",
"@types/bun": "1.3.14", "@types/bun": "1.3.14",
"lz-string": "1.5.0", "lz-string": "1.5.0",
"solid-js": "1.9.14", "solid-js": "1.9.14",
"typescript": "7.0.2", "typescript": "7.0.2",
"vite": "8.1.4", "vite": "8.2.0",
"vite-plugin-solid": "2.11.12" "vite-plugin-solid": "2.11.14"
}, },
"imports": { "imports": {
"#/": "./*" "#/": "./*"
workshop/README.md
+4
View File
@@ -53,5 +53,9 @@ the top rung *is* a working engine.
- [x] `10-move-and-slide` — the full loop: multiple obstacles, iteration cap (relative velocity explained) - [x] `10-move-and-slide` — the full loop: multiple obstacles, iteration cap (relative velocity explained)
- [x] `11-capstone` — a canvas demo (no test — just run it and play) - [x] `11-capstone` — a canvas demo (no test — just run it and play)
**Batch 5 — hardening (unlocked by your own capstone finds):**
- [x] `12-overlap` — the overlap trap: why positions go `NaN` when you start inside a collider, and the depenetration (minimum-translation-vector) fix
- [ ] `13-crush` — when one push lands you in the next wall: iterative depenetration, and the honest answer for gaps narrower than the hero
When step 11 is green you'll have re-derived your own engine's heart — and walking When step 11 is green you'll have re-derived your own engine's heart — and walking
back into `sweptAABB` should feel like reading your own handwriting again. back into `sweptAABB` should feel like reading your own handwriting again.
workshop/steps/11-capstone/game.js
+46 -1
View File
@@ -133,6 +133,51 @@ function drawBox(b, fill, stroke) {
ctx.strokeRect(b.x + 0.5, b.y + 0.5, b.w - 1, b.h - 1); ctx.strokeRect(b.x + 0.5, b.y + 0.5, b.w - 1, b.h - 1);
} }
} }
/**
* How to push `a` OUT of `b`, by the smallest possible single-axis move.
*
* Returns the push as a vector to ADD to a's position, or null if the boxes
* don't strictly overlap (merely touching edges is not overlapping).
*
* There are four ways out (left, right, up, down) — measure all four
* distances and return the shortest one. See the README.
*/
function penetrationVector(a, b) {
const outLeft = a.x + a.w - b.x;
const outRight = b.x + b.w - a.x;
const outUp = a.y + a.h - b.y;
const outDown = b.y + b.h - a.y;
const minX = Math.min(outLeft, outRight);
const minY = Math.min(outUp, outDown);
if (minX > 0 && minY > 0) {
return minX > minY
? { x: 0, y: outDown > outUp ? -minY : minY }
: { x: outLeft > outRight ? minX : -minX, y: 0 };
}
return null;
}
/**
* moveAndSlide, but immune to the overlap trap: first push `box` out of any
* wall it is already inside (plus an EPSILON of slack, same idea as the
* backoff in the loop), THEN run the normal sweep loop from the safe spot.
*
* Everything you need is penetrationVector above and given.ts.
*/
function safeMoveAndSlide(box, v, walls) {
for (const wall of walls) {
const pv = penetrationVector(box, wall);
if (pv) {
box.x += pv.x > 0 ? pv.x + EPSILON : pv.x - EPSILON;
box.y += pv.y > 0 ? pv.y + EPSILON : pv.y - EPSILON;
}
}
return moveAndSlide(box, v, walls);
}
let then = performance.now(); let then = performance.now();
function frame(now) { function frame(now) {
@@ -156,7 +201,7 @@ function frame(now) {
// full-frame displacement is velocity * delta — exactly what moveAndSlide expects // full-frame displacement is velocity * delta — exactly what moveAndSlide expects
const displacement = scale(velocity, delta); const displacement = scale(velocity, delta);
const next = moveAndSlide(player, displacement, walls); const next = safeMoveAndSlide(player, displacement, walls);
player.x = next.x; player.x = next.x;
player.y = next.y; player.y = next.y;
workshop/steps/12-overlap/README.md
+108
View File
@@ -0,0 +1,108 @@
# Step 12 — The overlap trap (when the sweep has no answer)
You found this one yourself, in the capstone: start a box **inside** another
collider, press a key, and the position turns into `NaN`. That's not a typo in
your code from steps 01–10 — the kernel is *correct* and still does this. It's a
**blind spot in the whole approach**, and every real engine has to patch it.
> This is a genuine hole in the finished kernel, shared by the capstone's
> `game.js`. It is a *third* thing, separate from the two bugs you're hunting in
> `engine/system/physics.ts` — no spoilers here.
## Why the sweep can't see it
Everything since step 05 answers one question: *"when, during this frame, will I
**enter** the box?"* The whole ladder quietly assumes the answer lies in the
future — that you start the frame **outside**.
Start inside, and "when will I enter?" has no sane answer. The math doesn't
refuse — it cheerfully reports that you entered *in the past*. Remember step 05:
what sign does `entry` have when `p` is already between `min` and `max`? Every
function above `sweepInterval` trusts that number without checking it.
## The autopsy (do this before reading on)
The `NaN` isn't born where you see it — it's the end of a chain, and each link
is one line you wrote. Reproduce it in a scratch file and trace it:
```ts
import { moveAndSlide, sweptAABB } from "./given.ts";
const box = { x: 10, y: 10, w: 2, h: 2 };
const wall = { x: 0, y: 0, w: 32, h: 32 };
console.log(sweptAABB(box, { x: 5, y: 0 }, wall));
console.log(moveAndSlide(box, { x: 5, y: 0 }, [wall]));
```
Work through these **in order, predicting each answer before checking** (add
`console.log`s inside your step-10 loop — it's your code, instrument it):
1. What `time` does `sweptAABB` report? Now flip the velocity so the box moves
*away* from the wall — why do you *still* get a hit? (This is why you can't
even walk out of a wall you're stuck in.)
2. Follow that `time` into the `else` branch of `moveAndSlide`. Three lines use
it. Which line is saved by the `Math.max(0, …)`? What happens to `vel` when
you `slide` against that normal? And what does `timeLeft = timeLeft * (1 - time)`
do when `time` is negative — shrink, or *grow*?
3. Next iteration: `vel` is now `(0, 0)` but the loop keeps going. What does
`sweepInterval` return for `v = 0` while inside the interval (look at the
first branch — you wrote it in step 05)? So what is `entry` now, and what
does `timeLeft` become after multiplying by `(1 - entry)`?
4. Last link. In JavaScript, what is `0 * Infinity`? That's `scale(vel, timeLeft)`
on iteration three. And once one `NaN` exists, every comparison against it is
`false` — so which branch of the loop does the poisoned move fall into, and
what does `pos = add(pos, move)` do then?
Four links: **overlap → a hit in the past → dead velocity + growing time debt →
`0 × ∞`**. When you can retell that chain from memory, you own it.
## The fix: measure the overlap, push out
The sweep is *continuous* detection — it prevents overlap but can't recover from
it. So real engines pair it with a *discrete* partner: if you're already inside,
don't ask "when do I enter?" — ask **"how deep am I, and what's the shortest way
out?"**, then teleport that far and *only then* sweep.
That shortest-way-out is the **penetration vector** (the famous *minimum
translation vector*). For two overlapping AABBs there are exactly four escapes —
push `a` left, right, up, or down until the boxes just separate:
```
outLeft = (a.x + a.w) - b.x // slide a left this far -> separated
outRight = (b.x + b.w) - a.x // slide a right this far -> separated
outUp = (a.y + a.h) - b.y
outDown = (b.y + b.h) - a.y
```
Two things to convince yourself of (don't skip — the tests check both):
- The boxes strictly overlap **iff all four distances are positive**. (What is
`outLeft` when `a` sits fully to the right of `b`? When they merely touch?)
- The answer is the **smallest** of the four, as a vector, with the sign that
moves `a` *away*. Smallest, because depenetration is a teleport the player can
see — one pixel of pop beats being flung across the room. Note this handles
`a` fully *swallowed* by `b` too, where "the overlap of the intervals" would
lie to you — one of the tests is exactly that case.
## Task
Two functions in `overlap.ts`:
1. `penetrationVector(a, b)` — the smallest single-axis push that separates the
boxes, or `null` if they don't strictly overlap.
2. `safeMoveAndSlide(box, v, walls)` — check every wall; if the box is inside
one, apply the push **plus an `EPSILON` of slack in the push direction**
(same idea as the backoff in the loop: land *flush* on the wall and next
frame's sweep starts half-trapped again). Then run the given `moveAndSlide`
from the safe position.
```sh
bun test workshop/steps/12-overlap
```
## Make the capstone unbreakable (optional)
Port both functions into `11-capstone/game.js`, swap the `moveAndSlide` call for
`safeMoveAndSlide`, and set the player's spawn inside the pillar. It should pop
out and play on like nothing happened. Then the question you actually care
about: does your *real* engine survive the same experiment?
workshop/steps/12-overlap/given.ts
+113
View File
@@ -0,0 +1,113 @@
// The whole kernel you've built, steps 01-10, finished. Reuse it.
export type Vec = { x: number; y: number };
export type AABB = { x: number; y: number; w: number; h: number };
export type Span = { entry: number; exit: number };
export type Hit = { time: number; normal: Vec };
/** A hair of slack so we stop just short of a wall instead of inside it. */
export const EPSILON = 1e-4;
export const vec = (x: number, y: number): Vec => ({ x, y });
export const add = (a: Vec, b: Vec): Vec => ({ x: a.x + b.x, y: a.y + b.y });
export const sub = (a: Vec, b: Vec): Vec => ({ x: a.x - b.x, y: a.y - b.y });
export const scale = (a: Vec, s: number): Vec => ({ x: a.x * s, y: a.y * s });
export const dot = (a: Vec, b: Vec): number => a.x * b.x + a.y * b.y;
/** Step 04, finished. Strict overlap — merely touching edges is false. */
export function aabbOverlap(a: AABB, b: AABB): boolean {
return (
a.x < b.x + b.w && b.x < a.x + a.w && a.y < b.y + b.h && b.y < a.y + a.h
);
}
export function sweepInterval(
p: number,
v: number,
min: number,
max: number,
): Span | null {
if (v === 0) {
return min <= p && p <= max ? { entry: -Infinity, exit: Infinity } : null;
}
let t1 = (min - p) / v;
let t2 = (max - p) / v;
if (t1 > t2) {
[t1, t2] = [t2, t1];
}
return { entry: t1, exit: t2 };
}
export function rayVsAABB(p: Vec, v: Vec, box: AABB): Hit | null {
const spanX = sweepInterval(p.x, v.x, box.x, box.x + box.w);
const spanY = sweepInterval(p.y, v.y, box.y, box.y + box.h);
if (spanX === null || spanY === null) {
return null;
}
const entry = Math.max(spanX.entry, spanY.entry);
const exit = Math.min(spanX.exit, spanY.exit);
if (entry > exit || entry >= 1 || exit <= 0) {
return null;
}
const normal =
spanX.entry > spanY.entry
? { x: v.x > 0 ? -1 : 1, y: 0 }
: { x: 0, y: v.y > 0 ? -1 : 1 };
return { time: entry, normal };
}
export function sweptAABB(a: AABB, v: Vec, b: AABB): Hit | null {
const inflated: AABB = {
x: b.x - a.w,
y: b.y - a.h,
w: b.w + a.w,
h: b.h + a.h,
};
return rayVsAABB({ x: a.x, y: a.y }, v, inflated);
}
export function slide(v: Vec, normal: Vec): Vec {
return sub(v, scale(normal, dot(v, normal)));
}
/** Step 10, finished — your loop, exactly as you wrote it. */
export function moveAndSlide(box: AABB, v: Vec, walls: AABB[]): Vec {
let pos: Vec = { x: box.x, y: box.y };
let vel: Vec = { x: v.x, y: v.y };
let timeLeft = 1;
let i = 0;
while (i++ < 4 && timeLeft > 0) {
const move = scale(vel, timeLeft);
let nearest: Hit = {
normal: { x: 0, y: 0 },
time: 2,
};
for (const wall of walls) {
const hit = sweptAABB(
{
x: pos.x,
y: pos.y,
w: box.w,
h: box.h,
},
move,
wall,
);
if (hit !== null) {
nearest = hit.time < nearest.time ? hit : nearest;
}
}
if (nearest.time === 2) {
pos = add(pos, move);
break;
} else {
pos = add(pos, scale(move, Math.max(0, nearest.time - EPSILON)));
vel = slide(vel, nearest.normal);
timeLeft = timeLeft * (1 - nearest.time);
}
}
return pos;
}
workshop/steps/12-overlap/overlap.test.ts
+102
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@@ -0,0 +1,102 @@
import { expect, test } from "bun:test";
import { type AABB, aabbOverlap, vec } from "./given.ts";
import { penetrationVector, safeMoveAndSlide } from "./overlap.ts";
// --- penetrationVector -------------------------------------------------------
test("separated boxes -> null", () => {
const a: AABB = { x: 0, y: 0, w: 2, h: 2 };
const b: AABB = { x: 5, y: 5, w: 2, h: 2 };
expect(penetrationVector(a, b)).toBeNull();
});
test("touching edges (no strict overlap) -> null", () => {
const a: AABB = { x: 0, y: 0, w: 2, h: 2 };
const b: AABB = { x: 2, y: 0, w: 2, h: 2 };
expect(penetrationVector(a, b)).toBeNull();
});
test("shallow on x, deep on y -> pushes left (the short way out)", () => {
// a pokes 1 unit into b's left side; getting out via y would cost 6
const a: AABB = { x: 0, y: 0, w: 4, h: 4 };
const b: AABB = { x: 3, y: -2, w: 4, h: 8 };
expect(penetrationVector(a, b)).toEqual(vec(-1, 0));
});
test("mirrored -> pushes right", () => {
const a: AABB = { x: 4, y: 0, w: 4, h: 4 };
const b: AABB = { x: 1, y: -2, w: 4, h: 8 };
expect(penetrationVector(a, b)).toEqual(vec(1, 0));
});
test("shallow on y -> pushes up", () => {
const a: AABB = { x: 0, y: 0, w: 4, h: 4 };
const b: AABB = { x: -2, y: 3, w: 8, h: 4 };
expect(penetrationVector(a, b)).toEqual(vec(0, -1));
});
test("fully contained -> still gets out (all the way past the nearest edge)", () => {
// a is swallowed by b: the push must clear the whole distance to an edge,
// not just the 2-unit "overlap" of the intervals
const a: AABB = { x: 10, y: 10, w: 2, h: 2 };
const b: AABB = { x: 0, y: 0, w: 32, h: 32 };
const p = penetrationVector(a, b);
expect(p).not.toBeNull();
if (p !== null) {
const moved: AABB = { ...a, x: a.x + p.x, y: a.y + p.y };
expect(aabbOverlap(moved, b)).toBe(false);
}
});
// --- safeMoveAndSlide --------------------------------------------------------
const player: AABB = { x: 0, y: 0, w: 2, h: 2 };
test("no overlap at start -> behaves exactly like moveAndSlide", () => {
// step 10's diagonal test: x blocked at 3, y keeps going
const walls: AABB[] = [{ x: 5, y: -10, w: 2, h: 40 }];
const p = safeMoveAndSlide(player, vec(10, 10), walls);
expect(p.x).toBeCloseTo(3);
expect(p.y).toBeCloseTo(10);
});
test("starting inside a wall -> position stays a number", () => {
const inside: AABB = { x: 10, y: 10, w: 2, h: 2 };
const wall: AABB = { x: 0, y: 0, w: 32, h: 32 };
const p = safeMoveAndSlide(inside, vec(5, 0), [wall]);
expect(Number.isFinite(p.x)).toBe(true);
expect(Number.isFinite(p.y)).toBe(true);
});
test("starting inside a wall -> ends free of it", () => {
const inside: AABB = { x: 10, y: 10, w: 2, h: 2 };
const wall: AABB = { x: 0, y: 0, w: 32, h: 32 };
const p = safeMoveAndSlide(inside, vec(5, 0), [wall]);
expect(aabbOverlap({ ...inside, x: p.x, y: p.y }, wall)).toBe(false);
});
test("overlapping and walking AWAY -> actually gets away", () => {
// pokes 1 into the wall's left side; pushed out to x≈8, then walks -5
const stuck: AABB = { x: 9, y: 0, w: 2, h: 2 };
const wall: AABB = { x: 10, y: -5, w: 4, h: 10 };
const p = safeMoveAndSlide(stuck, vec(-5, 0), [wall]);
expect(p.x).toBeCloseTo(3);
expect(p.y).toBeCloseTo(0);
});
test("overlapping and pushing IN -> freed, then held at the wall", () => {
// pushed out to x≈8 first; the sweep then stops the rightward move there
const stuck: AABB = { x: 9, y: 0, w: 2, h: 2 };
const wall: AABB = { x: 10, y: -5, w: 4, h: 10 };
const p = safeMoveAndSlide(stuck, vec(5, 0), [wall]);
expect(p.x).toBeCloseTo(8);
expect(p.y).toBeCloseTo(0);
});
test("overlapping and pushing IN (rtl) -> freed, then held at the wall", () => {
const stuck: AABB = { x: 9, y: 0, w: 2, h: 2 };
const wall: AABB = { x: 10, y: -5, w: 4, h: 10 };
const p = safeMoveAndSlide(stuck, vec(-5, 0), [wall]);
expect(p.x).toBeCloseTo(3);
expect(p.y).toBeCloseTo(0);
});
workshop/steps/12-overlap/overlap.ts
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import { type AABB, EPSILON, moveAndSlide, type Vec } from "./given.ts";
/**
* How to push `a` OUT of `b`, by the smallest possible single-axis move.
*
* Returns the push as a vector to ADD to a's position, or null if the boxes
* don't strictly overlap (merely touching edges is not overlapping).
*
* There are four ways out (left, right, up, down) — measure all four
* distances and return the shortest one. See the README.
*/
export function penetrationVector(a: AABB, b: AABB): Vec | null {
const outLeft = a.x + a.w - b.x;
const outRight = b.x + b.w - a.x;
const outUp = a.y + a.h - b.y;
const outDown = b.y + b.h - a.y;
const minX = Math.min(outLeft, outRight);
const minY = Math.min(outUp, outDown);
if (minX > 0 && minY > 0) {
return minX > minY
? { x: 0, y: outDown > outUp ? -minY : minY }
: { x: outLeft > outRight ? minX : -minX, y: 0 };
}
return null;
}
/**
* moveAndSlide, but immune to the overlap trap: first push `box` out of any
* wall it is already inside (plus an EPSILON of slack, same idea as the
* backoff in the loop), THEN run the normal sweep loop from the safe spot.
*
* Everything you need is penetrationVector above and given.ts.
*/
export function safeMoveAndSlide(box: AABB, v: Vec, walls: AABB[]): Vec {
for (const wall of walls) {
const pv = penetrationVector(box, wall);
if (pv) {
box.x += pv.x > 0 ? pv.x + EPSILON : pv.x - EPSILON;
box.y += pv.y > 0 ? pv.y + EPSILON : pv.y - EPSILON;
}
}
return moveAndSlide(box, v, walls);
}
workshop/steps/13-crush/README.md
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# Step 13 — The crush (when there is no way out)
You found this one yourself too, chasing the capstone's ledge: the hero gets
pushed out of the moving ledge, lands **inside the pillar**, and the `NaN` you
buried in step 12 climbs right back out of its grave. Your autopsy chain from
last time is unchanged — the only new thing is *how a box you just freed ends
up inside a wall again in the very same frame*.
> Still a *fourth* thing, separate from the two bugs you're hunting in
> `engine/system/physics.ts` — no spoilers there.
## Why one pass isn't enough
Step 12's `safeMoveAndSlide` walks the walls **once, in array order**, fixing
each overlap it meets. For one wall that's airtight. But a depenetration push is
a *teleport* — and a teleport can land you inside a wall the loop already
checked and cleared, or one it hasn't reached yet (in which case it works, by
luck of the ordering). A resolver whose correctness depends on the order of the
wall array isn't a resolver — it's a coin flip.
Two experiments in a scratch file, **predicting each outcome before running**
(use your step-12 code as-is):
1. Hero `{x: 9, y: 1, w: 2, h: 2}`, walls `A = {x: 10, y: 0, w: 4, h: 4}` and
`B = {x: 4, y: 0, w: 4.5, h: 1.4}`. The hero overlaps only `A`. Run one pass
with the array `[A, B]`, then with `[B, A]`. Where does the hero end up in
each case, and is it free? Explain the difference before moving on.
2. Walls `{x: 10, y: -5, w: 4, h: 10}` and `{x: 6.5, y: -5, w: 2, h: 10}` — a
gap 1.5 wide. Hero (2 wide) at `{x: 9, y: 0}`. Apply `penetrationVector`
pushes in a loop and log `x` each time. Does it converge? What number does
`x` bounce between, and *why will it never stop*?
## The negotiation, and when it honestly fails
The fix for experiment 1 is patience: don't do one pass — **repeat whole passes
until a full pass finds nothing to fix**. That clean pass is your proof of
freedom. Each pass is cheap, and in sane geometry it settles in one or two.
But experiment 2 shows the negotiation can be *unwinnable*: when the gap is
narrower than the box, **no overlap-free position exists**. No amount of math
fixes that, because it isn't a math problem — it's a game-design question, and
every game answers it differently. Mario between a Thwomp and the floor:
crushed = death. Some engines let the wall shove you *through* its partner.
Zelda-flavored games mostly refuse the situation: solid wins, the hero holds
still until the gap opens. We take that one — it's the smallest honest answer:
**cap the passes, and if the cap fires, report it** (`settled: false`) instead
of pretending. You already believe in caps; your step-10 loop carries one for
exactly the same reason.
Last session you proposed armoring `sweepInterval` against the `Infinity`
directly. You can — see the optional section — but notice what that answer
skips over: even with the `NaN` gone, *what should a crushed hero do?* The
kernel can't know; it only measures. Deciding is the resolver's job. Keeping
**detection** and **policy** separate is the actual lesson of this step.
## Task
Two functions in `crush.ts`:
1. `resolveOverlaps(box, walls)` — the negotiation: passes until clean or
capped, returning `{x, y, settled}`.
2. `safeMoveAndSlide(box, v, walls)` — step 12's version rebuilt on top of it.
Settled → sweep as usual. Crushed → **don't feed the sweep an overlapping
box** (you know its opinion of those); the box stays where the resolver left
it and waits.
One warning on the `EPSILON` slack: apply it **only along the axis you actually
pushed**. Before you port your step-12 slack code verbatim, play computer with
`pv = { x: -3, y: 0 }` and watch what your two lines do to `y`. (That was my
"bonus" question last session — it's still open, and one of the tests refuses
to look away.)
```sh
bun test workshop/steps/13-crush
```
## Optional 1 — the airbag
Defense in depth: even if some future caller hands `moveAndSlide` an
overlapping box directly, it should return finite numbers — wrong-ish, maybe,
but *finite*. You traced in step 12 exactly which value poisons the well. The
loop already clamps it once (`Math.max(0, …)`) — find the **other** line that
trusts `nearest.time` to be non-negative. The fix is almost nothing. Then write
the test step 12 should have had: `moveAndSlide` (not `safe…`) with an
overlapping start returns finite coordinates.
## Optional 2 — the capstone payoff
Port `resolveOverlaps` into `11-capstone/game.js` and rebuild its
`safeMoveAndSlide` on it. Now let the ledge squeeze the hero against the pillar,
and against the border. Watch closely: instead of vanishing, the hero should
squirt around the ledge like a watermelon seed pinched between two fingers.
Then earn the effect: the ledge is 16 tall and the hero is 12. As the ledge digs
deeper, which of `penetrationVector`'s four escapes wins, and at what depth does
the winner change? That flip *is* the watermelon seed.
workshop/steps/13-crush/crush.test.ts
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import { expect, test } from "bun:test";
import { resolveOverlaps, safeMoveAndSlide } from "./crush.ts";
import { type AABB, aabbOverlap, vec } from "./given.ts";
// --- resolveOverlaps ---------------------------------------------------------
test("free box -> untouched, settled", () => {
const r = resolveOverlaps({ x: 0, y: 0, w: 2, h: 2 }, [
{ x: 5, y: 5, w: 2, h: 2 },
]);
expect(r.settled).toBe(true);
expect(r.x).toBe(0);
expect(r.y).toBe(0);
});
test("single overlap -> pushed out, settled", () => {
const r = resolveOverlaps({ x: 9, y: 0, w: 2, h: 2 }, [
{ x: 10, y: -5, w: 4, h: 10 },
]);
expect(r.settled).toBe(true);
expect(r.x).toBeCloseTo(8);
// the push was x-only: the axis that needed no fixing must come back
// EXACTLY untouched — not "close to" untouched
expect(r.y).toBe(0);
});
// pushed out of A (left) -> lands inside B -> a second push (downward, B is
// shallow) frees it. One pass can't see this coming; the negotiation can.
const chainA: AABB = { x: 10, y: 0, w: 4, h: 4 };
const chainB: AABB = { x: 4, y: 0, w: 4.5, h: 1.4 };
test("a push that lands you in the NEXT wall still resolves", () => {
const hero: AABB = { x: 9, y: 1, w: 2, h: 2 };
const r = resolveOverlaps(hero, [chainA, chainB]);
expect(r.settled).toBe(true);
const moved = { ...hero, x: r.x, y: r.y };
expect(aabbOverlap(moved, chainA)).toBe(false);
expect(aabbOverlap(moved, chainB)).toBe(false);
});
test("...and the answer must not depend on wall order", () => {
const hero: AABB = { x: 9, y: 1, w: 2, h: 2 };
const r = resolveOverlaps(hero, [chainB, chainA]);
expect(r.settled).toBe(true);
const moved = { ...hero, x: r.x, y: r.y };
expect(aabbOverlap(moved, chainA)).toBe(false);
expect(aabbOverlap(moved, chainB)).toBe(false);
});
// the gap between these two walls is 1.5 wide; the hero is 2 wide.
// there is NO overlap-free position — the pushes ping-pong forever.
const vice: AABB[] = [
{ x: 10, y: -5, w: 4, h: 10 },
{ x: 6.5, y: -5, w: 2, h: 10 },
];
test("gap narrower than the box -> reports the crush, stays finite", () => {
const r = resolveOverlaps({ x: 9, y: 0, w: 2, h: 2 }, vice);
expect(r.settled).toBe(false);
expect(Number.isFinite(r.x)).toBe(true);
expect(Number.isFinite(r.y)).toBe(true);
});
// --- safeMoveAndSlide --------------------------------------------------------
test("no overlap at start -> behaves exactly like moveAndSlide", () => {
// step 10's diagonal test: x blocked at 3, y keeps going
const walls: AABB[] = [{ x: 5, y: -10, w: 2, h: 40 }];
const p = safeMoveAndSlide({ x: 0, y: 0, w: 2, h: 2 }, vec(10, 10), walls);
expect(p.x).toBeCloseTo(3);
expect(p.y).toBeCloseTo(10);
});
test("resolvable overlap, then walking away -> freed and gone", () => {
const p = safeMoveAndSlide({ x: 9, y: 0, w: 2, h: 2 }, vec(-5, 0), [
{ x: 10, y: -5, w: 4, h: 10 },
]);
expect(p.x).toBeCloseTo(3);
expect(p.y).toBeCloseTo(0);
});
test("crushed with zero velocity -> a number, not a ghost", () => {
// the capstone bug: ledge pushes hero into the pillar, hero holds still
const p = safeMoveAndSlide({ x: 9, y: 0, w: 2, h: 2 }, vec(0, 0), vice);
expect(Number.isFinite(p.x)).toBe(true);
expect(Number.isFinite(p.y)).toBe(true);
// still pinched between the walls — not flung across the room
expect(p.x).toBeGreaterThan(7);
expect(p.x).toBeLessThan(9.5);
});
test("crushed and still pushing -> the walls win", () => {
const p = safeMoveAndSlide({ x: 9, y: 0, w: 2, h: 2 }, vec(5, 0), vice);
expect(Number.isFinite(p.x)).toBe(true);
expect(Number.isFinite(p.y)).toBe(true);
expect(p.x).toBeGreaterThan(7);
expect(p.x).toBeLessThan(9.5);
});
workshop/steps/13-crush/crush.ts
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import {
type AABB,
moveAndSlide,
penetrationVector,
type Vec,
} from "./given.ts";
export type Resolution = { x: number; y: number; settled: boolean };
/**
* Push `box` out of EVERY wall — even when one push shoves it into another.
*
* One pass over the walls is not enough: a push is a teleport, and a teleport
* can land you inside a wall the loop already cleared. So: run whole passes
* over the wall list, applying pushes (with the EPSILON slack — on the pushed
* axis only!), until a full pass finds nothing to fix. That pass proves you're
* settled.
*
* But some arrangements have NO free spot (a gap narrower than the box), and
* the passes would ping-pong forever. Cap them — 8 is plenty — and if the cap
* fires, report `settled: false`. You already believe in caps: your step-10
* loop has one for exactly the same reason.
*
* Returns where the box ended up and whether it truly got free.
*/
export function resolveOverlaps(box: AABB, walls: AABB[]): Resolution {
throw new Error("not implemented");
}
/**
* Step 12's safeMoveAndSlide, rebuilt on resolveOverlaps.
*
* Settled -> sweep from the safe spot, business as usual.
* Crushed (not settled) -> the sweep would be handed an overlapping box and
* you know exactly what it does with one of those. Don't feed it. Our crush
* policy: the walls win — the box stays where the resolver left it, finite,
* and waits for the gap to open.
*/
export function safeMoveAndSlide(box: AABB, v: Vec, walls: AABB[]): Vec {
throw new Error("not implemented");
}
workshop/steps/13-crush/given.ts
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// The whole kernel you've built, steps 01-10, finished. Reuse it.
export type Vec = { x: number; y: number };
export type AABB = { x: number; y: number; w: number; h: number };
export type Span = { entry: number; exit: number };
export type Hit = { time: number; normal: Vec };
/** A hair of slack so we stop just short of a wall instead of inside it. */
export const EPSILON = 1e-4;
export const vec = (x: number, y: number): Vec => ({ x, y });
export const add = (a: Vec, b: Vec): Vec => ({ x: a.x + b.x, y: a.y + b.y });
export const sub = (a: Vec, b: Vec): Vec => ({ x: a.x - b.x, y: a.y - b.y });
export const scale = (a: Vec, s: number): Vec => ({ x: a.x * s, y: a.y * s });
export const dot = (a: Vec, b: Vec): number => a.x * b.x + a.y * b.y;
/** Step 04, finished. Strict overlap — merely touching edges is false. */
export function aabbOverlap(a: AABB, b: AABB): boolean {
return (
a.x < b.x + b.w && b.x < a.x + a.w && a.y < b.y + b.h && b.y < a.y + a.h
);
}
export function sweepInterval(
p: number,
v: number,
min: number,
max: number,
): Span | null {
if (v === 0) {
return min <= p && p <= max ? { entry: -Infinity, exit: Infinity } : null;
}
let t1 = (min - p) / v;
let t2 = (max - p) / v;
if (t1 > t2) {
[t1, t2] = [t2, t1];
}
return { entry: t1, exit: t2 };
}
export function rayVsAABB(p: Vec, v: Vec, box: AABB): Hit | null {
const spanX = sweepInterval(p.x, v.x, box.x, box.x + box.w);
const spanY = sweepInterval(p.y, v.y, box.y, box.y + box.h);
if (spanX === null || spanY === null) {
return null;
}
const entry = Math.max(spanX.entry, spanY.entry);
const exit = Math.min(spanX.exit, spanY.exit);
if (entry > exit || entry >= 1 || exit <= 0) {
return null;
}
const normal =
spanX.entry > spanY.entry
? { x: v.x > 0 ? -1 : 1, y: 0 }
: { x: 0, y: v.y > 0 ? -1 : 1 };
return { time: entry, normal };
}
export function sweptAABB(a: AABB, v: Vec, b: AABB): Hit | null {
const inflated: AABB = {
x: b.x - a.w,
y: b.y - a.h,
w: b.w + a.w,
h: b.h + a.h,
};
return rayVsAABB({ x: a.x, y: a.y }, v, inflated);
}
export function slide(v: Vec, normal: Vec): Vec {
return sub(v, scale(normal, dot(v, normal)));
}
/** Step 10, finished — your loop, exactly as you wrote it. */
export function moveAndSlide(box: AABB, v: Vec, walls: AABB[]): Vec {
let pos: Vec = { x: box.x, y: box.y };
let vel: Vec = { x: v.x, y: v.y };
let timeLeft = 1;
let i = 0;
while (i++ < 4 && timeLeft > 0) {
const move = scale(vel, timeLeft);
let nearest: Hit = {
normal: { x: 0, y: 0 },
time: 2,
};
for (const wall of walls) {
const hit = sweptAABB(
{
x: pos.x,
y: pos.y,
w: box.w,
h: box.h,
},
move,
wall,
);
if (hit !== null) {
nearest = hit.time < nearest.time ? hit : nearest;
}
}
if (nearest.time === 2) {
pos = add(pos, move);
break;
} else {
pos = add(pos, scale(move, Math.max(0, nearest.time - EPSILON)));
vel = slide(vel, nearest.normal);
timeLeft = timeLeft * (1 - nearest.time);
}
}
return pos;
}
/** Step 12, finished — your penetrationVector, exactly as you wrote it. */
export function penetrationVector(a: AABB, b: AABB): Vec | null {
const outLeft = a.x + a.w - b.x;
const outRight = b.x + b.w - a.x;
const outUp = a.y + a.h - b.y;
const outDown = b.y + b.h - a.y;
const minX = Math.min(outLeft, outRight);
const minY = Math.min(outUp, outDown);
if (minX > 0 && minY > 0) {
return minX > minY
? { x: 0, y: outDown > outUp ? -minY : minY }
: { x: outLeft > outRight ? minX : -minX, y: 0 };
}
return null;
}