app/node_modules/@ionic/core/components/cubic-bezier.js

/*!
 * (C) Ionic http://ionicframework.com - MIT License
 */
/**
 * Based on:
 * https://stackoverflow.com/questions/7348009/y-coordinate-for-a-given-x-cubic-bezier
 * https://math.stackexchange.com/questions/26846/is-there-an-explicit-form-for-cubic-b%C3%A9zier-curves
 */
/**
 * EXPERIMENTAL
 * Given a cubic-bezier curve, get the x value (time) given
 * the y value (progression).
 * Ex: cubic-bezier(0.32, 0.72, 0, 1);
 * P0: (0, 0)
 * P1: (0.32, 0.72)
 * P2: (0, 1)
 * P3: (1, 1)
 *
 * If you give a cubic bezier curve that never reaches the
 * provided progression, this function will return an empty array.
 */
const getTimeGivenProgression = (p0, p1, p2, p3, progression) => {
    return solveCubicBezier(p0[1], p1[1], p2[1], p3[1], progression).map((tValue) => {
        return solveCubicParametricEquation(p0[0], p1[0], p2[0], p3[0], tValue);
    });
};
/**
 * Solve a cubic equation in one dimension (time)
 */
const solveCubicParametricEquation = (p0, p1, p2, p3, t) => {
    const partA = 3 * p1 * Math.pow(t - 1, 2);
    const partB = -3 * p2 * t + 3 * p2 + p3 * t;
    const partC = p0 * Math.pow(t - 1, 3);
    return t * (partA + t * partB) - partC;
};
/**
 * Find the `t` value for a cubic bezier using Cardano's formula
 */
const solveCubicBezier = (p0, p1, p2, p3, refPoint) => {
    p0 -= refPoint;
    p1 -= refPoint;
    p2 -= refPoint;
    p3 -= refPoint;
    const roots = solveCubicEquation(p3 - 3 * p2 + 3 * p1 - p0, 3 * p2 - 6 * p1 + 3 * p0, 3 * p1 - 3 * p0, p0);
    return roots.filter((root) => root >= 0 && root <= 1);
};
const solveQuadraticEquation = (a, b, c) => {
    const discriminant = b * b - 4 * a * c;
    if (discriminant < 0) {
        return [];
    }
    else {
        return [(-b + Math.sqrt(discriminant)) / (2 * a), (-b - Math.sqrt(discriminant)) / (2 * a)];
    }
};
const solveCubicEquation = (a, b, c, d) => {
    if (a === 0) {
        return solveQuadraticEquation(b, c, d);
    }
    b /= a;
    c /= a;
    d /= a;
    const p = (3 * c - b * b) / 3;
    const q = (2 * b * b * b - 9 * b * c + 27 * d) / 27;
    if (p === 0) {
        return [Math.pow(-q, 1 / 3)];
    }
    else if (q === 0) {
        return [Math.sqrt(-p), -Math.sqrt(-p)];
    }
    const discriminant = Math.pow(q / 2, 2) + Math.pow(p / 3, 3);
    if (discriminant === 0) {
        return [Math.pow(q / 2, 1 / 2) - b / 3];
    }
    else if (discriminant > 0) {
        return [
            Math.pow(-(q / 2) + Math.sqrt(discriminant), 1 / 3) - Math.pow(q / 2 + Math.sqrt(discriminant), 1 / 3) - b / 3,
        ];
    }
    const r = Math.sqrt(Math.pow(-(p / 3), 3));
    const phi = Math.acos(-(q / (2 * Math.sqrt(Math.pow(-(p / 3), 3)))));
    const s = 2 * Math.pow(r, 1 / 3);
    return [
        s * Math.cos(phi / 3) - b / 3,
        s * Math.cos((phi + 2 * Math.PI) / 3) - b / 3,
        s * Math.cos((phi + 4 * Math.PI) / 3) - b / 3,
    ];
};

export { getTimeGivenProgression as g };