'use strict'; /** * Easing and interpolation functions for variable lerping. * * @module engine/anime/easing */ /** * Easing functions. */ const Easing = { Linear: { None: function(k) { return k; }, }, Quadratic: { In: function(k) { return k * k; }, Out: function(k) { return k * (2 - k); }, InOut: function(k) { if ((k *= 2) < 1) {return 0.5 * k * k;} return -0.5 * (--k * (k - 2) - 1); }, }, Cubic: { In: function(k) { return k * k * k; }, Out: function(k) { return --k * k * k + 1; }, InOut: function(k) { if ((k *= 2) < 1) {return 0.5 * k * k * k;} return 0.5 * ((k -= 2) * k * k + 2); }, }, Quartic: { In: function(k) { return k * k * k * k; }, Out: function(k) { return 1 - (--k * k * k * k); }, InOut: function(k) { if ((k *= 2) < 1) {return 0.5 * k * k * k * k;} return -0.5 * ((k -= 2) * k * k * k - 2); }, }, Quintic: { In: function(k) { return k * k * k * k * k; }, Out: function(k) { return --k * k * k * k * k + 1; }, InOut: function(k) { if ((k *= 2) < 1) {return 0.5 * k * k * k * k * k;} return 0.5 * ((k -= 2) * k * k * k * k + 2); }, }, Sinusoidal: { In: function(k) { return 1 - Math.cos(k * Math.PI / 2); }, Out: function(k) { return Math.sin(k * Math.PI / 2); }, InOut: function(k) { return 0.5 * (1 - Math.cos(Math.PI * k)); }, }, Exponential: { In: function(k) { return k === 0 ? 0 : Math.pow(1024, k - 1); }, Out: function(k) { return k === 1 ? 1 : 1 - Math.pow(2, -10 * k); }, InOut: function(k) { if (k === 0) {return 0;} if (k === 1) {return 1;} if ((k *= 2) < 1) {return 0.5 * Math.pow(1024, k - 1);} return 0.5 * (-Math.pow(2, -10 * (k - 1)) + 2); }, }, Circular: { In: function(k) { return 1 - Math.sqrt(1 - k * k); }, Out: function(k) { return Math.sqrt(1 - (--k * k)); }, InOut: function(k) { if ((k *= 2) < 1) {return -0.5 * (Math.sqrt(1 - k * k) - 1);} return 0.5 * (Math.sqrt(1 - (k -= 2) * k) + 1); }, }, Elastic: { In: function(k) { var s, a = 0.1, 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)); }, Out: function(k) { var s, a = 0.1, 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); }, InOut: function(k) { var s, a = 0.1, 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);} if ((k *= 2) < 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; }, }, Back: { In: function(k) { var s = 1.70158; return k * k * ((s + 1) * k - s); }, Out: function(k) { var s = 1.70158; return --k * k * ((s + 1) * k + s) + 1; }, InOut: function(k) { var s = 1.70158 * 1.525; if ((k *= 2) < 1) {return 0.5 * (k * k * ((s + 1) * k - s));} return 0.5 * ((k -= 2) * k * ((s + 1) * k + s) + 2); }, }, Bounce: { In: function(k) { return 1 - Easing.Bounce.Out(1 - k); }, Out: function(k) { 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; } }, InOut: function(k) { if (k < 0.5) {return Easing.Bounce.In(k * 2) * 0.5;} return Easing.Bounce.Out(k * 2 - 1) * 0.5 + 0.5; }, }, }; /** * Interpolation functions. */ const Interpolation = { Linear: function(v, k) { var m = v.length - 1, f = m * k, i = Math.floor(f), fn = Interpolation.Utils.Linear; if (k < 0) {return fn(v[0], v[1], f);} if (k > 1) {return fn(v[m], v[m - 1], m - f);} return fn(v[i], v[i + 1 > m ? m : i + 1], f - i); }, Bezier: function(v, k) { var b = 0, n = v.length - 1, pw = Math.pow, bn = Interpolation.Utils.Bernstein, i; for (i = 0; i <= n; i++) { b += pw(1 - k, n - i) * pw(k, i) * v[i] * bn(n, i); } return b; }, CatmullRom: function(v, k) { var m = v.length - 1, f = m * k, i = Math.floor(f), fn = Interpolation.Utils.CatmullRom; if (v[0] === v[m]) { if (k < 0) {i = Math.floor(f = m * (1 + k));} return fn(v[(i - 1 + m) % m], v[i], v[(i + 1) % m], v[(i + 2) % m], f - i); } else { if (k < 0) {return v[0] - (fn(v[0], v[0], v[1], v[1], -f) - v[0]);} if (k > 1) {return v[m] - (fn(v[m], v[m], v[m - 1], v[m - 1], f - m) - v[m]);} return fn(v[i ? i - 1 : 0], v[i], v[m < i + 1 ? m : i + 1], v[m < i + 2 ? m : i + 2], f - i); } }, Utils: { Linear: function(p0, p1, t) { return (p1 - p0) * t + p0; }, Bernstein: function(n, i) { var fc = Interpolation.Utils.Factorial; return fc(n) / fc(i) / fc(n - i); }, Factorial: (function() { var a = [1]; return function(n) { var s = 1, i; if (a[n]) {return a[n];} for (i = n; i > 1; i--) {s *= i;} return a[n] = s; }; })(), CatmullRom: function(p0, p1, p2, p3, t) { var v0 = (p2 - p0) * 0.5, v1 = (p3 - p1) * 0.5, t2 = t * t, t3 = t * t2; return (2 * p1 - 2 * p2 + v0 + v1) * t3 + (-3 * p1 + 3 * p2 - 2 * v0 - v1) * t2 + v0 * t + p1; }, }, }; module.exports.Easing = Easing; module.exports.Interpolation = Interpolation;