cocos-engine/cocos/core/easing/easing.ts

/*
 Copyright (c) 2020 Xiamen Yaji Software Co., Ltd.

 https://www.cocos.com/

 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated engine source code (the "Software"), a limited,
 worldwide, royalty-free, non-assignable, revocable and non-exclusive license
 to use Cocos Creator solely to develop games on your target platforms. You shall
 not use Cocos Creator software for developing other software or tools that's
 used for developing games. You are not granted to publish, distribute,
 sublicense, and/or sell copies of Cocos Creator.

 The software or tools in this License Agreement are licensed, not sold.
 Xiamen Yaji Software Co., Ltd. reserves all rights not expressly granted to you.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 */

export function constant () {
    return 0;
}

export function linear (k: number) {
    return k;
}

export function quadIn (k: number) {
    return k * k;
}

export function quadOut (k: number) {
    return k * (2 - k);
}

export function quadInOut (k: number) {
    k *= 2;
    if (k < 1) {
        return 0.5 * k * k;
    }
    return -0.5 * (--k * (k - 2) - 1);
}

export function cubicIn (k: number) {
    return k * k * k;
}

export function cubicOut (k: number) {
    return --k * k * k + 1;
}

export function cubicInOut (k: number) {
    k *= 2;
    if (k < 1) {
        return 0.5 * k * k * k;
    }
    return 0.5 * ((k -= 2) * k * k + 2);
}

export function quartIn (k: number) {
    return k * k * k * k;
}

export function quartOut (k: number) {
    return 1 - (--k * k * k * k);
}

export function quartInOut (k: number) {
    k *= 2;
    if (k < 1) {
        return 0.5 * k * k * k * k;
    }
    return -0.5 * ((k -= 2) * k * k * k - 2);
}

export function quintIn (k: number) {
    return k * k * k * k * k;
}

export function quintOut (k: number) {
    return --k * k * k * k * k + 1;
}

export function quintInOut (k: number) {
    k *= 2;
    if (k < 1) {
        return 0.5 * k * k * k * k * k;
    }
    return 0.5 * ((k -= 2) * k * k * k * k + 2);
}

export function sineIn (k: number) {
    if (k === 1) {
        return 1;
    }
    return 1 - Math.cos(k * Math.PI / 2);
}

export function sineOut (k: number) {
    return Math.sin(k * Math.PI / 2);
}

export function sineInOut (k: number) {
    return 0.5 * (1 - Math.cos(Math.PI * k));
}

export function expoIn (k: number) {
    return k === 0 ? 0 : Math.pow(1024, k - 1);
}

export function expoOut (k: number) {
    return k === 1 ? 1 : 1 - Math.pow(2, -10 * k);
}

export function expoInOut (k: number) {
    if (k === 0) {
        return 0;
    }
    if (k === 1) {
        return 1;
    }
    k *= 2;
    if (k < 1) {
        return 0.5 * Math.pow(1024, k - 1);
    }
    return 0.5 * (-Math.pow(2, -10 * (k - 1)) + 2);
}

export function circIn (k: number) {
    return 1 - Math.sqrt(1 - k * k);
}

export function circOut (k: number) {
    return Math.sqrt(1 - (--k * k));
}

export function circInOut (k: number) {
    k *= 2;
    if (k < 1) {
        return -0.5 * (Math.sqrt(1 - k * k) - 1);
    }
    return 0.5 * (Math.sqrt(1 - (k -= 2) * k) + 1);
}

export function elasticIn (k: number) {
    let s;
    let a = 0.1;
    const p = 0.4;
    if (k === 0) {
        return 0;
    }
    if (k === 1) {
        return 1;
    }
    if (!a || a < 1) {
        a = 1;
        s = p / 4;
    } else {
        s = p * Math.asin(1 / a) / (2 * Math.PI);
    }
    return -(a * Math.pow(2, 10 * (k -= 1)) * Math.sin((k - s) * (2 * Math.PI) / p));
}

export function elasticOut (k: number) {
    let s;
    let a = 0.1;
    const p = 0.4;
    if (k === 0) {
        return 0;
    }
    if (k === 1) {
        return 1;
    }
    if (!a || a < 1) {
        a = 1;
        s = p / 4;
    } else {
        s = p * Math.asin(1 / a) / (2 * Math.PI);
    }
    return (a * Math.pow(2, -10 * k) * Math.sin((k - s) * (2 * Math.PI) / p) + 1);
}

export function elasticInOut (k: number) {
    let s;
    let a = 0.1;
    const p = 0.4;
    if (k === 0) {
        return 0;
    }
    if (k === 1) {
        return 1;
    }
    if (!a || a < 1) {
        a = 1;
        s = p / 4;
    } else {
        s = p * Math.asin(1 / a) / (2 * Math.PI);
    }
    k *= 2;
    if (k < 1) {
        return -0.5
            * (a * Math.pow(2, 10 * (k -= 1)) * Math.sin((k - s) * (2 * Math.PI) / p));
    }
    return a * Math.pow(2, -10 * (k -= 1)) * Math.sin((k - s) * (2 * Math.PI) / p) * 0.5 + 1;
}

export function backIn (k: number) {
    if (k === 1) {
        return 1;
    }
    const s = 1.70158;
    return k * k * ((s + 1) * k - s);
}

export function backOut (k: number) {
    if (k === 0) {
        return 0;
    }
    const s = 1.70158;
    return --k * k * ((s + 1) * k + s) + 1;
}

export function backInOut (k: number) {
    const s = 1.70158 * 1.525;
    k *= 2;
    if (k < 1) {
        return 0.5 * (k * k * ((s + 1) * k - s));
    }
    return 0.5 * ((k -= 2) * k * ((s + 1) * k + s) + 2);
}

export function bounceIn (k: number) {
    return 1 - bounceOut(1 - k);
}

export function bounceOut (k: number) {
    if (k < (1 / 2.75)) {
        return 7.5625 * k * k;
    } else if (k < (2 / 2.75)) {
        return 7.5625 * (k -= (1.5 / 2.75)) * k + 0.75;
    } else if (k < (2.5 / 2.75)) {
        return 7.5625 * (k -= (2.25 / 2.75)) * k + 0.9375;
    } else {
        return 7.5625 * (k -= (2.625 / 2.75)) * k + 0.984375;
    }
}

export function bounceInOut (k: number) {
    if (k < 0.5) {
        return bounceIn(k * 2) * 0.5;
    }
    return bounceOut(k * 2 - 1) * 0.5 + 0.5;
}

export function smooth (k: number) {
    if (k <= 0) {
        return 0;
    }
    if (k >= 1) {
        return 1;
    }
    return k * k * (3 - 2 * k);
}

export function fade (k: number) {
    if (k <= 0) {
        return 0;
    }
    if (k >= 1) {
        return 1;
    }
    return k * k * k * (k * (k * 6 - 15) + 10);
}

export const quadOutIn = _makeOutIn(quadIn, quadOut);
export const cubicOutIn = _makeOutIn(cubicIn, cubicOut);
export const quartOutIn = _makeOutIn(quartIn, quartOut);
export const quintOutIn = _makeOutIn(quintIn, quintOut);
export const sineOutIn = _makeOutIn(sineIn, sineOut);
export const expoOutIn = _makeOutIn(expoIn, expoOut);
export const circOutIn = _makeOutIn(circIn, circOut);
export const elasticOutIn = _makeOutIn(elasticIn, elasticOut);
export const backOutIn = _makeOutIn(backIn, backOut);
export const bounceOutIn = _makeOutIn(bounceIn, bounceOut);

function _makeOutIn (fnIn: (k: number) => number, fnOut: (k: number) => number) {
    return (k: number) => {
        if (k < 0.5) {
            return fnOut(k * 2) / 2;
        }
        return fnIn(2 * k - 1) / 2 + 0.5;
    };
}