Motion

1import type { Schedule, Pose } from "../frost";
2
3export const SETTLE = 2.8;
4export const ATTACK = 0.65; // anticipation before each break
5const clamp01 = (x: number) => Math.max(0, Math.min(1, x));
6
7/** C2 turn envelopes: continuous velocity/acceleration over an ongoing drift. */
8export function makePoseAt(S: Schedule, P: Pose) {
9  const flowEase = (u: number) => {
10    u = clamp01(u);
11    return u * u * u * (u * (u * 6 - 15) + 10);
12  };
13  /** Quintic rise and fall meet with zero velocity and acceleration at the crest. */
14  const bump = (u: number, a: number) =>
15    u <= a ? flowEase(u / Math.max(a, 1e-6)) : 1 - flowEase((u - a) / Math.max(1 - a, 1e-6));
16  type Turn = {
17    t0: number;
18    tBreakEnd: number;
19    t1: number;
20    yaw: number;
21    pitch: number;
22    z: number;
23    keep: boolean;
24  };
25  const turns: Turn[] = [
26    {
27      t0: S.logoBreak - ATTACK,
28      tBreakEnd: S.form1,
29      t1: S.form1 + SETTLE,
30      yaw: P.turnYaw,
31      pitch: P.turnPitch,
32      z: P.approach,
33      keep: false,
34    },
35    {
36      t0: S.break1 - ATTACK,
37      tBreakEnd: S.form2,
38      t1: S.form2 + SETTLE,
39      yaw: P.turnYaw2,
40      pitch: P.turnPitch2,
41      z: -P.retreat,
42      keep: false,
43    },
44    {
45      t0: S.break2 - ATTACK,
46      tBreakEnd: S.fadeOut + 1.5,
47      t1: S.fadeOut + 1.5,
48      yaw: P.finalYaw,
49      pitch: P.finalPitch,
50      z: P.approach + P.zoomIn,
51      keep: true,
52    },
53  ];
54  /** the keyed part of the path (without drift / idle), in degrees and units */
55  function keyPoseAt(t: number) {
56    let yaw = 0,
57      pitch = 0,
58      z = 0;
59    for (const k of turns) {
60      const u = (t - k.t0) / Math.max(k.t1 - k.t0, 1e-6);
61      if (u <= 0) continue;
62      yaw += k.yaw * flowEase(u);
63      const a = (k.tBreakEnd - k.t0) / Math.max(k.t1 - k.t0, 1e-6);
64      const b = k.keep ? flowEase(u) : bump(u, a);
65      pitch += k.pitch * b;
66      z += k.z * b;
67    }
68    return { yaw, pitch, z };
69  }
70  const driftYawAt = (t: number) => P.driftYaw * t;
71  const idleYawAt = (t: number) => P.idleYaw * Math.sin((2 * Math.PI * t) / 9);
72  return function poseAt(t: number) {
73    const k = keyPoseAt(t);
74    const sway = P.driftSway * Math.sin((2 * Math.PI * t) / 11);
75    return {
76      yaw: k.yaw + driftYawAt(t) + idleYawAt(t),
77      pitch: k.pitch + sway,
78      z: k.z + 0.0875 * P.driftSway * Math.sin((2 * Math.PI * t) / 11),
79    };
80  };
81}