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

/**

 * Everybody else, drawn between the things the server said about them.

 *

 * A remote body is only ever heard about a few dozen times a second, so it

 * has to be drawn somewhere in between. The old way was an exponential chase

 * — `now.x += (x - now.x) * 0.35` every frame — which is wrong twice: it is a

 * different speed at 60Hz than at 144Hz, and it is a pursuit that never

 * arrives, so every other player was permanently behind and rubbery.

 *

 * This is entity interpolation instead. Each body keeps the last few samples

 * with the times they landed, and the frame is drawn at `now - delay`, about

 * a snapshot interval in the past. That moment falls between two samples on

 * hand, so the body moves at exactly the speed the server moved it and

 * arrives exactly where the server put it — one interval late, which nobody

 * can see. A handful of samples rather than strictly two is what buys the

 * delay a margin: a snapshot that arrives late or early still brackets the

 * moment being drawn instead of stalling the body.

 *

 * When a snapshot really is missed the newest pair's own velocity is carried

 * forward for one interval and then held: a guess that long is better than a

 * stall, and a guess longer than that is fiction. The delay follows the rate

 * snapshots actually arrive at, so the same code is right at 15Hz and at

 * 30Hz without being told which it is.

 *

 * Nothing here is ever sent anywhere: it is a drawing, and the server is

 * still the only thing that says where anybody is.

 */

/** The render delay, as a multiple of the interval snapshots arrive at. */

export const LAG = 1.3;

/** ...never tighter than this, never looser, in seconds. */

export const LAG_MIN = 0.045;

export const LAG_MAX = 0.13;

/** How many samples a body keeps: enough to bracket the delay, and no more. */

export const KEEP = 4;

/** How fast the measured interval follows the arrivals. */

const INTERVAL_PULL = 0.1;

/** How fast the even clock snapshots are filed under is pulled toward the arrivals. */

const STAMP_PULL = 0.1;

/** How much of the even clock's lateness is read as the interval being wrong. */

const INTERVAL_TRIM = 0.02;

/** How far the moment drawn may run fast or slow to reach its delay: a share of real time. */

export const SLEW = 0.02;

/** A render clock this far off its mark is not late, it is stopped: start it again. */

const RESYNC = 0.25;

/** A gap this long means the body was gone, not slow: start it again. */

export const GONE = 0.4;

/** Faster than anything can run: a respawn, or a body back from nowhere. */

const TOP_SPEED = 400;

const clamp = (n, low, high) => (n < low ? low : n > high ? high : n);

/** The short way round from one angle to another, in (-π, π]. */

export const shortWay = (from, to) => ((to - from + Math.PI * 3) % (Math.PI * 2)) - Math.PI;

/**

 * One timeline for the whole snapshot stream: the bodies, the rate, the even

 * clock (`stamp`) and the moment being drawn (`drawAt`). `restarts` counts

 * the times a body was started again rather than walked: every one is a jump.

 */

export const makeTimeline = (interval = 1 / 30) => ({

  bodies: new Map(),

  interval,

  at: 0,

  stamp: 0,

  drawAt: 0,

  drawnNow: 0,

  restarts: 0,

});

/**

 * A snapshot landed at `at` seconds. The gap since the last one is what the

 * render delay is built out of; a gap wilder than any real rate (a tab that

 * was in the background, a reconnect) says nothing about the rate and is

 * left out of it.

 *

 * Returns the time the snapshot is filed under, which is not the time it

 * landed. The server sends thirty a second, evenly; the network hands them

 * over in a rhythm of its own, a few milliseconds early or late, sometimes

 * two nearly together. A sample filed under its arrival time carries that

 * wobble into the walk between samples — a body drawn between a sample that

 * came early and one that came late moves slow, then fast — and into the

 * age of your own snapshot, which is how far ahead your own keys are

 * carried. So arrivals are filed on an even clock instead: one interval

 * after the last, pulled a tenth of the way toward when they really came so

 * it never drifts. A rate is not a rhythm; this is the rhythm.

 */

export function arrive(timeline, at) {

  const gap = at - timeline.at;

  const steady = timeline.at > 0 && gap > 1 / 120 && gap < 0.5;

  if (steady) timeline.interval += (gap - timeline.interval) * INTERVAL_PULL;

  const expected = timeline.stamp + timeline.interval;

  const off = at - expected;

  // Within an interval of the beat, keep the beat; further out (a pause, a

  // reconnect, the rate itself changing) the arrival is the only clock there is.

  let stamp = at;

  if (timeline.at > 0 && gap < 0.5 && Math.abs(off) < timeline.interval) {

    stamp = expected + off * STAMP_PULL;

    // Arrivals that keep landing on the same side of the beat mean the beat

    // is wrong, not late: trim the interval by a little of the lateness.

    timeline.interval += off * INTERVAL_TRIM;

  }

  // A sample is never filed before the one before it, and never more than

  // half a beat before it actually came: a burst of snapshots (a tab coming

  // back from the background) must not walk the clock off into the future.

  if (stamp <= timeline.stamp) stamp = timeline.stamp + timeline.interval / 4;

  stamp = Math.max(Math.min(stamp, at + timeline.interval / 2), timeline.stamp);

  timeline.at = at;

  timeline.stamp = stamp;

  return stamp;

}

/** How far behind the present this timeline is drawn, in seconds. */

export const delay = (timeline) => clamp(timeline.interval * LAG, LAG_MIN, LAG_MAX);

/**

 * The moment being drawn, given the clock now.

 *

 * Not simply `now - delay`: the delay follows the measured rate, and a delay

 * that moves between frames moves the moment being drawn with it, so a

 * frame after a late snapshot drew twelve milliseconds of motion and the

 * next nineteen — the beat of the wire showing through as a stutter. The

 * moment drawn now advances at real time, and creeps toward where the delay

 * says it should be at no more than two percent of that: a speed nobody can

 * see. Only a clock a quarter second off — a tab that was in the background,

 * the first frame — is started again where it belongs.

 */

export function renderTime(timeline, now) {

  const want = now - delay(timeline);

  const dt = now - timeline.drawnNow;

  timeline.drawnNow = now;

  const ahead = timeline.drawAt + dt;

  if (timeline.drawAt === 0 || dt <= 0 || dt > RESYNC || Math.abs(want - ahead) > RESYNC) {

    timeline.drawAt = want;

    return want;

  }

  timeline.drawAt = ahead + clamp(want - ahead, -dt * SLEW, dt * SLEW);

  return timeline.drawAt;

}

const mark = (at, body) => ({ t: at, x: body.x, y: body.y, angle: body.angle });

/**

 * What the server just said about one body. Out-of-order samples are

 * dropped; a body that has been away, or that has moved further than anyone

 * can run, starts fresh rather than sliding across the map to its new place.

 *

 * The drawn position lives on the track — one object per body, so a caller

 * may hold the answer it was given while asking about somebody else.

 */

export function feed(timeline, id, body, at) {

  const track = timeline.bodies.get(id);

  if (!track) {

    timeline.bodies.set(id, { marks: [mark(at, body)], out: { x: 0, y: 0, angle: 0 } });

    return timeline;

  }

  const last = track.marks[track.marks.length - 1];

  if (at <= last.t) return timeline;

  const gap = at - last.t;

  // Two samples filed close together are still a tick apart on the server,

  // so a body is allowed at least an interval's run between them.

  const jumped = Math.hypot(body.x - last.x, body.y - last.y) > TOP_SPEED * Math.max(gap, timeline.interval) + 4;

  if (gap > GONE || jumped) {

    track.marks.length = 0;

    timeline.restarts += 1;

  }

  track.marks.push(mark(at, body));

  if (track.marks.length > KEEP) track.marks.shift();

  return timeline;

}

/**

 * Where a body was at a moment, given the samples it has — ascending in

 * time, and at least one.

 *

 * Between two samples this is a straight walk from one to the other at the

 * server's own speed. Before the oldest it holds, because running backwards

 * to meet a moment we have no answer for would be inventing one. After the

 * newest it carries the last pair's velocity for one interval — no more,

 * ever — and then holds there.

 */

export function sample(marks, when, out = { x: 0, y: 0, angle: 0 }) {

  const last = marks[marks.length - 1];

  if (marks.length === 1 || when >= last.t) return beyond(marks, when, out);

  if (when <= marks[0].t) return at(marks[0], marks[0], 0, out);

  let i = marks.length - 2;

  while (i > 0 && marks[i].t > when) i -= 1;

  const from = marks[i];

  const to = marks[i + 1];

  const span = to.t - from.t;

  return at(from, to, span > 0 ? (when - from.t) / span : 1, out);

}

/** Past the newest sample: one interval of the last pair's velocity, held. */

function beyond(marks, when, out) {

  const last = marks[marks.length - 1];

  const before = marks[marks.length - 2];

  if (!before) return at(last, last, 0, out);

  const span = last.t - before.t;

  if (span <= 0) return at(last, last, 0, out);

  return at(before, last, clamp((when - before.t) / span, 1, 2), out);

}

/** A point `u` of the way from one sample to another; the turn is short. */

function at(from, to, u, out) {

  out.x = from.x + (to.x - from.x) * u;

  out.y = from.y + (to.y - from.y) * u;

  out.angle = from.angle + shortWay(from.angle, to.angle) * u;

  return out;

}

/**

 * Where to draw a body out of a snapshot. One with no samples yet — the

 * first frame it is seen on — is drawn where the server says, which is the

 * only honest answer available.

 */

export function bodyAt(timeline, body, when, out = null) {

  const track = timeline.bodies.get(body.id);

  if (!track) return body;

  return sample(track.marks, when, out ?? track.out);

}