import { isHandleEnabled, worldMatrixOf } from '../../core/graph';
import { applyVector, determinant, IDENTITY, invert, linearOf, type Mat } from '../../core/model/matrix';
import type { Vec2 } from '../../core/model/Properties';
import { dot } from '../../core/util/vec';
import { findAssetOf } from '../../core/model/Project';
import { liveTilemap, type TileEdits } from '../../core/model/liveTilemap';
import { identityToken } from '../../core/model/tilemapMemo';
import {
  type CellPolygon,
  cellPolygonShape,
  type CellRect,
  cellRectShape,
  cellsMeet,
  cellsWithin,
  oneWayAngles,
  solidPolygons,
  solidRects,
  type TileMaterial,
  tileMaterials,
} from '../../core/model/tilemapCollision';
import { parentChain } from '../../core/model/walk';
import {
  type CollisionFilter,
  collisionFilterOf,
  layersMeet,
  maskHas,
} from '../../core/model/collisionLayers';
import {
  boundsMeet,
  type ColliderShape,
  colliderShape,
  contactBetween,
  exitDistance,
  grownBounds,
  isTrigger,
  landsOn,
  movedShape,
  oneWayCone,
  oneWayFacing,
  type OneWaySide,
  overlapDepth,
  shapeBounds,
  type ShapeBounds,
  shapeExtent,
  shapesOverlap,
} from '../../core/properties/collider';
import { rayCast } from '../../core/properties/ray';
import { colliderMaterial } from '../../core/properties/rigidbody';
import type { Entity } from '../Entity';
import type { World } from '../World';

/** Upper bound for the sub-steps of a single sweep, so a huge delta cannot stall a frame. */
const MAX_STEPS = 256;
/** A move is swept this many times at most: into a contact, along it, into the next one, and on. */
const MAX_PASSES = 4;
/** Deepening an overlap by no more than this is rounding, not moving in. */
const DEEPER = 1e-9;
/** A normal this close to square with an axis does not stand against a move along it. */
const SQUARE = 1e-6;
/** What the broad phase adds to the reach of a move, so rounding never drops a shape (#184). */
const REACH_SLACK = 1e-6;

/**
 * Two bodies that overlap (or overlapped) – always the same pair order per key. Either side is a
 * collider or a placed tilemap, which takes part as a whole with its solid cells (#132).
 * `normal` points from `b` towards `a`, `impulse` is how hard they met and `point` where; they are
 * only known where the physics engine saw the contact begin (#146), and zero elsewhere.
 */
export interface CollisionPair {
  a: Entity;
  b: Entity;
  normal?: Vec2;
  impulse?: number;
  point?: Vec2;
  /** Set where `b` is a map and `a` overlaps a trigger tile of it (#160) – a pair of its own, next to the map's. */
  tile?: TileContact;
}

/**
 * Which trigger tile of a map a collider overlaps (#160). A pair stands either for one cell or for a
 * whole area of the tile; an area names the cell of it nearest to the collider.
 */
export interface TileContact {
  tileId: string;
  cell: { x: number; y: number };
  area: string;
  perCell: boolean;
}

/** What a pair is known by from one tick to the next. */
export function pairKey({ a, b, tile }: CollisionPair): string {
  const key = `${a.id}|${b.id}`;
  if (!tile) return key;
  return `${key}|${tile.tileId}|${tile.perCell ? `cell ${tile.cell.x},${tile.cell.y}` : `area ${tile.area}`}`;
}

/**
 * What a move ran into: the collider or tilemap in the way, the world direction into it (against
 * the contact normal), and how far the whole move wanted to go that way (world units).
 */
export interface Blocked {
  by: Entity;
  along: Vec2;
  distance: number;
}

/**
 * What `Move` with "Collide with solids" reports: which of the object's own axes something stood
 * against, whether it hit anything, and the normal of the first contact (world, pointing away from
 * what was hit; zero without a hit).
 */
export interface MoveResult {
  blockedX: boolean;
  blockedY: boolean;
  hit: boolean;
  normal: Vec2;
}

export const NOT_BLOCKED: MoveResult = Object.freeze({
  blockedX: false,
  blockedY: false,
  hit: false,
  normal: Object.freeze({ x: 0, y: 0 }),
});

/**
 * A shape of a collider or tilemap, and for a one-way one the world direction it blocks from (#155):
 * only a contact whose normal lies within its angle of it stops anything (#159).
 */
export interface SolidShape {
  shape: ColliderShape;
  facing: OneWaySide | null;
  /** A tilemap cell's surface (#193); a collider's is read off its own props (see `surfaceOf`). */
  surface?: TileMaterial;
}

/** A shape in the mover's way and the collider or tilemap it belongs to. */
interface Obstacle extends SolidShape {
  body: Entity;
  /** Which layers it is on and meets (#152) – the same for every shape of one tilemap. */
  filter: CollisionFilter;
}

/** One of the mover's own colliders, with the layers it may meet. */
interface Mover {
  collider: Entity;
  filter: CollisionFilter;
}

/** What a ray met (#153): the collider or tilemap, where, the face's normal and how far along the ray. */
export interface RayResult {
  collider: Entity;
  point: Vec2;
  normal: Vec2;
  distance: number;
}

/**
 * Which colliders a ray looks at: all but those of `ignore` and below it, triggers only when asked,
 * and only what sits on a layer of `layers` (#158). That last one is one-sided on purpose – a ray is
 * not a collider, so the collider's own "Collides with" has no say over who may look at it.
 */
export interface RayFilter {
  ignore: Entity | null;
  triggers: boolean;
  layers: number;
}

/** Where a sweep stopped: what it met, with which own collider, the normal, and the move left over. */
interface SweepContact {
  by: Entity;
  /** The surface of the shape met when it is a tile's (#193). */
  surface?: TileMaterial;
  own: Entity;
  normal: Vec2;
  left: Vec2;
}

/** What the behaviors read of collisions, whichever system works them out. */
export interface CollisionSource {
  readonly enters: CollisionPair[];
  readonly stays: CollisionPair[];
  readonly exits: CollisionPair[];
  touching(world: World, a: Entity, b: Entity): boolean;
  moveAndSlide(world: World, entity: Entity, dx: number, dy: number): MoveResult;
  raycast(world: World, from: Vec2, direction: Vec2, length: number, filter: RayFilter): RayResult | null;
  /** Every solid on the line, nearest first; `maxHits` above 0 keeps that many of them (#157). */
  raycastAll(
    world: World,
    from: Vec2,
    direction: Vec2,
    length: number,
    filter: RayFilter,
    maxHits?: number,
  ): RayResult[];
  /**
   * How a pair that stays in contact touches right now (#149): the normal from `b` towards `a`, the
   * impulse of the last physics step and the middle of the contact points; null where nothing
   * simulates the contact (the editor run).
   */
  contactOf(pair: CollisionPair): Contact | null;
}

/** A contact as the physics engine knows it (see `CollisionSource.contactOf`). */
export interface Contact {
  normal: Vec2;
  impulse: number;
  point: Vec2;
}

/**
 * The world as `Move` with "Collide with solids" sees it: the shapes of every collider and every
 * placed tilemap, and the move that stops at them and slides along.
 */
export class Solids {
  /**
   * The blocking rectangles and outlined cells of each tilemap, in cells. Worked out once per tick –
   * painting is picked up by the next one, a behavior's `Set tile` at once – and turned into world
   * shapes only when asked, since the map may move in between.
   */
  private blocks = new Map<Entity, { edits: TileEdits | undefined; blocks: TilemapBlocks }>();

  /** Forgets the cells, so the next tick works them out afresh. */
  reset(): void {
    this.blocks = new Map();
  }

  private blocksOf(world: World, tilemap: Entity): TilemapBlocks {
    let held = this.blocks.get(tilemap);
    // A `Set tile` replaces the edits, so a move later in the same tick already meets the new cell.
    if (!held || held.edits !== tilemap.tileEdits) {
      const stored = findAssetOf(world.project, tilemap.assetId, 'tilemap');
      const asset = stored && liveTilemap(stored, tilemap.tileEdits);
      const { project } = world;
      const { props } = tilemap;
      // One group per side and surface, so cells only merge with cells that block alike (#159, #193).
      const groups = (angle: number | null) =>
        tileMaterials(project, asset!, angle ?? false).map((material) => ({
          angle,
          material,
          rects: solidRects(project, props, asset!, angle ?? false, material),
          polygons: solidPolygons(project, props, asset!, angle ?? false, material),
        }));
      const blocks = asset ? [...groups(null), ...oneWayAngles(project, asset).flatMap(groups)] : [];
      held = { edits: tilemap.tileEdits, blocks };
      this.blocks.set(tilemap, held);
    }
    return held.blocks;
  }

  /**
   * Stands for the map's blocking cells: the same as long as they are, since the same cells hand out
   * the very same rectangles and polygons (`tilemapCollision.ts`).
   */
  blocksToken(world: World, tilemap: Entity): string {
    return this.blocksOf(world, tilemap)
      .map(({ angle, material, rects, polygons }) =>
        [angle, material.friction, material.bounciness, identityToken(rects), identityToken(polygons)].join(
          ':',
        ),
      )
      .join(',');
  }

  /**
   * The shapes a body occupies in the world: one for a collider; for a tilemap one box per merged
   * rectangle and one polygon per outlined cell (#141), the one-way cells blocking from the map's
   * top (#155) within their tile's angle (#159). A tilemap placed before the first tick is worked out
   * on the spot.
   */
  solidShapesOf(world: World, body: Entity, within?: ShapeBounds): SolidShape[] {
    const m = worldMatrixOf(body);
    if (body.type !== 'tilemap')
      return [
        { shape: colliderShape(body.props, m, body.wornFrame?.()), facing: oneWayFacing(body.props, m) },
      ];
    const up = oneWayFacing({ oneWay: true }, m);
    // A map is many solids under one entity, so the cells out of reach are dropped before any of
    // them is worked out in world units at all (#184).
    const range = within ? cellsWithin(body.props, m, within) : null;
    const near = (x: number, y: number, w?: number, h?: number) => !range || cellsMeet(range, x, y, w, h);
    return this.blocksOf(world, body).flatMap(({ angle, material: surface, rects, polygons }) => {
      const facing = angle === null ? null : up && { ...up, cone: oneWayCone(angle) };
      return [
        ...rects
          .filter((rect) => near(rect.x, rect.y, rect.w, rect.h))
          .map((rect) => ({ shape: cellRectShape(body.props, rect, m), facing, surface })),
        ...polygons
          .filter((polygon) => near(polygon.x, polygon.y))
          .map((polygon) => ({ shape: cellPolygonShape(body.props, polygon, m), facing, surface })),
      ];
    });
  }

  shapesOf(world: World, body: Entity, within?: ShapeBounds): ColliderShape[] {
    return this.solidShapesOf(world, body, within).map(({ shape }) => shape);
  }

  /**
   * The first solid the ray from `from` along `direction` meets within `length` (world units): any
   * blocking collider or tilemap cell on one of the filter's layers (#158), triggers when asked, a
   * one-way one only on the side it blocks from. What the ray starts inside is not met (see `rayCast`).
   */
  raycast(world: World, from: Vec2, direction: Vec2, length: number, filter: RayFilter): RayResult | null {
    const d = unitOf(direction);
    if ((d.x === 0 && d.y === 0) || !(length > 0)) return null;
    const area = rayBounds(from, d, length);
    let best: RayResult | null = null;
    for (const body of this.rayBodies(world, filter)) {
      for (const { shape, facing } of this.solidShapesOf(world, body, area)) {
        const hit = rayCast(shape, from, d, best?.distance ?? length);
        if (!hit || (facing && !landsOn(hit.normal, facing))) continue;
        if (best && hit.distance >= best.distance) continue;
        best = this.rayResult(body, from, d, hit);
      }
    }
    return best;
  }

  /**
   * Everything the ray meets within `length`, nearest first (#157). One entry per collider – the
   * first face it enters, however many convex pieces it is made of – and one per tilemap cell the
   * ray goes through, since a map is many solids under one entity. `maxHits` above 0 keeps that many
   * of the nearest and stops there; the filter is the one `raycast` uses.
   */
  raycastAll(
    world: World,
    from: Vec2,
    direction: Vec2,
    length: number,
    filter: RayFilter,
    maxHits = 0,
  ): RayResult[] {
    const d = unitOf(direction);
    if ((d.x === 0 && d.y === 0) || !(length > 0)) return [];
    const area = rayBounds(from, d, length);
    const hits: RayResult[] = [];
    for (const body of this.rayBodies(world, filter)) {
      // One solid shape is one hit, except for a collider: its pieces are one shape to the world,
      // so only the nearest of them counts (a polygon in three parts is not three enemies).
      const perShape = body.type === 'tilemap';
      let nearest: RayResult | null = null;
      for (const { shape, facing } of this.solidShapesOf(world, body, area)) {
        const hit = rayCast(shape, from, d, length);
        if (!hit || (facing && !landsOn(hit.normal, facing))) continue;
        const result = this.rayResult(body, from, d, hit);
        if (perShape) hits.push(result);
        else if (!nearest || result.distance < nearest.distance) nearest = result;
      }
      if (nearest) hits.push(nearest);
    }
    hits.sort((a, b) => a.distance - b.distance);
    return maxHits > 0 ? hits.slice(0, maxHits) : hits;
  }

  /** The bodies a ray is allowed to look at, in world order (see `RayFilter`). */
  private *rayBodies(world: World, filter: RayFilter): Generator<Entity> {
    for (const body of world.entities) {
      if (!isCollisionBody(body) || !isHandleEnabled(body)) continue;
      if (body.type === 'collider' && isTrigger(body.props) && !filter.triggers) continue;
      if (filter.ignore && travelsWith(body, filter.ignore)) continue;
      if (!maskHas(filter.layers, collisionFilterOf(body.props).layer)) continue;
      yield body;
    }
  }

  private rayResult(body: Entity, from: Vec2, d: Vec2, hit: { normal: Vec2; distance: number }): RayResult {
    return {
      collider: body,
      point: { x: from.x + d.x * hit.distance, y: from.y + d.y * hit.distance },
      normal: hit.normal,
      distance: hit.distance,
    };
  }

  /**
   * Moves the object towards (dx, dy) and, where a solid is in the way, stops flush at it and goes
   * on along its surface: what is left of the move loses the part into the surface, and friction
   * takes off the part along it in proportion (Coulomb) – so a circle rolls off an edge, and a
   * pressed object slides the less the rougher the pair (#150). An existing overlap is never
   * resolved (no jolt) but never deepened, so an object can leave a wall but not burrow in.
   * (dx, dy) are in the entity's own axes: under a turned parent, "x" runs wherever that parent
   * points it. `onBlocked` hears each solid the move ran into, once.
   */
  moveAndSlide(
    world: World,
    entity: Entity,
    dx: number,
    dy: number,
    onBlocked?: (blocked: Blocked) => void,
  ): MoveResult {
    const own: Mover[] = blockingCollidersOf(world, entity).map((collider) => ({
      collider,
      filter: collisionFilterOf(collider.props),
    }));
    const frame = parentFrame(entity);
    const wanted = applyVector(frame, { x: dx, y: dy });
    if (own.length === 0) {
      entity.x += dx;
      entity.y += dy;
      return NOT_BLOCKED;
    }
    // Nothing that blocks moves while this one does, so its shapes are taken once for the whole
    // move. Only what the move can reach is kept: sliding never lengthens what is left, so the
    // mover never gets farther from where it starts than the whole move is long (#184).
    const reach = own.map((a) =>
      grownBounds(shapeBounds(shapeOf(a.collider)), Math.hypot(wanted.x, wanted.y) + REACH_SLACK),
    );
    const area = reach.reduce(unionBounds);
    const obstacles: Obstacle[] = world.entities
      .filter((c) => blocksMover(c, entity))
      .flatMap((body) => {
        const filter = collisionFilterOf(body.props);
        if (!own.some((a) => layersMeet(a.filter, filter))) return [];
        return this.solidShapesOf(world, body, area)
          .filter((solid) => reach.some((near) => boundsMeet(near, shapeBounds(solid.shape))))
          .map((solid) => ({ ...solid, body, filter }));
      });
    // A one-way solid the mover is inside already, or told to fall through, lets it pass for the
    // whole move: it is on its way through, from below or from the side.
    const ignoring = world.ignoresOneWay(entity);
    const passing = new Set(
      obstacles.filter(
        (o) =>
          o.facing &&
          (ignoring || own.some((a) => meets(a, o) && shapesOverlap(shapeOf(a.collider), o.shape))),
      ),
    );
    const contacts: SweepContact[] = [];
    let rest = wanted;
    for (let pass = 0; pass < MAX_PASSES && (rest.x !== 0 || rest.y !== 0); pass++) {
      const contact = sweep(entity, frame, own, obstacles, passing, rest);
      if (!contact) break;
      contacts.push(contact);
      rest = slideAlong(
        contact.left,
        contact.normal,
        frictionBetween(contact.own, contact.by, contact.surface),
      );
    }
    if (contacts.length === 0) return NOT_BLOCKED;
    const pushed = new Set<Entity>();
    for (const { by, normal } of contacts) {
      if (pushed.has(by)) continue;
      pushed.add(by);
      const along = { x: -normal.x, y: -normal.y };
      onBlocked?.({ by, along, distance: Math.max(0, dot(wanted, along)) });
    }
    const against = (axis: Vec2, delta: number) =>
      delta !== 0 && contacts.some(({ normal }) => Math.sign(delta) * dot(normal, unitOf(axis)) < -SQUARE);
    const first = contacts[0]!.normal;
    return {
      blockedX: against({ x: frame.a, y: frame.b }, dx),
      blockedY: against({ x: frame.c, y: frame.d }, dy),
      hit: true,
      normal: { x: first.x || 0, y: first.y || 0 },
    };
  }
}

/**
 * The linear map from the entity's own axes to the world: its parent's. A parent scaled to nothing
 * leaves no direction to move in, so there the world's axes stand in.
 */
function parentFrame(entity: Entity): Mat {
  const parent = entity.parent ? linearOf(worldMatrixOf(entity.parent)) : IDENTITY;
  return Math.abs(determinant(parent)) < 1e-12 ? IDENTITY : parent;
}

/**
 * Moves the entity along `move` (world) in steps no solid is thinner than, until a step runs into
 * one: then it is set back flush against it and the contact is reported with what is left of the move.
 * A one-way solid met anywhere but on its blocking side joins `passing` instead.
 */
function sweep(
  entity: Entity,
  frame: Mat,
  own: Mover[],
  obstacles: Obstacle[],
  passing: Set<Obstacle>,
  move: Vec2,
): SweepContact | null {
  const distance = Math.hypot(move.x, move.y);
  const forward = { x: move.x / distance, y: move.y / distance };
  const steps = Math.min(MAX_STEPS, Math.max(1, Math.ceil(distance / stepLimit(own, obstacles, forward))));
  const step = distance / steps;
  const toLocal = invert(frame);
  const shift = (length: number) => {
    const local = applyVector(toLocal, { x: forward.x * length, y: forward.y * length });
    entity.x += local.x;
    entity.y += local.y;
  };
  for (let i = 0; i < steps; i++) {
    // How deep each pair already overlaps. A step may never deepen that, but resolving it is not
    // our job (no jolt, and leaving a wall is always possible).
    const before = own.map((a) => {
      const mover = shapeOf(a.collider);
      return obstacles.map(({ shape }) => overlapDepth(contactBetween(mover, shape, forward).separation));
    });
    shift(step);
    let correction = 0;
    let found: { own: Entity; obstacle: Obstacle } | null = null;
    for (const [k, a] of own.entries()) {
      const mover = shapeOf(a.collider);
      for (const [j, obstacle] of obstacles.entries()) {
        if (passing.has(obstacle) || !meets(a, obstacle)) continue;
        const was = before[k]![j]!;
        if (overlapDepth(contactBetween(mover, obstacle.shape, forward).separation) <= was + DEEPER) continue;
        // Coming from outside, the step goes back exactly to where the two met; from inside, all
        // of it is taken back.
        const back =
          was === 0
            ? Math.min(step, exitDistance(mover, obstacle.shape, { x: -forward.x, y: -forward.y }))
            : step;
        if (obstacle.facing) {
          const met = movedShape(mover, (p) => ({ x: p.x - forward.x * back, y: p.y - forward.y * back }), 0);
          if (!landsOn(contactBetween(met, obstacle.shape, forward).normal, obstacle.facing)) {
            passing.add(obstacle);
            continue;
          }
        }
        if (back > correction || !found) {
          correction = back;
          found = { own: a.collider, obstacle };
        }
      }
    }
    if (!found) continue;
    const { own: collider, obstacle } = found;
    shift(-correction);
    const left = distance - i * step - (step - correction);
    return {
      by: obstacle.body,
      surface: obstacle.surface,
      own: collider,
      normal: contactBetween(shapeOf(collider), obstacle.shape, forward).normal,
      left: { x: forward.x * left, y: forward.y * left },
    };
  }
  return null;
}

/**
 * What of a move goes on after a contact: nothing into the surface, and along it what friction
 * leaves – shortened by `friction` times the part that pressed into the surface, down to nothing.
 */
function slideAlong(move: Vec2, normal: Vec2, friction: number): Vec2 {
  const into = dot(move, normal);
  if (into >= 0) return move;
  const along = { x: move.x - into * normal.x, y: move.y - into * normal.y };
  const length = Math.hypot(along.x, along.y);
  const kept = length - friction * -into;
  if (kept <= 0 || length === 0) return { x: 0, y: 0 };
  return { x: (along.x * kept) / length, y: (along.y * kept) / length };
}

/**
 * The friction of a pair, as the physics engine combines it for its bodies (the average), so an
 * object moved by the graph slides as far as one the engine moves. A tile brings its own (#193).
 */
function frictionBetween(own: Entity, obstacle: Entity, surface?: TileMaterial): number {
  return (surfaceOf(own).friction + surfaceOf(obstacle, surface).friction) / 2;
}

/** What a shape of `body` offers to what meets it: a tile's own surface, else the collider's material. */
export function surfaceOf(body: Entity, surface?: TileMaterial): TileMaterial {
  return surface ?? colliderMaterial(body.type === 'collider' ? body.props : {});
}

/** The rectangle around every shape, or null without one – nothing to narrow anything down with. */
export function boundsAround(shapes: readonly ColliderShape[]): ShapeBounds | undefined {
  return shapes.length > 0 ? shapes.map(shapeBounds).reduce(unionBounds) : undefined;
}

/** The rectangle around both rectangles. */
function unionBounds(a: ShapeBounds, b: ShapeBounds): ShapeBounds {
  return {
    left: Math.min(a.left, b.left),
    top: Math.min(a.top, b.top),
    right: Math.max(a.right, b.right),
    bottom: Math.max(a.bottom, b.bottom),
  };
}

/** The rectangle around a ray, so a map only works out the cells it runs through (#184). */
function rayBounds(from: Vec2, d: Vec2, length: number): ShapeBounds {
  const to = { x: from.x + d.x * length, y: from.y + d.y * length };
  return grownBounds(
    {
      left: Math.min(from.x, to.x),
      top: Math.min(from.y, to.y),
      right: Math.max(from.x, to.x),
      bottom: Math.max(from.y, to.y),
    },
    REACH_SLACK,
  );
}

function unitOf(v: Vec2): Vec2 {
  const length = Math.hypot(v.x, v.y);
  return length > 0 ? { x: v.x / length, y: v.y / length } : v;
}

/**
 * A map's blocking cells, one group per surface (#193) and side: `angle` null for the cells that
 * block from everywhere, else the angle one-way cells land things within (#159).
 */
type TilemapBlocks = {
  angle: number | null;
  material: TileMaterial;
  rects: readonly CellRect[];
  polygons: readonly CellPolygon[];
}[];

export function shapeOf(collider: Entity): ColliderShape {
  return colliderShape(collider.props, worldMatrixOf(collider), collider.wornFrame?.());
}

/** What of an entity stops at walls when it moves: its solid colliders that are switched on. */
export function blockingCollidersOf(world: World, entity: Entity): Entity[] {
  return collidersOf(world, entity).filter((c) => !isTrigger(c.props) && isHandleEnabled(c));
}

/** Whether `body` (a collider or a tilemap) stands in the way of `mover`. */
function blocksMover(body: Entity, mover: Entity): boolean {
  return (
    isCollisionBody(body) &&
    !(body.type === 'collider' && isTrigger(body.props)) &&
    isHandleEnabled(body) &&
    !travelsWith(body, mover)
  );
}

/** Whether `collider` belongs to `entity` or to something parented (at any depth) under it. */
function travelsWith(collider: Entity, entity: Entity): boolean {
  for (const e of parentChain(collider, (c) => c.parent)) if (e === entity) return true;
  return false;
}

/**
 * Longest safe step in world units: half of the thinnest collider involved, measured along the
 * travel as the colliders sit in the world (never below 1).
 */
function stepLimit(own: Mover[], obstacles: Obstacle[], along: Vec2): number {
  let min = Infinity;
  for (const { collider } of own) min = Math.min(min, shapeExtent(shapeOf(collider), along));
  for (const { shape } of obstacles) min = Math.min(min, shapeExtent(shape, along));
  return Math.max(1, min / 2);
}

/** Whether the mover's collider and that obstacle are on layers that meet (#152). */
function meets(mover: Mover, obstacle: Obstacle): boolean {
  return layersMeet(mover.filter, obstacle.filter);
}

/**
 * Whether two colliders (or a collider and a tilemap) may meet at all, by their layers – the one
 * rule the physics engine, `Solids` and the event pair search all answer by.
 */
export function collidersMeet(a: Entity, b: Entity): boolean {
  return layersMeet(collisionFilterOf(a.props), collisionFilterOf(b.props));
}

/** What takes part in collisions: colliders, and placed tilemaps with their solid cells. */
export function isCollisionBody(entity: Entity): boolean {
  return entity.type === 'collider' || entity.type === 'tilemap';
}

/**
 * Whose layer an object is on (#211): a collider or tilemap its own, anything else that of its first
 * collider child, switched on or not – the layer is set either way.
 */
export function layerHolderOf(world: World, entity: Entity): Entity | undefined {
  return isCollisionBody(entity) ? entity : world.childrenOf(entity).find((e) => e.type === 'collider');
}

/**
 * The object a collider belongs to: its parent, or the collider itself when top-level. A tilemap
 * is its own body wherever it is placed – its cells are the thing, not a shape stuck on one.
 */
export function bodyOf(collider: Entity): Entity {
  if (collider.type === 'tilemap') return collider;
  return collider.parent ?? collider;
}

/** What a body touches with: a tilemap its cells, anything else its colliders (see `collidersOf`). */
export function partsOf(world: World, entity: Entity): Entity[] {
  return entity.type === 'tilemap' ? [entity] : collidersOf(world, entity);
}

/**
 * A collider stands for itself; any other entity stands for its direct collider children – a
 * tilemap as well when it is the one being moved: its cells only ever take part as an obstacle.
 */
function collidersOf(world: World, entity: Entity): Entity[] {
  if (entity.type === 'collider') return [entity];
  return world.childrenOf(entity).filter((e) => e.type === 'collider' && isHandleEnabled(e));
}