In-world UX

cubicBezier.js

@@ -0,0 +1,111 @@
+/**
+ * https://github.com/gre/bezier-easing
+ * BezierEasing - use bezier curve for transition easing function
+ * by Gaëtan Renaudeau 2014 - 2015 – MIT License
+ */
+
+const cubicBezier = (() => {
+
+// These values are established by empiricism with tests (tradeoff: performance VS precision)
+var NEWTON_ITERATIONS = 4;
+var NEWTON_MIN_SLOPE = 0.001;
+var SUBDIVISION_PRECISION = 0.0000001;
+var SUBDIVISION_MAX_ITERATIONS = 10;
+
+var kSplineTableSize = 11;
+var kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);
+
+var float32ArraySupported = typeof Float32Array === 'function';
+
+function A (aA1, aA2) { return 1.0 - 3.0 * aA2 + 3.0 * aA1; }
+function B (aA1, aA2) { return 3.0 * aA2 - 6.0 * aA1; }
+function C (aA1)      { return 3.0 * aA1; }
+
+// Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
+function calcBezier (aT, aA1, aA2) { return ((A(aA1, aA2) * aT + B(aA1, aA2)) * aT + C(aA1)) * aT; }
+
+// Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
+function getSlope (aT, aA1, aA2) { return 3.0 * A(aA1, aA2) * aT * aT + 2.0 * B(aA1, aA2) * aT + C(aA1); }
+
+function binarySubdivide (aX, aA, aB, mX1, mX2) {
+  var currentX, currentT, i = 0;
+  do {
+    currentT = aA + (aB - aA) / 2.0;
+    currentX = calcBezier(currentT, mX1, mX2) - aX;
+    if (currentX > 0.0) {
+      aB = currentT;
+    } else {
+      aA = currentT;
+    }
+  } while (Math.abs(currentX) > SUBDIVISION_PRECISION && ++i < SUBDIVISION_MAX_ITERATIONS);
+  return currentT;
+}
+
+function newtonRaphsonIterate (aX, aGuessT, mX1, mX2) {
+ for (var i = 0; i < NEWTON_ITERATIONS; ++i) {
+   var currentSlope = getSlope(aGuessT, mX1, mX2);
+   if (currentSlope === 0.0) {
+     return aGuessT;
+   }
+   var currentX = calcBezier(aGuessT, mX1, mX2) - aX;
+   aGuessT -= currentX / currentSlope;
+ }
+ return aGuessT;
+}
+
+function LinearEasing (x) {
+  return x;
+}
+
+return function bezier (mX1, mY1, mX2, mY2) {
+  if (!(0 <= mX1 && mX1 <= 1 && 0 <= mX2 && mX2 <= 1)) {
+    throw new Error('bezier x values must be in [0, 1] range');
+  }
+
+  if (mX1 === mY1 && mX2 === mY2) {
+    return LinearEasing;
+  }
+
+  // Precompute samples table
+  var sampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);
+  for (var i = 0; i < kSplineTableSize; ++i) {
+    sampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
+  }
+
+  function getTForX (aX) {
+    var intervalStart = 0.0;
+    var currentSample = 1;
+    var lastSample = kSplineTableSize - 1;
+
+    for (; currentSample !== lastSample && sampleValues[currentSample] <= aX; ++currentSample) {
+      intervalStart += kSampleStepSize;
+    }
+    --currentSample;
+
+    // Interpolate to provide an initial guess for t
+    var dist = (aX - sampleValues[currentSample]) / (sampleValues[currentSample + 1] - sampleValues[currentSample]);
+    var guessForT = intervalStart + dist * kSampleStepSize;
+
+    var initialSlope = getSlope(guessForT, mX1, mX2);
+    if (initialSlope >= NEWTON_MIN_SLOPE) {
+      return newtonRaphsonIterate(aX, guessForT, mX1, mX2);
+    } else if (initialSlope === 0.0) {
+      return guessForT;
+    } else {
+      return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize, mX1, mX2);
+    }
+  }
+
+  return function BezierEasing (x) {
+    // Because JavaScript number are imprecise, we should guarantee the extremes are right.
+    if (x === 0) {
+      return 0;
+    }
+    if (x === 1) {
+      return 1;
+    }
+    return calcBezier(getTForX(x), mY1, mY2);
+  };
+};
+
+})();