easeBezier

with In, Out and InOut for symmetry with the others

closes #3

src/bezier.js

@@ -0,0 +1,51 @@
+// import {abs, epsilon} from "./math.js";
+
+const epsilon = 1e-6, {abs} = Math;
+
+
+function bezier(x1, y1, x2, y2) {
+  function bezier(x1, x2) {
+    const a = 1 - 3 * x2 + 3 * x1,
+      b = 3 * x2 - 6 * x1,
+      c = 3 * x1;
+    return t => ((a * t + b) * t + c) * t;
+  }
+  function bezierDerivate(x1, x2) {
+    const a = 3 - 9 * x2 + 9 * x1,
+      b = 6 * x2 - 12 * x1,
+      c = 3 * x1;
+    return t => (a * t + b) * t + c;
+  }
+  function solve(f, fp, y) {
+    let x = y;
+    for (let i = 0; i < 100; i++) {
+      const delta = (y - f(x)) / (fp(x) || epsilon),
+        absd = abs(delta);
+      x += absd < 0.1 ? delta : (0.1 * delta) / absd;
+      if (absd < 1e-9) break;
+    }
+    return x < 0 ? 0 : x > 1 ? 1 : x;
+  }
+  return x1 === y1 && x2 === y2 // useless(?) shortcut when y===x
+    ? x => x
+    : x => bezier(y1, y2)(solve(bezier(x1, x2), bezierDerivate(x1, x2), x));
+}
+
+function custom(x1, y1, x2, y2, dir) {
+  x1 = +x1;
+  y1 = +y1;
+  x2 = +x2;
+  y2 = +y2;
+  if (x1 < 0 || x1 > 1 || x2 < 0 || x2 > 1) throw new RangeError("Parameter out of range");
+
+  const b = bezier(x1, y1, x2, y2),
+    _out = t => 1 - b(1 - t),
+    _inout = t => ((t *= 2) < 1 ? b(t) : 2 - b(2 - t)) / 2,
+    f = dir === "out" ? _out : dir === "inout" ? _inout : b;
+  f.points = (x1, y1, x2, y2) => custom(x1, y1, x2, y2, dir);
+  return f;
+}
+
+export const bezierIn = custom(0, 0, 1, 1);
+export const bezierOut = custom(0, 0, 1, 1, "out");
+export const bezierInOut = custom(0, 0, 1, 1, "inout");

src/index.js

@@ -2,6 +2,13 @@ export {
   linear as easeLinear
 } from "./linear.js";
 
+export {
+  bezierIn as easeBezier,
+  bezierIn as easeBezierIn,
+  bezierOut as easeBezierOut,
+  bezierInOut as easeBezierInOut
+} from "./bezier.js";
+
 export {
   quadInOut as easeQuad,
   quadIn as easeQuadIn,