緩動函式 Easing Functions

緩動函式 自定義引數隨時間變化的速率。

常見效果

Linear：無緩動效果；
Quadratic：二次方的緩動（t^2）；
Sinusoidal：正弦曲線的緩動（sin(t)）；
Exponential：指數曲線的緩動（2^t）；
Circular：圓形曲線的緩動（sqrt(1-t^2)）；
Cubic：三次方的緩動（t^3）；
Quartic：四次方的緩動（t^4）；
Quintic：五次方的緩動（t^5）；
Elastic：指數衰減的正弦曲線緩動；
Back：超過範圍的三次方緩動（(s+1)t^3 - st^2）；
Bounce：指數衰減的反彈緩動。

緩動方式

每個效果都分三個緩動方式（方法），分別是：
easeIn：從0開始加速的緩動；
easeOut：減速到0的緩動；
easeInOut：前半段從0開始加速，後半段減速到0的緩動。

具體如圖所示：

函式引數說明

每個函式包含 t、b、c 和 d 四個引數

• t = Time - 表示動畫開始以來經過的時間。通常從0開始，通過遊戲迴圈或update函式來緩慢增加。
• b = Beginning value - 動畫的起點，預設從0開始。
• c = Change in value - 從起點到終點的差值。
• d = Duration - 完成動畫所需的時間。

使用示例

t = 0 - 動畫從0s開始
b = 200 - 物件 x 座標的起始位置為200
c = 300 - 物件必須向右移動 300，到500 結束
d = 1 - 物件用 1 秒時間來完成從 200 到 500 的移動

Linear 線性

function easeLinear (t, b, c, d) {
    return c * t / d + b;
}

Quadratic 二次漸變

Quadratic easing in

function easeInQuad (t, b, c, d) {
    return c * (t /= d) * t + b;
}

Quadratic easing out

function easeOutQuad (t, b, c, d) {
    return -c * (t /= d) * (t - 2) + b;
}

Quadratic easing in and out

function easeInOutQuad (t, b, c, d) {
    if ((t /= d / 2) < 1) return c / 2 * t * t + b;
    return -c / 2 * ((--t) * (t - 2) - 1) + b;
}

Sinusoidal 正弦漸變

Sinusoidal easing in

function easeInSine (t, b, c, d) {
    return -c * Math.cos(t / d * (Math.PI / 2)) + c + b;
}

Sinusoidal easing out

function easeOutSine (t, b, c, d) {
    return c * Math.sin(t / d * (Math.PI / 2)) + b;
}

Sinusoidal easing in and out

function easeInOutSine (t, b, c, d) {
    return -c / 2 * (Math.cos(Math.PI * t / d) - 1) + b;
}

Exponential 指數漸變

Exponential easing in

function easeInExpo (t, b, c, d) {
    return (t == 0) ? b : c * Math.pow(2, 10 * (t / d - 1)) + b;
}

Exponential easing out

function easeOutExpo (t, b, c, d) {
    return (t == d) ? b + c : c * (-Math.pow(2, -10 * t / d) + 1) + b;
}

Exponential easing in and out

function easeInOutExpo (t, b, c, d) {
    if (t == 0) return b;
    if (t == d) return b + c;
    if ((t /= d / 2) < 1) return c / 2 * Math.pow(2, 10 * (t - 1)) + b;
    return c / 2 * (-Math.pow(2, -10 * --t) + 2) + b;
}

Circular 圓形曲線

Circular easing in

function easeInCirc (t, b, c, d) {
    return -c * (Math.sqrt(1 - (t /= d) * t) - 1) + b;
}

Circular easing out

function easeOutCirc (t, b, c, d) {
    return c * Math.sqrt(1 - (t = t / d - 1) * t) + b;
}

Circular easing in and out

function easeInOutCirc (t, b, c, d) {
    if ((t /= d / 2) < 1) return -c / 2 * (Math.sqrt(1 - t * t) - 1) + b;
    return c / 2 * (Math.sqrt(1 - (t -= 2) * t) + 1) + b;
}

Cubic 三次方

Cubic easing in

function easeInCubic (t, b, c, d) {
    return c * (t /= d) * t * t + b;
}

Cubic easing out

function easeOutCubic (t, b, c, d) {
    return c * ((t = t / d - 1) * t * t + 1) + b;
}

Cubic easing in and out

function easeInOutCubic (t, b, c, d) {
    if ((t /= d / 2) < 1) return c / 2 * t * t * t + b;
    return c / 2 * ((t -= 2) * t * t + 2) + b;
}

Quartic 四次方

Quartic easing in

function easeInQuart (t, b, c, d) {
    return c * (t /= d) * t * t * t + b;
}

Quartic easing out

function easeOutQuart (t, b, c, d) {
    return -c * ((t = t / d - 1) * t * t * t - 1) + b;
}

Quartic easing in and out

function easeInOutQuart (t, b, c, d) {
    if ((t /= d / 2) < 1) return c / 2 * t * t * t * t + b;
    return -c / 2 * ((t -= 2) * t * t * t - 2) + b;
}

Quintic 五次方

Quintic easing in

function easeInQuint (t, b, c, d) {
    return c * (t /= d) * t * t * t * t + b;
}

Quintic easing out

function easeOutQuint (t, b, c, d) {
    return c * ((t = t / d - 1) * t * t * t * t + 1) + b;
}

Quintic easing in and out

function easeInOutQuint (t, b, c, d) {
    if ((t /= d / 2) < 1) return c / 2 * t * t * t * t * t + b;
    return c / 2 * ((t -= 2) * t * t * t * t + 2) + b;
}

Elastic 指數衰減正弦曲線

Elastic easing in

function easeInElastic (t, b, c, d) {
    var s = 1.70158;
    var p = 0;
    var a = c;
    if (t == 0) return b;
    if ((t /= d) == 1) return b + c;
    if (!p) p = d * .3;
    if (a < Math.abs(c)) {
        a = c;
        var s = p / 4;
    }
    else var s = p / (2 * Math.PI) * Math.asin(c / a);
    return -(a * Math.pow(2, 10 * (t -= 1)) * Math.sin((t * d - s) * (2 * Math.PI) / p)) + b;
}

Elastic easing out

function easeOutElastic (t, b, c, d) {
    var s = 1.70158;
    var p = 0;
    var a = c;
    if (t == 0) return b;
    if ((t /= d) == 1) return b + c;
    if (!p) p = d * .3;
    if (a < Math.abs(c)) {
        a = c;
        var s = p / 4;
    }
    else var s = p / (2 * Math.PI) * Math.asin(c / a);
    return a * Math.pow(2, -10 * t) * Math.sin((t * d - s) * (2 * Math.PI) / p) + c + b;
}

Elastic easing in and out

function easeInOutElastic (t, b, c, d) {
    var s = 1.70158;
    var p = 0;
    var a = c;
    if (t == 0) return b;
    if ((t /= d / 2) == 2) return b + c;
    if (!p) p = d * (.3 * 1.5);
    if (a < Math.abs(c)) {
        a = c;
        var s = p / 4;
    }
    else var s = p / (2 * Math.PI) * Math.asin(c / a);
    if (t < 1) return -.5 * (a * Math.pow(2, 10 * (t -= 1)) * Math.sin((t * d - s) * (2 * Math.PI) / p)) + b;
    return a * Math.pow(2, -10 * (t -= 1)) * Math.sin((t * d - s) * (2 * Math.PI) / p) * .5 + c + b;
}

Back

Back easing in

function easeInBack (t, b, c, d) {
    if (s == undefined) s = 1.70158;
    return c * (t /= d) * t * ((s + 1) * t - s) + b;
}

Back easing out

function easeOutBack (t, b, c, d) {
    if (s == undefined) s = 1.70158;
    return c * ((t = t / d - 1) * t * ((s + 1) * t + s) + 1) + b;
}

Back easing in and out

function easeInOutBack (t, b, c, d) {
    if (s == undefined) s = 1.70158;
    if ((t /= d / 2) < 1) return c / 2 * (t * t * (((s *= (1.525)) + 1) * t - s)) + b;
    return c / 2 * ((t -= 2) * t * (((s *= (1.525)) + 1) * t + s) + 2) + b;
}

Bounce

Bounce easing in

function easeInBounce(t, b, c, d) {
   return c - easeOutBounce(d - t, 0, c, d) + b;
}

Bounce easing out

function easeOutBounce(t, b, c, d) {
    if ((t/=d) < (1/2.75)) {
      return c*(7.5625*t*t) + b;
    } else if (t < (2/2.75)) {
      return c*(7.5625*(t-=(1.5/2.75))*t + .75) + b;
    } else if (t < (2.5/2.75)) {
      return c*(7.5625*(t-=(2.25/2.75))*t + .9375) + b;
    } else {
      return c*(7.5625*(t-=(2.625/2.75))*t + .984375) + b;
    }
  }

Bounce easing in and out

function easeInOutBounce(t, b, c, d) {
    if (t < d/2) return easeInBounce (t*2, 0, c, d) * .5 + b;
    return easeOutBounce (t*2-d, 0, c, d) * .5 + c*.5 + b;
  }

參考資料

Easing Functions Cheat Sheet

EASING FUNCTIONS FOR JAVASCRIPT