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feat: Support for new speed events easings in RPE 1.7.0 #37

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5e5ecc4
feat: integral calculation
IcedDog Dec 22, 2025
d0fe792
fix: integral now WORKS
IcedDog Jan 14, 2026
077c532
feat: apply integral func according to RPEVersion
IcedDog Jan 14, 2026
ff988fe
Merge branch 'main' into rpe-170-speed-fix
Naptie Jan 14, 2026
2763991
refactor: merge two getIntegral functions into one and introduce a bo…
Naptie Jan 14, 2026
3894bc9
docs(readme): introduce integrateSpeedEasings
Naptie Jan 14, 2026
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19 changes: 10 additions & 9 deletions README.md
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Expand Up @@ -79,15 +79,16 @@ The Z indexes of judgment lines whose `zIndex` is not present (see [Chart enhanc

Aside from adding support for RPE features, we've also designed some original properties for judgment lines & notes.

| Property | Value(s) | Example | Description |
| -------------------- | --------------------------------------------------- | ------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| `scaleOnNotes` | `0`: none; `1`: scale; `2`: clip | `"scaleOnNotes": 2` | Belongs to a judgment line. Decides how `scaleX` events affect notes. Defaults to `0`. |
| `appearanceOnAttach` | `0`: hidden; `1`: white colored; `2`: FC/AP colored | `"appearanceOnAttach": 2` | Belongs to a judgment line. Decides how the line will be displayed when a UI component or any video is attached to it. Color events will override the color defined by these options. Defaults to `0`. |
| `zIndex` | an integer or a float | `"zIndex": 3.5` | Belongs to a judgment line or note. Sets the Z index for the object. For a judgment line, this property, if set, overrides the `zOrder` property, allowing for more control over on which layer the line should be displayed. For default values, see [Z indexes](#z-indexes). |
| `zIndexHitEffects` | an integer or a float | `"zIndexHitEffects": 6.5` | Belongs to a note. Sets the Z index for the hit effects of the note. Defaults to `7`. |
| `tint` | [R, G, B], as seen in `colorEvents`; `null` | `"tint": [255, 0, 0]` | Belongs to a note. Sets the tint for the note. Defaults to `null`. |
| `tintHitEffects` | [R, G, B], as seen in `colorEvents`; `null` | `"tintHitEffects": [255, 0, 0]` | Belongs to a note. Sets the tint for the hit effects of the note. Defaults to `null`. |
| `judgeSize` | a positive number or 0 | `"judgeSize": 1.5` | Belongs to a note. Determines the width of the judgment area of the note. Defaults to `size`. |
| Property | Value(s) | Example | Description |
| ----------------------- | -------------------------------------------------------------------------------------------------------------------------------- | ------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| `scaleOnNotes` | `0`: none; `1`: scale; `2`: clip | `"scaleOnNotes": 2` | Belongs to a judgment line. Decides how `scaleX` events affect notes. Defaults to `0`. |
| `appearanceOnAttach` | `0`: hidden; `1`: white colored; `2`: FC/AP colored | `"appearanceOnAttach": 2` | Belongs to a judgment line. Decides how the line will be displayed when a UI component or any video is attached to it. Color events will override the color defined by these options. Defaults to `0`. |
| `integrateSpeedEasings` | `false`: treat non-linear speed easings directly as height over time; `true`: integrate speed easings to obtain height functions | `"integrateSpeedEasings": true` | Belongs to a judgment line. Decides how the easing functions of all speed events of the line will be interpreted. Defaults to `false` for pre-1.7 charts and `true` for charts on 1.7 and later versions. |
| `zIndex` | an integer or a float | `"zIndex": 3.5` | Belongs to a judgment line or note. Sets the Z index for the object. For a judgment line, this property, if set, overrides the `zOrder` property, allowing for more control over on which layer the line should be displayed. For default values, see [Z indexes](#z-indexes). |
| `zIndexHitEffects` | an integer or a float | `"zIndexHitEffects": 6.5` | Belongs to a note. Sets the Z index for the hit effects of the note. Defaults to `7`. |
| `tint` | [R, G, B], as seen in `colorEvents`; `null` | `"tint": [255, 0, 0]` | Belongs to a note. Sets the tint for the note. Defaults to `null`. |
| `tintHitEffects` | [R, G, B], as seen in `colorEvents`; `null` | `"tintHitEffects": [255, 0, 0]` | Belongs to a note. Sets the tint for the hit effects of the note. Defaults to `null`. |
| `judgeSize` | a positive number or 0 | `"judgeSize": 1.5` | Belongs to a note. Determines the width of the judgment area of the note. Defaults to `size`. |

### Video enhancements

Expand Down
14 changes: 11 additions & 3 deletions src/lib/player/objects/Line.ts
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Expand Up @@ -44,6 +44,7 @@ export class Line {
private _rotationModifier: 1 | -1 = 1;
private _rotationOffset: 0 | 180 = 0;
private _rotateWithParent: boolean = false;
private _integrateSpeedEasings: boolean = false;

private _curX = [];
private _curY = [];
Expand Down Expand Up @@ -109,6 +110,8 @@ export class Line {

this._hasAttach = !!this._data.attachUI;
this._rotateWithParent = this._data.rotateWithFather ?? false;
this._integrateSpeedEasings =
this._data.integrateSpeedEasings ?? this._scene.chart.META.RPEVersion >= 170;
this._line.setScale(
this._scene.p(1) * (this._scaleX ?? 1),
(this._hasCustomTexture
Expand Down Expand Up @@ -430,18 +433,23 @@ export class Line {
}
while (cur[layerIndex] < events.length - 1 && beat > events[cur[layerIndex] + 1].startBeat) {
this._lastHeight +=
getIntegral(events[cur[layerIndex]], this._scene.bpmList) +
getIntegral(events[cur[layerIndex]], this._scene.bpmList, this._integrateSpeedEasings) +
events[cur[layerIndex]].end *
(getTimeSec(this._scene.bpmList, events[cur[layerIndex] + 1].startBeat) -
getTimeSec(this._scene.bpmList, events[cur[layerIndex]].endBeat));
cur[layerIndex]++;
}
let height = this._lastHeight;
if (beat <= events[cur[layerIndex]].endBeat) {
height += getIntegral(events[cur[layerIndex]], this._scene.bpmList, beat);
height += getIntegral(
events[cur[layerIndex]],
this._scene.bpmList,
this._integrateSpeedEasings,
beat,
);
} else {
height +=
getIntegral(events[cur[layerIndex]], this._scene.bpmList) +
getIntegral(events[cur[layerIndex]], this._scene.bpmList, this._integrateSpeedEasings) +
events[cur[layerIndex]].end *
(getTimeSec(this._scene.bpmList, beat) -
getTimeSec(this._scene.bpmList, events[cur[layerIndex]].endBeat));
Expand Down
212 changes: 208 additions & 4 deletions src/lib/player/utils.ts
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Expand Up @@ -90,6 +90,172 @@ const EASINGS: ((x: number) => number)[] = [
(x) => (x < 0.5 ? (1 - EASINGS[25](1 - 2 * x)) / 2 : (1 + EASINGS[25](2 * x - 1)) / 2),
];

const EASING_INTEGRALS: ((x: number) => number)[] = [
(x) => (x * x) / 2,
(x) => (2 / Math.PI) * (1 - Math.cos((x * Math.PI) / 2)),
(x) => x - (2 / Math.PI) * Math.sin((x * Math.PI) / 2),
(x) => x * x - (x * x * x) / 3,
(x) => (x * x * x) / 3,
(x) => x / 2 - Math.sin(Math.PI * x) / (2 * Math.PI),
(x) => (x < 0.5 ? (2 / 3) * Math.pow(x, 3) : 2 * x * x - (2 / 3) * Math.pow(x, 3) - x + 1 / 6),
(x) => (3 / 2) * x * x - x * x * x + Math.pow(x, 4) / 4,
(x) => Math.pow(x, 4) / 4,
(x) => 2 * x * x - 2 * Math.pow(x, 3) + Math.pow(x, 4) - Math.pow(x, 5) / 5,
(x) => Math.pow(x, 5) / 5,
(x) =>
x < 0.5 ? Math.pow(x, 4) : -3 * x + 6 * x * x - 4 * Math.pow(x, 3) + Math.pow(x, 4) + 0.5,
(x) =>
x < 0.5
? (8 / 5) * Math.pow(x, 5)
: -7 * x +
16 * x * x -
16 * Math.pow(x, 3) +
8 * Math.pow(x, 4) -
(8 / 5) * Math.pow(x, 5) +
11 / 10,
(x) =>
(5 / 2) * x * x -
(10 / 3) * Math.pow(x, 3) +
(5 / 2) * Math.pow(x, 4) -
Math.pow(x, 5) +
Math.pow(x, 6) / 6,
(x) => Math.pow(x, 6) / 6,
(x) => x - (1 - Math.pow(2, -10 * x)) / (10 * Math.LN2),
(x) => (Math.pow(2, 10 * x - 10) - Math.pow(2, -10)) / (10 * Math.LN2),
(x) =>
0.5 * ((x - 1) * Math.sqrt(Math.max(0, 1 - Math.pow(x - 1, 2))) + Math.asin(x - 1)) +
Math.PI / 4,
(x) =>
x - 0.5 * (x * Math.sqrt(Math.max(0, 1 - x * x)) + Math.asin(Math.max(-1, Math.min(1, x)))),
(x) => {
const a = 2.70158;
const b = 1.70158;
return (
(1 - a + b) * x +
((3 * a - 2 * b) / 2) * x * x +
((-3 * a + b) / 3) * Math.pow(x, 3) +
(a / 4) * Math.pow(x, 4)
);
},
(x) => (2.70158 / 4) * Math.pow(x, 4) - (1.70158 / 3) * Math.pow(x, 3),
(x) =>
x < 0.5
? 0.5 * x -
0.25 * x * Math.sqrt(Math.max(0, 1 - 4 * x * x)) -
0.125 * Math.asin(Math.max(-1, Math.min(1, 2 * x)))
: 0.5 * x -
0.25 * (1 - x) * Math.sqrt(Math.max(0, 1 - 4 * (1 - x) * (1 - x))) -
0.125 * Math.asin(Math.max(-1, Math.min(1, 2 * (1 - x)))),
(x) => {
const s = 2.59491;
x = clamp(x, 0, 1);
if (x <= 0.5) return (s + 1) * Math.pow(x, 4) - (2 * s * Math.pow(x, 3)) / 3;
const Ihalf = (s + 1) * Math.pow(0.5, 4) - (2 * s * Math.pow(0.5, 3)) / 3;
const F = (t: number) =>
(s + 1) * Math.pow(t, 4) -
((10 * s + 12) / 3) * Math.pow(t, 3) +
((8 * s + 12) / 2) * t * t -
(2 * s + 3) * t;
return Ihalf + (F(x) - F(0.5));
},
// 23
(x) => {
x = clamp(x, 0, 1);
const K = 10 * Math.LN2;
const A = ((2 * Math.PI) / 3) * 10;
const B = -0.75 * ((2 * Math.PI) / 3);
const H = (t: number) =>
(Math.exp(-K * t) * (-K * Math.sin(A * t + B) - A * Math.cos(A * t + B))) / (A * A + K * K);
return x + (H(x) - H(0));
},
(x) => {
x = clamp(x, 0, 1);
const K = 10 * Math.LN2;
const A = ((2 * Math.PI) / 3) * 10;
const B = -10.75 * ((2 * Math.PI) / 3);
const C = Math.pow(2, -10);
const G = (t: number) =>
(-C * Math.exp(K * t) * (K * Math.sin(A * t + B) - A * Math.cos(A * t + B))) /
(A * A + K * K);
return G(x) - G(0);
},
(x) => {
x = clamp(x, 0, 1);
const A = 7.5625;
const b1 = 1 / 2.75;
const b2 = 2 / 2.75;
const b3 = 2.5 / 2.75;
const c1 = 1.5 / 2.75;
const c2 = 2.25 / 2.75;
const c3 = 2.625 / 2.75;
const I_b1 = (A * Math.pow(b1, 3)) / 3;
const I_b2 = I_b1 + (A / 3) * (Math.pow(b2 - c1, 3) - Math.pow(b1 - c1, 3)) + 0.75 * (b2 - b1);
const I_b3 =
I_b2 + (A / 3) * (Math.pow(b3 - c2, 3) - Math.pow(b2 - c2, 3)) + 0.9375 * (b3 - b2);
if (x < b1) return (A * Math.pow(x, 3)) / 3;
if (x < b2)
return I_b1 + (A / 3) * (Math.pow(x - c1, 3) - Math.pow(b1 - c1, 3)) + 0.75 * (x - b1);
if (x < b3)
return I_b2 + (A / 3) * (Math.pow(x - c2, 3) - Math.pow(b2 - c2, 3)) + 0.9375 * (x - b2);
return I_b3 + (A / 3) * (Math.pow(x - c3, 3) - Math.pow(b3 - c3, 3)) + 0.984375 * (x - b3);
},
(x) => {
x = clamp(x, 0, 1);
const A = 7.5625;
const b1 = 1 / 2.75;
const b2 = 2 / 2.75;
const b3 = 2.5 / 2.75;
const c1 = 1.5 / 2.75;
const c2 = 2.25 / 2.75;
const c3 = 2.625 / 2.75;
const outIntegral = (u: number) => {
u = clamp(u, 0, 1);
const I_b1 = (A * Math.pow(b1, 3)) / 3;
const I_b2 =
I_b1 + (A / 3) * (Math.pow(b2 - c1, 3) - Math.pow(b1 - c1, 3)) + 0.75 * (b2 - b1);
const I_b3 =
I_b2 + (A / 3) * (Math.pow(b3 - c2, 3) - Math.pow(b2 - c2, 3)) + 0.9375 * (b3 - b2);
if (u < b1) return (A * Math.pow(u, 3)) / 3;
if (u < b2)
return I_b1 + (A / 3) * (Math.pow(u - c1, 3) - Math.pow(b1 - c1, 3)) + 0.75 * (u - b1);
if (u < b3)
return I_b2 + (A / 3) * (Math.pow(u - c2, 3) - Math.pow(b2 - c2, 3)) + 0.9375 * (u - b2);
return I_b3 + (A / 3) * (Math.pow(u - c3, 3) - Math.pow(b3 - c3, 3)) + 0.984375 * (u - b3);
};
const I1 = outIntegral(1);
return x - (I1 - outIntegral(1 - x));
},
(x) => {
x = clamp(x, 0, 1);
const A = 7.5625;
const b1 = 1 / 2.75;
const b2 = 2 / 2.75;
const b3 = 2.5 / 2.75;
const c1 = 1.5 / 2.75;
const c2 = 2.25 / 2.75;
const c3 = 2.625 / 2.75;
const outIntegral = (u: number) => {
u = clamp(u, 0, 1);
const I_b1 = (A * Math.pow(b1, 3)) / 3;
const I_b2 =
I_b1 + (A / 3) * (Math.pow(b2 - c1, 3) - Math.pow(b1 - c1, 3)) + 0.75 * (b2 - b1);
const I_b3 =
I_b2 + (A / 3) * (Math.pow(b3 - c2, 3) - Math.pow(b2 - c2, 3)) + 0.9375 * (b3 - b2);
if (u < b1) return (A * Math.pow(u, 3)) / 3;
if (u < b2)
return I_b1 + (A / 3) * (Math.pow(u - c1, 3) - Math.pow(b1 - c1, 3)) + 0.75 * (u - b1);
if (u < b3)
return I_b2 + (A / 3) * (Math.pow(u - c2, 3) - Math.pow(b2 - c2, 3)) + 0.9375 * (u - b2);
return I_b3 + (A / 3) * (Math.pow(u - c3, 3) - Math.pow(b3 - c3, 3)) + 0.984375 * (u - b3);
};
const I1 = outIntegral(1);
if (x <= 0.5) {
return x / 2 + (I1 - outIntegral(1 - 2 * x)) / 4;
}
return x / 2 + (I1 + outIntegral(2 * x - 1)) / 4;
},
];

const calculateEasingValue = (
func: (x: number) => number,
x: number,
Expand Down Expand Up @@ -121,6 +287,22 @@ const EASING_DERIVATIVE_ENDS = EASINGS.map((func) => [
calculateDerivativeValue(func, 1),
]);

const calculateEasingIntegral = (
type: number,
x: number,
easingLeft = 0,
easingRight = 1,
): number => {
const scaledX = easingLeft + (easingRight - easingLeft) * x;

if (type < 1 || type > EASING_INTEGRALS.length) {
return (scaledX * scaledX) / 2;
}
const func = EASING_INTEGRALS[type - 1];
// ∫[left to scaledX] f(t) dt = F(scaledX) - F(left)
return func(scaledX) - func(easingLeft);
};

const sanitizeEasingParams = (type: number, x: number, easingLeft: number, easingRight: number) => {
return {
type: type > 0 && type <= EASINGS.length ? type : 1,
Expand Down Expand Up @@ -673,18 +855,34 @@ export const integrate = (
return k * calculateEasingValue(EASINGS[p.type - 1], p.x, p.easingLeft, p.easingRight) + b * p.x;
};

export const integrate2 = (
type: number,
x: number,
k: number,
c: number,
easingLeft = 0,
easingRight = 1,
): number => {
const integral = calculateEasingIntegral(type, x, easingLeft, easingRight);
return k * integral + c * x;
};

export const getIntegral = (
event: SpeedEvent | undefined,
bpmList: Bpm[],
integrateEasings: boolean,
beat: number | undefined = undefined,
): number => {
if (!event) return 0;
if (beat === undefined || beat >= event.endBeat) beat = event.endBeat;
const startSec = getTimeSec(bpmList, event.startBeat);
const progressedSec = getTimeSec(bpmList, beat) - startSec;
if ('easingType' in event && event.easingType > 1) {
const easingLeft = 'easingLeft' in event ? event.easingLeft : 0;
const easingRight = 'easingRight' in event ? event.easingRight : 1;
if (!('easingType' in event) || event.easingType <= 1) {
return ((event.start + (getEventValue(beat, event) as number)) * progressedSec) / 2;
}
const easingLeft = 'easingLeft' in event ? event.easingLeft : 0;
const easingRight = 'easingRight' in event ? event.easingRight : 1;
if (!integrateEasings) {
const df0 = derivative(event.easingType, 0, easingLeft, easingRight);
const df1 = derivative(event.easingType, 1, easingLeft, easingRight);
const k = (event.end - event.start) / (df1 - df0);
Expand All @@ -695,8 +893,14 @@ export const getIntegral = (
(integrate(event.easingType, x, k, b, easingLeft, easingRight) * lengthSec) /
(event.endBeat - event.startBeat)
);
} else {
const x = (beat - event.startBeat) / (event.endBeat - event.startBeat);
const easingIntegral = calculateEasingIntegral(event.easingType, x, easingLeft, easingRight);
const scaledIntegral =
event.start * x + ((event.end - event.start) * easingIntegral) / (easingRight - easingLeft);
const lengthSec = getTimeSec(bpmList, event.endBeat) - startSec;
return scaledIntegral * lengthSec;
}
return ((event.start + (getEventValue(beat, event) as number)) * progressedSec) / 2;
};

export const getJudgmentPosition = (input: PointerTap | PointerDrag, line: Line) => {
Expand Down
1 change: 1 addition & 0 deletions src/lib/types.ts
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Expand Up @@ -111,6 +111,7 @@ export interface JudgeLine {
extended?: Extended;
father: number;
rotateWithFather?: boolean;
integrateSpeedEasings?: boolean;
isCover: number;
isGif?: boolean;
notes?: Note[];
Expand Down