quill/val Public Public: anyone can read this; nobody can change it.

/**

 * Entity interpolation: a pure function of two samples and a time.

 *

 * What is checked here is what a browser cannot be asked about — that the

 * body walks between the pair at the server's own speed, that a missed

 * snapshot is carried exactly one interval and no further, that the turn is

 * taken the short way round, and that a time between the pair never draws

 * the body anywhere but between them.

 */

import { expect, test } from "bun:test";

import { arrive, bodyAt, delay, feed, GONE, LAG, LAG_MAX, LAG_MIN, makeTimeline, sample } from "../static/interp.js";

type Mark = { t: number; x: number; y: number; angle: number };

const pair = (a: Mark, b: Mark) => [a, b];

const walk = pair({ t: 10, x: 100, y: 200, angle: 0 }, { t: 10.1, x: 120, y: 200, angle: 1 });

test("between the pair it walks at the speed the server moved it", () => {

  expect(sample(walk, 10)).toMatchObject({ x: 100, y: 200 });

  expect(sample(walk, 10.05).x).toBeCloseTo(110, 6);

  expect(sample(walk, 10.1)).toMatchObject({ x: 120, y: 200 });

  // Constant speed: equal steps of time are equal steps of distance, which

  // is the whole difference from an exponential chase that never arrives.

  const a = sample(walk, 10.02).x;

  const b = sample(walk, 10.04).x;

  const c = sample(walk, 10.06).x;

  expect(b - a).toBeCloseTo(c - b, 6);

});

test("a time inside the pair is never a position outside it", () => {

  const diagonal = pair({ t: 1, x: -30, y: 80, angle: 2 }, { t: 1.07, x: 45, y: -10, angle: -2 });

  for (let when = 1; when <= 1.07; when += 0.002) {

    const at = sample(diagonal, when);

    expect(at.x).toBeGreaterThanOrEqual(-30);

    expect(at.x).toBeLessThanOrEqual(45);

    expect(at.y).toBeGreaterThanOrEqual(-10);

    expect(at.y).toBeLessThanOrEqual(80);

  }

});

test("before the older sample it holds rather than running backwards", () => {

  expect(sample(walk, 9.5)).toMatchObject({ x: 100, y: 200 });

  expect(sample(walk, 0)).toMatchObject({ x: 100, y: 200 });

});

test("a missed snapshot is carried one interval and then held", () => {

  // Half an interval late: half an interval of the pair's own velocity.

  expect(sample(walk, 10.15).x).toBeCloseTo(130, 6);

  // A whole one: exactly one more interval of it.

  expect(sample(walk, 10.2).x).toBeCloseTo(140, 6);

  // And never a step further, however long the silence lasts.

  expect(sample(walk, 10.3).x).toBeCloseTo(140, 6);

  expect(sample(walk, 30).x).toBeCloseTo(140, 6);

  expect(sample(walk, 30).angle).toBeCloseTo(2, 6);

});

test("two samples at one instant are one sample", () => {

  const still = pair({ t: 5, x: 7, y: 8, angle: 0.5 }, { t: 5, x: 7, y: 8, angle: 0.5 });

  expect(sample(still, 9)).toMatchObject({ x: 7, y: 8, angle: 0.5 });

});

test("the turn is taken the short way round", () => {

  const spin = pair({ t: 0, x: 0, y: 0, angle: 3.0 }, { t: 0.1, x: 0, y: 0, angle: -3.0 });

  // Not back through zero: onward past π, by a sixth of a radian or so.

  expect(sample(spin, 0.05).angle).toBeCloseTo(3.0 + 0.2831853 / 2, 6);

  const back = pair({ t: 0, x: 0, y: 0, angle: -3.0 }, { t: 0.1, x: 0, y: 0, angle: 3.0 });

  expect(sample(back, 0.05).angle).toBeCloseTo(-3.0 - 0.2831853 / 2, 6);

});

// ------------------------------------------------------------- the timeline

const body = (id: string, x: number, y = 0, angle = 0) => ({ id, x, y, angle });

test("a body is drawn where the server says until there are two of it", () => {

  const timeline = makeTimeline();

  const first = body("a", 50);

  expect(bodyAt(timeline, first, 10)).toBe(first);

  feed(timeline, "a", first, 10);

  expect(bodyAt(timeline, first, 10.2)).toMatchObject({ x: 50, y: 0 });

  feed(timeline, "a", body("a", 60), 10.1);

  expect(bodyAt(timeline, body("a", 60), 10.05).x).toBeCloseTo(55, 6);

});

test("each body keeps its own answer: one can be held while another is asked", () => {

  const timeline = makeTimeline();

  feed(timeline, "a", body("a", 0), 1);

  feed(timeline, "a", body("a", 10), 1.1);

  feed(timeline, "b", body("b", 100), 1);

  feed(timeline, "b", body("b", 110), 1.1);

  const a = bodyAt(timeline, body("a", 10), 1.05);

  const b = bodyAt(timeline, body("b", 110), 1.05);

  expect(a.x).toBeCloseTo(5, 6);

  expect(b.x).toBeCloseTo(105, 6);

});

test("a body that was out of sight starts again rather than sliding back", () => {

  const timeline = makeTimeline();

  feed(timeline, "a", body("a", 0), 1);

  feed(timeline, "a", body("a", 10), 1.1);

  feed(timeline, "a", body("a", 900), 1.1 + GONE + 0.1);

  expect(bodyAt(timeline, body("a", 900), 1.1 + GONE + 0.15).x).toBeCloseTo(900, 6);

});

test("a jump no one could have run is a respawn, not a walk", () => {

  const timeline = makeTimeline();

  feed(timeline, "a", body("a", 0), 1);

  feed(timeline, "a", body("a", 10), 1.1);

  // A third of a second's running is 80-odd units; 600 is a teleport.

  feed(timeline, "a", body("a", 610), 1.2);

  expect(bodyAt(timeline, body("a", 610), 1.25).x).toBeCloseTo(610, 6);

});

test("a sample that arrives out of order is dropped", () => {

  const timeline = makeTimeline();

  feed(timeline, "a", body("a", 0), 1);

  feed(timeline, "a", body("a", 10), 1.1);

  feed(timeline, "a", body("a", 999), 1.05);

  expect(bodyAt(timeline, body("a", 10), 1.1).x).toBeCloseTo(10, 6);

});

test("the delay follows the rate the snapshots actually arrive at", () => {

  const slow = makeTimeline();

  for (let i = 0; i < 60; i++) arrive(slow, 10 + i / 15);

  const fast = makeTimeline();

  for (let i = 0; i < 60; i++) arrive(fast, 10 + i / 30);

  expect(delay(slow)).toBeGreaterThan(delay(fast));

  expect(delay(slow)).toBeCloseTo((1 / 15) * LAG, 3);

  // Thirty a second wants less of a delay, and both stay inside the bounds.

  for (const d of [delay(slow), delay(fast)]) {

    expect(d).toBeGreaterThanOrEqual(LAG_MIN);

    expect(d).toBeLessThanOrEqual(LAG_MAX);

  }

  // A pause — a backgrounded tab, a reconnect — says nothing about the rate.

  arrive(fast, 40);

  expect(delay(fast)).toBeCloseTo(LAG_MIN, 3);

});

test("the moment being drawn is always bracketed by samples on hand", () => {

  // Thirty snapshots a second, a frame every 16ms: the moment being drawn

  // always falls between the two samples on hand, never before them.

  const timeline = makeTimeline();

  let x = 0;

  let last = { t: 0, x: 0 };

  for (let i = 0; i < 40; i++) {

    const at = 10 + i / 30;

    arrive(timeline, at);

    x += 8;

    feed(timeline, "a", body("a", x), at);

    last = { t: at, x };

    if (i < 3) continue;

    for (let f = 0; f < 2; f++) {

      const now = at + f * 0.016;

      const marks = timeline.bodies.get("a")!.marks as Mark[];

      const when = now - delay(timeline);

      expect(when).toBeGreaterThanOrEqual(marks[0]!.t - 1e-9);

      expect(when).toBeLessThanOrEqual(marks[marks.length - 1]!.t + 1e-9);

    }

  }

  // And late is what late means: behind the newest word by the delay, which

  // at eight units an interval is between one and two of them.

  const drawn = bodyAt(timeline, body("a", last.x), last.t - delay(timeline));

  expect(last.x - drawn.x).toBeGreaterThan(0);

  expect(last.x - drawn.x).toBeLessThan(20);

});

// --------------------------------------------- against the real simulation

/**

 * The match's own motion, sampled at the rate the server broadcasts it and

 * drawn at the rate a browser draws: what a bot walking across the map

 * actually looks like. The samples carry exactly what a snapshot carries —

 * a position rounded to a tenth, thirty times a second.

 *

 * The measure is the spread of the per-frame steps. A body drawn at the

 * server's speed takes even steps; the exponential chase this replaced took

 * a long step just after each snapshot and shorter ones after it, which is

 * choppiness with a number on it — twice this spread, measured the same way.

 */

test("the simulation's own motion is drawn at an even speed", async () => {

  const { runBots } = await import("./bots.ts");

  const { newMatch, tick } = await import("./match.ts");

  const round2 = (n: number) => Math.round(n * 10) / 10;

  // A match of its own: nothing here touches the arena everybody shares.

  const state = newMatch();

  const step = () => {

    runBots(state, 1 / 30);

    tick(state, 1 / 30);

  };

  for (let i = 0; i < 30 * 40 && state.phase !== "live"; i++) step();

  const stream: { t: number; bodies: { id: string; x: number; y: number; angle: number }[] }[] = [];

  for (let i = 0; i < 60; i++) {

    step();

    stream.push({

      t: i / 30,

      bodies: state.players.map((p) => ({ id: p.id, x: round2(p.x), y: round2(p.y), angle: round2(p.angle) })),

    });

  }

  const timeline = makeTimeline();

  const paths = new Map<string, { x: number; y: number }[]>();

  let next = 0;

  for (let f = 0; f / 60 < 1.8; f++) {

    const now = f / 60;

    while (next < stream.length && stream[next]!.t <= now) {

      arrive(timeline, stream[next]!.t);

      for (const p of stream[next]!.bodies) feed(timeline, p.id, p, stream[next]!.t);

      next += 1;

    }

    for (const p of stream[Math.max(0, next - 1)]!.bodies) {

      const at = bodyAt(timeline, p, now - delay(timeline));

      paths.set(p.id, [...(paths.get(p.id) ?? []), { x: at.x, y: at.y }]);

    }

  }

  // Whoever walked furthest in that second and a half.

  const walked = [...paths.values()]

    .filter((path) => path.length > 80)

    .map((path) => path.slice(1).map((at, i) => Math.hypot(at.x - path[i]!.x, at.y - path[i]!.y)))

    .map((steps) => steps.filter((step) => step > 0.001))

    .sort((a, b) => b.reduce((s, x) => s + x, 0) - a.reduce((s, x) => s + x, 0))[0]!;

  expect(walked.length).toBeGreaterThan(30);

  const mean = walked.reduce((s, x) => s + x, 0) / walked.length;

  const spread = Math.sqrt(walked.reduce((s, x) => s + (x - mean) ** 2, 0) / walked.length) / mean;

  // A body moving at the server's own speed: about four units every sixtieth

  // of a second, which is the run speed.

  expect(mean * 60).toBeGreaterThan(150);

  expect(spread).toBeLessThan(0.15);

});