| 1 | import type { Tile } from '../game/tiles'; |
| 2 | import type { SeatId } from '../game/types'; |
| 3 | |
| 4 | /** |
| 5 | * The tiles in the middle of the table, as things with weight. |
| 6 | * |
| 7 | * Pure and deterministic: no DOM, no clock, no randomness. Where the world's |
| 8 | * measurements come from is `geometry.ts`; what gets thrown into it and when is |
| 9 | * `pool.ts`; drawing it is `ui/Pool.tsx`. Anything random — the scatter on a |
| 10 | * placed tile, where a rebuilt pile's tiles sit — is decided by the caller and |
| 11 | * arrives as a spawn impulse, which is what lets the same hand come back to the |
| 12 | * same pile after a refresh. |
| 13 | * |
| 14 | * Tiles are rectangles and they are solved as rectangles: two of them can lean |
| 15 | * against each other at any angle but never share the same ground. Everything is |
| 16 | * in CSS pixels, table-local, and seconds. |
| 17 | */ |
| 18 | |
| 19 | /** One fixed step. Small enough that a hard flick can't tunnel a wall. */ |
| 20 | export const FIXED_DT = 1 / 120; |
| 21 | /** |
| 22 | * Most catch-up a single frame will simulate. A tab that was in the background |
| 23 | * for a minute comes back to a settled pile, not to a spin through 7200 steps. |
| 24 | */ |
| 25 | const MAX_SUBSTEPS = 8; |
| 26 | |
| 27 | /** Falls onto the felt in about half a second from a normal throw. */ |
| 28 | const GRAVITY = 2600; |
| 29 | /** Tiles are dense and land flat; they do not bounce much. */ |
| 30 | const Z_RESTITUTION = 0.34; |
| 31 | /** Below this the tile is flat on the felt: sliding, and in the way of others. */ |
| 32 | const ON_FELT = 8; |
| 33 | /** |
| 34 | * How high a standing stack of two reaches. A tile still above this sails over |
| 35 | * the wall — which is exactly what a *placed* tile does, and what a thrown one |
| 36 | * must not need to do. |
| 37 | */ |
| 38 | export const WALL_HEIGHT = 30; |
| 39 | |
| 40 | /** |
| 41 | * Felt friction: an exponential part that kills speed, and a constant part that |
| 42 | * actually brings it to a stop rather than to an asymptote. |
| 43 | * |
| 44 | * Deliberately light. A tile thrown hard should cross the square, come off the |
| 45 | * far side and barge through what is already lying there before it settles — |
| 46 | * heavier friction ate the throw in the first few inches and every discard |
| 47 | * ended up looking the same however it was let go of. |
| 48 | */ |
| 49 | const FELT_DAMP = 2.6; |
| 50 | const FELT_STOP = 70; |
| 51 | const SPIN_DAMP = 3.4; |
| 52 | const SPIN_STOP = 0.9; |
| 53 | |
| 54 | /** |
| 55 | * Roughly how much longer a tile keeps travelling after it lands, as a time. |
| 56 | * Aiming a throw means solving for where it comes to *rest*, not where it first |
| 57 | * touches down, so `pool.ts` adds this to the flight time. |
| 58 | */ |
| 59 | export const SLIDE_TIME = 1 / FELT_DAMP; |
| 60 | |
| 61 | /** Off the inside of the wall square, and off another tile. Bouncy enough that |
| 62 | * a hard throw ricochets instead of sticking where it first lands. */ |
| 63 | const BOUND_RESTITUTION = 0.55; |
| 64 | const BOUND_FRICTION = 0.9; |
| 65 | const TILE_RESTITUTION = 0.42; |
| 66 | /** How much of a glancing blow becomes spin. Tiles are light and skate. */ |
| 67 | const SPIN_TRANSFER = 0.06; |
| 68 | |
| 69 | /** Asleep after this many consecutive steps of going nowhere. */ |
| 70 | const SLEEP_SPEED = 7; |
| 71 | const SLEEP_SPIN = 0.2; |
| 72 | const SLEEP_STEPS = 10; |
| 73 | /** |
| 74 | * Overlap small enough to live with. Without this a crowded pool never sleeps: |
| 75 | * a tile squeezed between its neighbours and the pool's edge gets pushed out of |
| 76 | * contact and shoved back into it on every step, for ever. A fifth of a pixel is |
| 77 | * not something you can see, and it is what lets the pile go quiet. |
| 78 | */ |
| 79 | const CONTACT_SLOP = 0.2; |
| 80 | /** |
| 81 | * A body moving this slowly for this long is put to sleep whatever it thinks it |
| 82 | * is doing. The backstop that guarantees the pile always settles — counted from |
| 83 | * when it last woke, not from when it was thrown. |
| 84 | */ |
| 85 | const AWAKE_LIMIT = 600; |
| 86 | |
| 87 | /** Pulls a tile that landed short of the pool in towards the rest of them. */ |
| 88 | const ENTRY_PULL = 700; |
| 89 | /** |
| 90 | * How long a tile gets to find its own way into the pool before it is simply |
| 91 | * put there. A discard is game state made visible — it has to be in the middle |
| 92 | * where it can be seen and counted — so a tile that has got itself wedged |
| 93 | * against a standing stack, or is bouncing between two of them, cannot be left |
| 94 | * out there. Two seconds is far longer than any real throw takes to settle. |
| 95 | */ |
| 96 | const ENTRY_GRACE = 240; |
| 97 | |
| 98 | /** How fast a tile drawn at hand size shrinks to the size it is in the pool. */ |
| 99 | const SCALE_EASE = 6; |
| 100 | |
| 101 | /** Washing the tiles about: how much of a finger's speed a tile takes on, how |
| 102 | * hard it is nudged clear, and the fastest shove it will pass on. */ |
| 103 | const STIR_DRAG = 0.55; |
| 104 | const STIR_NUDGE = 30; |
| 105 | const STIR_MAX_SPEED = 1500; |
| 106 | |
| 107 | export const TAU = Math.PI * 2; |
| 108 | /** |
| 109 | * How quickly whatever is left of a tumble is taken up once the tile is down. |
| 110 | * A thrown tile turns over in the air a whole number of times, so it should be |
| 111 | * face up as it lands — but a bounce or a shove can leave it part-way round, and |
| 112 | * a mahjong tile on a table is never resting on its face. This takes up the |
| 113 | * remainder, and `sleep` guarantees the rest. |
| 114 | */ |
| 115 | const FLIP_SETTLE = 14; |
| 116 | |
| 117 | export interface Rect { |
| 118 | x: number; |
| 119 | y: number; |
| 120 | w: number; |
| 121 | h: number; |
| 122 | } |
| 123 | |
| 124 | /** Anything the collision routines can treat as a rotated rectangle. */ |
| 125 | interface Box { |
| 126 | x: number; |
| 127 | y: number; |
| 128 | w: number; |
| 129 | h: number; |
| 130 | angle: number; |
| 131 | } |
| 132 | |
| 133 | export interface Body { |
| 134 | tile: Tile; |
| 135 | /** Who threw it — for the fly-out when it is claimed, not for any marking. */ |
| 136 | seat: SeatId; |
| 137 | /** Centre on the felt plane. */ |
| 138 | x: number; |
| 139 | y: number; |
| 140 | vx: number; |
| 141 | vy: number; |
| 142 | /** Height above the felt, and its rate. Only ever >= 0. */ |
| 143 | z: number; |
| 144 | vz: number; |
| 145 | angle: number; |
| 146 | spin: number; |
| 147 | /** |
| 148 | * Turning over in the air, about an axis lying in the table — what a thrown |
| 149 | * tile does, as opposed to `angle`, which is it turning flat on the cloth. |
| 150 | * Zero, or any whole number of turns, is face up. |
| 151 | */ |
| 152 | flip: number; |
| 153 | flipSpin: number; |
| 154 | /** Which way that axis points: a tile tumbles across its line of travel. */ |
| 155 | flipAxis: number; |
| 156 | w: number; |
| 157 | h: number; |
| 158 | /** |
| 159 | * Render-only: what to multiply the drawn size by, easing to 1. A tile is |
| 160 | * drawn big in a hand so it can be read, and small in the pool because that is |
| 161 | * the size it is in the wall, so a thrown one has to settle from one to the |
| 162 | * other. Eased here rather than in the renderer so it does not run at a |
| 163 | * different speed on a different frame rate. |
| 164 | */ |
| 165 | scale: number; |
| 166 | /** |
| 167 | * Whether it has ever been inside the pool. Until it has, it is free to fly |
| 168 | * over the wall from a seat's edge; once it has, the pool keeps it. |
| 169 | */ |
| 170 | entered: boolean; |
| 171 | resting: boolean; |
| 172 | /** Consecutive slow steps, counting towards sleep. */ |
| 173 | still: number; |
| 174 | /** Steps lived, for the grace period on getting into the pool. */ |
| 175 | age: number; |
| 176 | /** Steps since it last woke, for the backstop on settling. */ |
| 177 | awake: number; |
| 178 | } |
| 179 | |
| 180 | /** A collision loud enough to hear. `strength` is 0..1. */ |
| 181 | export interface Impact { |
| 182 | x: number; |
| 183 | y: number; |
| 184 | strength: number; |
| 185 | } |
| 186 | |
| 187 | export interface World { |
| 188 | /** Where tiles come to rest — inside the wall square. */ |
| 189 | bounds: Rect; |
| 190 | /** Stacks of two still standing. Half and spent stacks are not obstacles. */ |
| 191 | walls: Rect[]; |
| 192 | bodies: Body[]; |
| 193 | /** Left-over time from the last frame, so steps stay a fixed size. */ |
| 194 | carry: number; |
| 195 | /** |
| 196 | * Overlaps pushed apart in the last step. The pile is not settled while this |
| 197 | * is non-zero, however still everything looks — two tiles asleep inside each |
| 198 | * other would otherwise stay that way for the rest of the hand, because a |
| 199 | * pile that has stopped moving stops being stepped. |
| 200 | */ |
| 201 | contacts: number; |
| 202 | /** Steps spent untangling a pile that is otherwise asleep, so it cannot spin. */ |
| 203 | relaxed: number; |
| 204 | } |
| 205 | |
| 206 | export interface Spawn { |
| 207 | tile: Tile; |
| 208 | seat: SeatId; |
| 209 | x: number; |
| 210 | y: number; |
| 211 | vx: number; |
| 212 | vy: number; |
| 213 | z: number; |
| 214 | vz: number; |
| 215 | angle: number; |
| 216 | spin: number; |
| 217 | /** Whole turns to make in the air. It lands face up whatever this is. */ |
| 218 | flipTurns?: number; |
| 219 | /** Seconds of flight those turns are spread over. */ |
| 220 | flipOver?: number; |
| 221 | flipAxis?: number; |
| 222 | w: number; |
| 223 | h: number; |
| 224 | /** Drawn this much bigger to start with, easing to its pool size. */ |
| 225 | scale?: number; |
| 226 | /** Already settled — a pile being rebuilt after a reload or an undo. */ |
| 227 | atRest?: boolean; |
| 228 | } |
| 229 | |
| 230 | export function createWorld(bounds: Rect, walls: Rect[] = []): World { |
| 231 | return { bounds, walls, bodies: [], carry: 0, contacts: 0, relaxed: 0 }; |
| 232 | } |
| 233 | |
| 234 | export function addBody(world: World, s: Spawn): Body { |
| 235 | const body: Body = { |
| 236 | tile: s.tile, |
| 237 | seat: s.seat, |
| 238 | x: s.x, |
| 239 | y: s.y, |
| 240 | vx: s.atRest ? 0 : s.vx, |
| 241 | vy: s.atRest ? 0 : s.vy, |
| 242 | z: s.atRest ? 0 : s.z, |
| 243 | vz: s.atRest ? 0 : s.vz, |
| 244 | angle: s.angle, |
| 245 | spin: s.atRest ? 0 : s.spin, |
| 246 | flip: 0, |
| 247 | // Spread the turns over the flight, so the tile comes down as it comes back |
| 248 | // round to face up rather than being snapped there on landing. |
| 249 | flipSpin: |
| 250 | s.atRest || !s.flipTurns || !s.flipOver ? 0 : (TAU * s.flipTurns) / s.flipOver, |
| 251 | flipAxis: s.flipAxis ?? 0, |
| 252 | w: s.w, |
| 253 | h: s.h, |
| 254 | scale: s.atRest ? 1 : s.scale ?? 1, |
| 255 | entered: !!s.atRest, |
| 256 | resting: !!s.atRest, |
| 257 | still: s.atRest ? SLEEP_STEPS : 0, |
| 258 | age: 0, |
| 259 | awake: 0, |
| 260 | }; |
| 261 | world.bodies.push(body); |
| 262 | if (s.atRest) { |
| 263 | // A tile dropped straight into a settled pile still has to make room. This |
| 264 | // is a first shove only — the relaxing below finishes the job, which matters |
| 265 | // for a whole pile rebuilt at once when a saved game is picked up. |
| 266 | separate(world, body); |
| 267 | world.contacts++; |
| 268 | } |
| 269 | return body; |
| 270 | } |
| 271 | |
| 272 | // ---- rotated rectangles --------------------------------------------------- |
| 273 | |
| 274 | /** Distance from a box's centre to its edge, measured along `ax`. */ |
| 275 | function reach(b: Box, ax: { x: number; y: number }): number { |
| 276 | const c = Math.cos(b.angle); |
| 277 | const s = Math.sin(b.angle); |
| 278 | return ( |
| 279 | Math.abs(c * ax.x + s * ax.y) * (b.w / 2) + Math.abs(-s * ax.x + c * ax.y) * (b.h / 2) |
| 280 | ); |
| 281 | } |
| 282 | |
| 283 | /** The rotated rectangle's own bounding box, for the pool's straight edges. */ |
| 284 | function aabbHalf(b: Box) { |
| 285 | const c = Math.abs(Math.cos(b.angle)); |
| 286 | const s = Math.abs(Math.sin(b.angle)); |
| 287 | return { x: (b.w / 2) * c + (b.h / 2) * s, y: (b.w / 2) * s + (b.h / 2) * c }; |
| 288 | } |
| 289 | |
| 290 | /** Enough to skip a pair without doing the real work. */ |
| 291 | const circumradius = (b: Box) => Math.hypot(b.w, b.h) / 2; |
| 292 | |
| 293 | /** |
| 294 | * Separating axis test between two rectangles at any angle. Returns the |
| 295 | * shallowest way out — the direction to push `b` away from `a`, and by how much |
| 296 | * — or null if they are clear of each other. |
| 297 | * |
| 298 | * Four axes is all a pair of rectangles needs: each box's two edge normals. |
| 299 | */ |
| 300 | function overlapOf(a: Box, b: Box): { nx: number; ny: number; depth: number } | null { |
| 301 | const ca = Math.cos(a.angle); |
| 302 | const sa = Math.sin(a.angle); |
| 303 | const cb = Math.cos(b.angle); |
| 304 | const sb = Math.sin(b.angle); |
| 305 | const axes = [ |
| 306 | { x: ca, y: sa }, |
| 307 | { x: -sa, y: ca }, |
| 308 | { x: cb, y: sb }, |
| 309 | { x: -sb, y: cb }, |
| 310 | ]; |
| 311 | |
| 312 | const dx = b.x - a.x; |
| 313 | const dy = b.y - a.y; |
| 314 | let depth = Infinity; |
| 315 | let nx = 0; |
| 316 | let ny = 0; |
| 317 | |
| 318 | for (const ax of axes) { |
| 319 | const gap = reach(a, ax) + reach(b, ax) - Math.abs(dx * ax.x + dy * ax.y); |
| 320 | if (gap <= 0) return null; |
| 321 | if (gap < depth) { |
| 322 | depth = gap; |
| 323 | // Always pointing from a towards b, so callers need not guess. |
| 324 | const sign = dx * ax.x + dy * ax.y < 0 ? -1 : 1; |
| 325 | nx = ax.x * sign; |
| 326 | ny = ax.y * sign; |
| 327 | } |
| 328 | } |
| 329 | return { nx, ny, depth }; |
| 330 | } |
| 331 | |
| 332 | /** A standing stack, as something the tests above can chew on. */ |
| 333 | const boxOf = (r: Rect): Box => ({ |
| 334 | x: r.x + r.w / 2, |
| 335 | y: r.y + r.h / 2, |
| 336 | w: r.w, |
| 337 | h: r.h, |
| 338 | angle: 0, |
| 339 | }); |
| 340 | |
| 341 | // ---- stepping ------------------------------------------------------------- |
| 342 | |
| 343 | const inside = (r: Rect, x: number, y: number) => |
| 344 | x >= r.x && x <= r.x + r.w && y >= r.y && y <= r.y + r.h; |
| 345 | |
| 346 | /** |
| 347 | * Run the world forward. `elapsed` is real seconds since the last call; it is |
| 348 | * consumed in fixed steps so the result does not depend on the frame rate. |
| 349 | * Returns the impacts worth a sound. |
| 350 | */ |
| 351 | export function advance(world: World, elapsed: number): Impact[] { |
| 352 | world.carry += Math.max(0, elapsed); |
| 353 | let steps = Math.floor(world.carry / FIXED_DT); |
| 354 | if (steps > MAX_SUBSTEPS) { |
| 355 | // Drop the backlog rather than working through it. |
| 356 | world.carry = 0; |
| 357 | steps = MAX_SUBSTEPS; |
| 358 | } else { |
| 359 | world.carry -= steps * FIXED_DT; |
| 360 | } |
| 361 | |
| 362 | const impacts: Impact[] = []; |
| 363 | for (let i = 0; i < steps; i++) step(world, impacts); |
| 364 | return impacts; |
| 365 | } |
| 366 | |
| 367 | /** One fixed step. Exported for the tests, which drive it directly. */ |
| 368 | export function step(world: World, impacts: Impact[] = []): Impact[] { |
| 369 | const dt = FIXED_DT; |
| 370 | world.contacts = 0; |
| 371 | |
| 372 | for (const b of world.bodies) { |
| 373 | if (b.scale !== 1) { |
| 374 | b.scale += (1 - b.scale) * Math.min(1, SCALE_EASE * dt); |
| 375 | if (Math.abs(b.scale - 1) < 0.002) b.scale = 1; |
| 376 | } |
| 377 | if (b.resting) continue; |
| 378 | b.age++; |
| 379 | b.awake++; |
| 380 | |
| 381 | // --- through the air --- |
| 382 | if (b.z > 0 || b.vz !== 0) { |
| 383 | b.vz -= GRAVITY * dt; |
| 384 | b.z += b.vz * dt; |
| 385 | if (b.z <= 0) { |
| 386 | const landing = Math.abs(b.vz); |
| 387 | b.z = 0; |
| 388 | // Below a knock it stops dead rather than shivering out a bounce. |
| 389 | b.vz = landing > 40 ? landing * Z_RESTITUTION : 0; |
| 390 | const strength = Math.min(1, landing / 900); |
| 391 | if (strength > 0.12) impacts.push({ x: b.x, y: b.y, strength }); |
| 392 | } |
| 393 | } |
| 394 | |
| 395 | b.x += b.vx * dt; |
| 396 | b.y += b.vy * dt; |
| 397 | b.angle += b.spin * dt; |
| 398 | |
| 399 | // Turning over. In the air it tumbles; once it is down, whatever is left of |
| 400 | // the turn is taken up so it ends flat on its back with its face showing. |
| 401 | if (b.flipSpin !== 0) { |
| 402 | if (b.z > 0) { |
| 403 | b.flip += b.flipSpin * dt; |
| 404 | } else { |
| 405 | const target = Math.round(b.flip / TAU) * TAU; |
| 406 | b.flip += (target - b.flip) * Math.min(1, FLIP_SETTLE * dt); |
| 407 | if (Math.abs(target - b.flip) < 0.01) { |
| 408 | b.flip = target; |
| 409 | b.flipSpin = 0; |
| 410 | } |
| 411 | } |
| 412 | } |
| 413 | |
| 414 | if (inside(world.bounds, b.x, b.y)) b.entered = true; |
| 415 | else if (b.age > ENTRY_GRACE) { |
| 416 | // Out of time going the long way round. Put it in, gently. |
| 417 | b.entered = true; |
| 418 | b.z = 0; |
| 419 | b.vz = 0; |
| 420 | clampInto(world.bounds, b); |
| 421 | } |
| 422 | |
| 423 | // --- on the felt --- |
| 424 | // Strictly z <= 0, not ON_FELT: friction is between the tile and the cloth, |
| 425 | // so a tile still in the air keeps the speed it was thrown with. ON_FELT is |
| 426 | // only about being low enough to be in another tile's way. |
| 427 | if (b.z <= 0) { |
| 428 | damp(b, dt); |
| 429 | // A tile that fell short skids in rather than sitting outside the pool. |
| 430 | if (!b.entered) pullIn(world, b, dt); |
| 431 | } |
| 432 | |
| 433 | // A tile still above the wall is clear of it. |
| 434 | if (b.z < WALL_HEIGHT) { |
| 435 | for (const wall of world.walls) hitWall(b, wall, impacts); |
| 436 | } |
| 437 | |
| 438 | // The pool's edge is the inside face of the wall, and it is only as tall as |
| 439 | // the wall — a tile lobbed high is over the top of it, not stopped by it. |
| 440 | if (b.entered && b.z < WALL_HEIGHT) keepInBounds(world, b, impacts); |
| 441 | } |
| 442 | |
| 443 | collideTiles(world, impacts); |
| 444 | // Being shoved by a neighbour can put a tile back over the edge, and a tile |
| 445 | // that then fell asleep out there would stay out there. Only awake ones need |
| 446 | // it: resolvePair never moves a tile that has settled. |
| 447 | // Resting tiles included: they get pushed about by the untangling above, and |
| 448 | // a tile shoved over the edge must not be left there just because it is asleep. |
| 449 | for (const b of world.bodies) { |
| 450 | if (b.entered && b.z < WALL_HEIGHT) clampInto(world.bounds, b); |
| 451 | } |
| 452 | // Deciding to sleep comes last, so it judges where the step actually left |
| 453 | // things — before, a contact resolved after the decision would undo it and a |
| 454 | // crowded pool would stay awake for ever. |
| 455 | for (const b of world.bodies) if (!b.resting) trySleep(b); |
| 456 | |
| 457 | // A pile that has stopped moving but is still untangling itself keeps being |
| 458 | // stepped, up to a point. Without the limit a configuration that cannot quite |
| 459 | // be resolved would keep the loop running for the rest of the hand. |
| 460 | world.relaxed = world.contacts > 0 && world.bodies.every((b) => b.resting) ? world.relaxed + 1 : 0; |
| 461 | return impacts; |
| 462 | } |
| 463 | |
| 464 | /** |
| 465 | * The table has been re-measured — the window resized, or the wall was eaten |
| 466 | * further back. The tiles keep where they are, but a pool that shrank must not |
| 467 | * leave any of them stranded outside it, and the ones it moves have to wake up |
| 468 | * so they can settle again. |
| 469 | */ |
| 470 | export function reshape(world: World, bounds: Rect, walls: Rect[]) { |
| 471 | world.bounds = bounds; |
| 472 | world.walls = walls; |
| 473 | for (const b of world.bodies) { |
| 474 | if (!b.entered) continue; |
| 475 | const x = b.x; |
| 476 | const y = b.y; |
| 477 | clampInto(bounds, b); |
| 478 | if (b.x !== x || b.y !== y) wake(b); |
| 479 | } |
| 480 | } |
| 481 | |
| 482 | function damp(b: Body, dt: number) { |
| 483 | const k = Math.exp(-FELT_DAMP * dt); |
| 484 | b.vx *= k; |
| 485 | b.vy *= k; |
| 486 | b.spin *= Math.exp(-SPIN_DAMP * dt); |
| 487 | |
| 488 | const speed = Math.hypot(b.vx, b.vy); |
| 489 | if (speed > 0) { |
| 490 | const next = Math.max(0, speed - FELT_STOP * dt); |
| 491 | b.vx = (b.vx / speed) * next; |
| 492 | b.vy = (b.vy / speed) * next; |
| 493 | } |
| 494 | const spin = Math.abs(b.spin); |
| 495 | if (spin > 0) b.spin = Math.sign(b.spin) * Math.max(0, spin - SPIN_STOP * dt); |
| 496 | } |
| 497 | |
| 498 | /** Nudges a tile that landed outside the pool towards the rest of them. */ |
| 499 | function pullIn(world: World, b: Body, dt: number) { |
| 500 | const cx = world.bounds.x + world.bounds.w / 2; |
| 501 | const cy = world.bounds.y + world.bounds.h / 2; |
| 502 | const dx = cx - b.x; |
| 503 | const dy = cy - b.y; |
| 504 | const d = Math.hypot(dx, dy) || 1; |
| 505 | b.vx += (dx / d) * ENTRY_PULL * dt; |
| 506 | b.vy += (dy / d) * ENTRY_PULL * dt; |
| 507 | } |
| 508 | |
| 509 | /** Bounce off a standing stack, corner to corner if that is how it hits. */ |
| 510 | function hitWall(b: Body, wall: Rect, impacts: Impact[]) { |
| 511 | const hit = overlapOf(boxOf(wall), b); |
| 512 | if (!hit || hit.depth <= CONTACT_SLOP) return; |
| 513 | |
| 514 | const speed = Math.hypot(b.vx, b.vy); |
| 515 | b.x += hit.nx * hit.depth; |
| 516 | b.y += hit.ny * hit.depth; |
| 517 | // Reflect whatever was heading into the wall; keep what was sliding along it. |
| 518 | const into = b.vx * hit.nx + b.vy * hit.ny; |
| 519 | if (into < 0) { |
| 520 | b.vx -= hit.nx * into * (1 + BOUND_RESTITUTION); |
| 521 | b.vy -= hit.ny * into * (1 + BOUND_RESTITUTION); |
| 522 | } |
| 523 | b.spin *= 0.7; |
| 524 | b.resting = false; |
| 525 | b.still = 0; |
| 526 | const strength = Math.min(1, speed / 1100); |
| 527 | if (strength > 0.12) impacts.push({ x: b.x, y: b.y, strength }); |
| 528 | } |
| 529 | |
| 530 | /** The pool's edge. Once a tile is in, it stays in — this is the invariant the |
| 531 | * tests pin, since a discard that slid off the table would be lost. */ |
| 532 | function keepInBounds(world: World, b: Body, impacts: Impact[]) { |
| 533 | const half = aabbHalf(b); |
| 534 | const { x, y, w, h } = world.bounds; |
| 535 | // A pool narrower than a tile would otherwise fight itself; centre instead. |
| 536 | const minX = w <= half.x * 2 ? x + w / 2 : x + half.x; |
| 537 | const maxX = w <= half.x * 2 ? x + w / 2 : x + w - half.x; |
| 538 | const minY = h <= half.y * 2 ? y + h / 2 : y + half.y; |
| 539 | const maxY = h <= half.y * 2 ? y + h / 2 : y + h - half.y; |
| 540 | |
| 541 | let hit = 0; |
| 542 | if (b.x < minX) { |
| 543 | b.x = minX; |
| 544 | hit = Math.max(hit, Math.abs(b.vx)); |
| 545 | b.vx = Math.abs(b.vx) * BOUND_RESTITUTION; |
| 546 | b.vy *= BOUND_FRICTION; |
| 547 | } else if (b.x > maxX) { |
| 548 | b.x = maxX; |
| 549 | hit = Math.max(hit, Math.abs(b.vx)); |
| 550 | b.vx = -Math.abs(b.vx) * BOUND_RESTITUTION; |
| 551 | b.vy *= BOUND_FRICTION; |
| 552 | } |
| 553 | if (b.y < minY) { |
| 554 | b.y = minY; |
| 555 | hit = Math.max(hit, Math.abs(b.vy)); |
| 556 | b.vy = Math.abs(b.vy) * BOUND_RESTITUTION; |
| 557 | b.vx *= BOUND_FRICTION; |
| 558 | } else if (b.y > maxY) { |
| 559 | b.y = maxY; |
| 560 | hit = Math.max(hit, Math.abs(b.vy)); |
| 561 | b.vy = -Math.abs(b.vy) * BOUND_RESTITUTION; |
| 562 | b.vx *= BOUND_FRICTION; |
| 563 | } |
| 564 | // Only a real knock counts as being disturbed. A tile held against the edge |
| 565 | // by its neighbours is clamped every single step, and treating that as a knock |
| 566 | // would keep the whole pool awake for ever. |
| 567 | if (hit > SLEEP_SPEED) { |
| 568 | b.still = 0; |
| 569 | const strength = Math.min(1, hit / 1100); |
| 570 | if (strength > 0.12) impacts.push({ x: b.x, y: b.y, strength }); |
| 571 | } |
| 572 | } |
| 573 | |
| 574 | /** |
| 575 | * Tile against tile. |
| 576 | * |
| 577 | * Only tiles flat on the felt take part, so a thrown tile passes over the pile |
| 578 | * instead of shouldering through it, and a cheap circle test throws out the pairs |
| 579 | * that are nowhere near before the real rectangle test runs. Pairs where both |
| 580 | * tiles have settled are left alone entirely, which is nearly all of them. |
| 581 | */ |
| 582 | function collideTiles(world: World, impacts: Impact[]) { |
| 583 | const bodies = world.bodies; |
| 584 | for (let i = 0; i < bodies.length; i++) { |
| 585 | const a = bodies[i]; |
| 586 | if (a.z > ON_FELT) continue; |
| 587 | for (let j = i + 1; j < bodies.length; j++) { |
| 588 | const b = bodies[j]; |
| 589 | if (b.z > ON_FELT) continue; |
| 590 | if (Math.hypot(b.x - a.x, b.y - a.y) > circumradius(a) + circumradius(b)) continue; |
| 591 | // Two tiles that have both settled are still pushed apart if they are |
| 592 | // inside each other — they are just not woken up for it. Skipping the pair |
| 593 | // outright was how a pile could end up with tiles sharing ground and stay |
| 594 | // that way, since nothing steps a pile that has stopped moving. |
| 595 | resolvePair(a, b, impacts, world); |
| 596 | } |
| 597 | } |
| 598 | } |
| 599 | |
| 600 | function resolvePair(a: Body, b: Body, impacts: Impact[], world: World) { |
| 601 | const hit = overlapOf(a, b); |
| 602 | if (!hit) return; |
| 603 | // Resting in contact is not a collision. See CONTACT_SLOP. |
| 604 | const depth = hit.depth - CONTACT_SLOP; |
| 605 | if (depth <= 0) return; |
| 606 | const { nx, ny } = hit; |
| 607 | |
| 608 | world.contacts++; |
| 609 | // Push apart. A tile that has settled is the heavy one: a tile thrown into a |
| 610 | // pool shoulders in, rather than the pool scattering out of its way. |
| 611 | const aShare = a.resting === b.resting ? 0.5 : a.resting ? 0 : 1; |
| 612 | const bShare = 1 - aShare; |
| 613 | a.x -= nx * depth * aShare; |
| 614 | a.y -= ny * depth * aShare; |
| 615 | b.x += nx * depth * bShare; |
| 616 | b.y += ny * depth * bShare; |
| 617 | |
| 618 | // Impulse along the way out, plus a spin kick off what is left over. |
| 619 | // |
| 620 | // Only a genuine approach speed counts, and only that wakes anything. Nudging |
| 621 | // two touching tiles apart is not a collision: a jammed corner of the pool is |
| 622 | // corrected by a fraction of a pixel every step for as long as it is jammed, |
| 623 | // and treating each of those as a shove would keep the pile awake for ever. |
| 624 | const rvx = b.vx - a.vx; |
| 625 | const rvy = b.vy - a.vy; |
| 626 | const along = rvx * nx + rvy * ny; |
| 627 | if (along >= -SLEEP_SPEED) return; |
| 628 | |
| 629 | const jolt = -along * (1 + TILE_RESTITUTION) * 0.5; |
| 630 | a.vx -= nx * jolt; |
| 631 | a.vy -= ny * jolt; |
| 632 | b.vx += nx * jolt; |
| 633 | b.vy += ny * jolt; |
| 634 | |
| 635 | const tangent = rvx * -ny + rvy * nx; |
| 636 | a.spin -= tangent * SPIN_TRANSFER * 0.06; |
| 637 | b.spin += tangent * SPIN_TRANSFER * 0.06; |
| 638 | |
| 639 | const strength = Math.min(1, Math.abs(along) / 900); |
| 640 | if (strength > 0.12) impacts.push({ x: b.x, y: b.y, strength }); |
| 641 | |
| 642 | // Whatever was asleep has been shoved, so it is awake now. |
| 643 | wake(a); |
| 644 | wake(b); |
| 645 | } |
| 646 | |
| 647 | function wake(b: Body) { |
| 648 | if (b.resting) b.awake = 0; |
| 649 | b.resting = false; |
| 650 | b.still = 0; |
| 651 | } |
| 652 | |
| 653 | function sleep(b: Body) { |
| 654 | b.vx = 0; |
| 655 | b.vy = 0; |
| 656 | b.spin = 0; |
| 657 | b.z = 0; |
| 658 | b.vz = 0; |
| 659 | // Face up, always. A tile lying face down in the discards would be a tile |
| 660 | // nobody can read, so this is a guarantee and not an easing. |
| 661 | b.flip = Math.round(b.flip / TAU) * TAU; |
| 662 | b.flipSpin = 0; |
| 663 | b.resting = true; |
| 664 | b.awake = 0; |
| 665 | } |
| 666 | |
| 667 | function trySleep(b: Body) { |
| 668 | const speed = Math.hypot(b.vx, b.vy); |
| 669 | const slow = |
| 670 | b.entered && |
| 671 | b.z <= 0 && |
| 672 | b.vz === 0 && |
| 673 | b.flipSpin === 0 && |
| 674 | speed < SLEEP_SPEED && |
| 675 | Math.abs(b.spin) < SLEEP_SPIN; |
| 676 | if (slow && ++b.still >= SLEEP_STEPS) return sleep(b); |
| 677 | if (!slow) b.still = 0; |
| 678 | // Backstop: shuffling about in a crowded pool for this long is settled enough. |
| 679 | if (b.entered && b.awake > AWAKE_LIMIT && speed < SLEEP_SPEED * 4) sleep(b); |
| 680 | } |
| 681 | |
| 682 | /** |
| 683 | * Make room for a tile placed straight into a settled pile, without running |
| 684 | * time. Used when a pile is rebuilt — a reload, an undo — where the tiles have |
| 685 | * to be somewhere sensible immediately and nothing should appear to move. |
| 686 | */ |
| 687 | function separate(world: World, body: Body, passes = 16) { |
| 688 | // Which way to go when two tiles are exactly on top of each other. Stepping |
| 689 | // by the golden angle fans successive tiles out in every direction, where a |
| 690 | // fixed axis would march them all one way and pack them against a pool edge. |
| 691 | const escape = world.bodies.indexOf(body) * 2.39996; |
| 692 | |
| 693 | for (let p = 0; p < passes; p++) { |
| 694 | let moved = false; |
| 695 | for (const other of world.bodies) { |
| 696 | if (other === body) continue; |
| 697 | const hit = overlapOf(other, body); |
| 698 | if (!hit || hit.depth <= CONTACT_SLOP) continue; |
| 699 | if (Math.hypot(body.x - other.x, body.y - other.y) < 0.0001) { |
| 700 | body.x += Math.cos(escape + p) * hit.depth; |
| 701 | body.y += Math.sin(escape + p) * hit.depth; |
| 702 | } else { |
| 703 | body.x += hit.nx * hit.depth; |
| 704 | body.y += hit.ny * hit.depth; |
| 705 | } |
| 706 | moved = true; |
| 707 | } |
| 708 | clampInto(world.bounds, body); |
| 709 | if (!moved) break; |
| 710 | } |
| 711 | } |
| 712 | |
| 713 | function clampInto(r: Rect, b: Body) { |
| 714 | const half = aabbHalf(b); |
| 715 | const minX = r.w <= half.x * 2 ? r.x + r.w / 2 : r.x + half.x; |
| 716 | const maxX = r.w <= half.x * 2 ? r.x + r.w / 2 : r.x + r.w - half.x; |
| 717 | const minY = r.h <= half.y * 2 ? r.y + r.h / 2 : r.y + half.y; |
| 718 | const maxY = r.h <= half.y * 2 ? r.y + r.h / 2 : r.y + r.h - half.y; |
| 719 | b.x = Math.min(maxX, Math.max(minX, b.x)); |
| 720 | b.y = Math.min(maxY, Math.max(minY, b.y)); |
| 721 | } |
| 722 | |
| 723 | /** |
| 724 | * How long a motionless pile is allowed to keep untangling itself before the |
| 725 | * result is accepted as good enough. Anything still overlapping after this is |
| 726 | * doing so by a fraction of a pixel, and the loop has better things to do than |
| 727 | * keep running over it. |
| 728 | */ |
| 729 | const RELAX_LIMIT = 90; |
| 730 | |
| 731 | /** Whether everything has settled — what the render loop idles on. */ |
| 732 | export const settled = (world: World) => |
| 733 | world.bodies.every((b) => b.resting && b.scale === 1) && |
| 734 | (world.contacts === 0 || world.relaxed > RELAX_LIMIT); |
| 735 | |
| 736 | /** How square-on the face is: 1 flat on its back, 0 edge-on, negative face down. |
| 737 | * The renderer squashes the tile by this along its tumbling axis. */ |
| 738 | export const faceOn = (b: Body) => Math.cos(b.flip); |
| 739 | |
| 740 | /** How far outside the pool a tile is sitting. The tests' invariant. */ |
| 741 | export function outside(b: Body, pool: Rect): number { |
| 742 | const half = aabbHalf(b); |
| 743 | return Math.max( |
| 744 | 0, |
| 745 | pool.x + half.x - b.x, |
| 746 | b.x - (pool.x + pool.w - half.x), |
| 747 | pool.y + half.y - b.y, |
| 748 | b.y - (pool.y + pool.h - half.y), |
| 749 | ); |
| 750 | } |
| 751 | |
| 752 | /** |
| 753 | * A finger, or a cursor, pushing the tiles about in the middle — 洗牌, the thing |
| 754 | * everybody does to a pool of discards while waiting for their turn. |
| 755 | * |
| 756 | * Modelled as a circle that simply cannot be inside a tile: anything it touches |
| 757 | * is shoved clear of it and handed some of the speed it was moving at. It has no |
| 758 | * mass and takes no impulse back, which is what a finger on a table is. |
| 759 | */ |
| 760 | export function stir( |
| 761 | world: World, |
| 762 | x: number, |
| 763 | y: number, |
| 764 | vx: number, |
| 765 | vy: number, |
| 766 | radius: number, |
| 767 | ) { |
| 768 | // A frantic swipe should not fire tiles off like bullets. |
| 769 | const speed = Math.hypot(vx, vy); |
| 770 | const trim = speed > STIR_MAX_SPEED ? STIR_MAX_SPEED / speed : 1; |
| 771 | |
| 772 | for (const b of world.bodies) { |
| 773 | if (b.z > ON_FELT) continue; |
| 774 | const dx = b.x - x; |
| 775 | const dy = b.y - y; |
| 776 | const clear = radius + circumradius(b); |
| 777 | const d = Math.hypot(dx, dy); |
| 778 | if (d > clear) continue; |
| 779 | |
| 780 | const nx = d < 0.001 ? 1 : dx / d; |
| 781 | const ny = d < 0.001 ? 0 : dy / d; |
| 782 | b.x = x + nx * clear; |
| 783 | b.y = y + ny * clear; |
| 784 | b.vx += vx * trim * STIR_DRAG + nx * STIR_NUDGE; |
| 785 | b.vy += vy * trim * STIR_DRAG + ny * STIR_NUDGE; |
| 786 | // Dragged past off-centre, a tile turns under your finger. |
| 787 | b.spin += (vx * trim * ny - vy * trim * nx) * 0.0016; |
| 788 | wake(b); |
| 789 | } |
| 790 | } |
| 791 | |
| 792 | /** Whether two tiles are sharing ground, which they must never do at rest. */ |
| 793 | export function overlapping(a: Body, b: Body): number { |
| 794 | const hit = overlapOf(a, b); |
| 795 | return hit ? hit.depth : 0; |
| 796 | } |
| 797 | |
| 798 | /** Scale a tile is drawn at, given how high it is. Sells the arc on a flat |
| 799 | * canvas; the renderer offsets the shadow by the same height. */ |
| 800 | export const zScale = (z: number) => 1 + z * 0.0016; |
| 801 | |
| 802 | /** |
| 803 | * The upward kick that puts a tile back on the felt after `seconds` in the air. |
| 804 | * How a throw is aimed: pick how long it should take, and the horizontal speed |
| 805 | * follows from the distance. |
| 806 | */ |
| 807 | export const liftFor = (seconds: number) => (GRAVITY * seconds) / 2; |
| 808 | |
| 809 | /** How high that kick gets — worth checking against WALL_HEIGHT. */ |
| 810 | export const peakOf = (vz: number) => (vz * vz) / (2 * GRAVITY); |