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/**
* CREDITS: Implementation based on Firefox's nsSMILKeySpline.cpp
* MIT license
*
* origin: https://github.com/d3/d3-ease/pull/14/commits/c6734e347c280eeb129ea273c975f57034f3ff8e
*/
const
BINARY_SEARCH_PRECISION = 1e-7,
BINARY_SEARCH_ITERATIONS = 10,
NEWTON_ITERATIONS = 4,
NEWTON_MIN_SLOPE = 0.02,
SAMPLES_COUNT = 11,
SAMPLES_LAST = SAMPLES_COUNT - 1,
SAMPLES_STEP = 1.0 / (SAMPLES_COUNT - 1),
FLOAT_ARRAYS_AVAILABLE = typeof Float32Array === "function";
/**
* @brief Calculate Px(t) or Py(t) given B and C points
* @param {number} t
* @param {number} b
* @param {number} c
* @return {number}
*/
function calcBezier(t, b, c) {
// eslint-disable-next-line
return (((1.0 + (b *= 3.0) - (c *= 3.0)) * t + c - 2.0 * b) * t + b) * t;
}
/**
* @brief Calculate (dPx/dt)(t) or (dPy/dt)(t) given B and C points
* @param {number} t
* @param {number} b
* @param {number} c
* @return {number}
*/
function calcSlope(t, b, c) {
// eslint-disable-next-line
return ((1.0 + (b *= 3.0) - (c *= 3.0)) * t * 3.0 + 2.0 * c - 4.0 * b) * t + b;
}
/**
* @brief Estimate t (from [t1, t2] interval) given x value and points B and C
* @param {number} x
* @param {number} t1
* @param {number} t2
* @param {number} b
* @param {number} c
* @return {number}
*/
function binarySearch(x, t1, t2, b, c) {
var t, i = 0, foundX;
do {
t = (t1 + t2) / 2.0;
if (x < (foundX = calcBezier(t, b, c))) {
t2 = t;
}
else {
t1 = t;
}
} while (++i < BINARY_SEARCH_ITERATIONS &&
Math.abs(x - foundX) > BINARY_SEARCH_PRECISION);
return t;
}
/**
* @brief Estimate t using Newton-Raphson method given points B and C
* @param {number} x
* @param {number} guessForT
* @param {number} b
* @param {number} c
* @return {number}
*/
function newtonRaphsonIterate(x, guessForT, b, c) {
var currentX, currentSlope;
for (var i = 0; i < NEWTON_ITERATIONS; ++i) {
currentX = calcBezier(guessForT, b, c) - x;
currentSlope = calcSlope(guessForT, b, c);
Iif (currentSlope === 0.0) {
return guessForT;
}
guessForT -= currentX / currentSlope;
}
return guessForT;
}
/**
* @brief Estimates t given points B and C, and a set of precalculated values
* @param {number} x
* @param {number} b
* @param {number} c
* @param {number[]|Float32Array} sampleValues
* @return {number}
*/
function estimateT(x, b, c, sampleValues) {
var currentSample = 0,
dist,
intervalStart,
initialSlope,
guessForT;
while (currentSample !== SAMPLES_LAST && sampleValues[currentSample] <= x) {
++currentSample;
}
intervalStart = --currentSample * SAMPLES_STEP;
// Interpolate to provide an initial guess for t
dist = (x - sampleValues[currentSample]) /
(sampleValues[currentSample + 1] - sampleValues[currentSample]);
guessForT = intervalStart + (dist * SAMPLES_STEP);
initialSlope = calcSlope(guessForT, b, c);
if (initialSlope >= NEWTON_MIN_SLOPE) {
return newtonRaphsonIterate(x, guessForT, b, c);
}
else if (initialSlope === 0.0) {
return guessForT;
}
else {
return binarySearch(x, intervalStart, intervalStart + SAMPLES_STEP, b, c);
}
}
/**
* @brief Assumes points A = (0, 0) and D = (1, 1)
* @param {number} bx
* @param {number} by
* @param {number} cx
* @param {number} cy
*/
export function cubicBezier(bx, by, cx, cy) {
var sampleValues = (FLOAT_ARRAYS_AVAILABLE ?
new Float32Array(SAMPLES_COUNT) :
new Array(SAMPLES_COUNT));
// Limit x to [0, 1] interval
bx = Math.max(0.0, Math.min(1.0, +bx));
cx = Math.max(0.0, Math.min(1.0, +cx));
by = +by;
cy = +cy;
// Precompute sample x-values
for (var i = 0; i < SAMPLES_COUNT; ++i) {
sampleValues[i] = calcBezier(i * SAMPLES_STEP, bx, cx);
}
function bezier(/** @type {number} */ x) {
var t = estimateT(x, bx, cx, sampleValues);
return calcBezier(t, by, cy);
}
return bezier;
}
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