緩動函數 Easing Functions
緩動函數 自定義參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：超過范圍的三次方緩動（(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，后半段減速到0的緩動。
具體如圖所示：
函數參數說明
每個函數包含 t、b、c 和 d 四個參數
- t = Time - 表示動畫開始以來經過的時間。通常從0開始，通過游戲循環或update函數來緩慢增加。
- b = Beginning value - 動畫的起點，默認從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 - 對象 x 坐標的起始位置為200
c = 300 - 對象必須向右移動 300，到500 結束
d = 1 - 對象用 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;
}