Method cubicRootAt

src/common/overlay/levelRenderer/Curve.js:131–205

* @function LevelRenderer.Tool.Curve.prototype.cubicRootAt * @description 计算三次贝塞尔方程根，使用盛金公式 * @param {number} p0 - 点p0。 * @param {number} p1 - 点p1。 * @param {number} p2 - 点p2。 * @param {number} p3 - 点p3。 * @param {number} val - 值。 * @param {Array. } roots -

(p0, p1, p2, p3, val, roots)

     * @returns {number} 有效根。
     */
    cubicRootAt(p0, p1, p2, p3, val, roots) {
        // Evaluate roots of cubic functions
        var a = p3 + 3 * (p1 - p2) - p0;
        var b = 3 * (p2 - p1 * 2 + p0);
        var c = 3 * (p1 - p0);
        var d = p0 - val;

        var A = b * b - 3 * a * c;
        var B = b * c - 9 * a * d;
        var C = c * c - 3 * b * d;

        var n = 0;

        if (this.isAroundZero(A) && this.isAroundZero(B)) {
            if (this.isAroundZero(b)) {
                roots[0] = 0;
            } else {
                let t1 = -c / b;  //t1, t2, t3, b is not zero
                if (t1 >= 0 && t1 <= 1) {
                    roots[n++] = t1;
                }
            }
        } else {
            var disc = B * B - 4 * A * C;

            if (this.isAroundZero(disc)) {
                var K = B / A;
                let t1 = -b / a + K;  // t1, a is not zero
                let t2 = -K / 2;  // t2, t3
                if (t1 >= 0 && t1 <= 1) {
                    roots[n++] = t1;
                }
                if (t2 >= 0 && t2 <= 1) {
                    roots[n++] = t2;
                }
            } else if (disc > 0) {
                let discSqrt = Math.sqrt(disc);
                let Y1 = A * b + 1.5 * a * (-B + discSqrt);
                let Y2 = A * b + 1.5 * a * (-B - discSqrt);
                if (Y1 < 0) {
                    Y1 = -Math.pow(-Y1, this.ONE_THIRD);
                } else {
                    Y1 = Math.pow(Y1, this.ONE_THIRD);
                }
                if (Y2 < 0) {
                    Y2 = -Math.pow(-Y2, this.ONE_THIRD);
                } else {
                    Y2 = Math.pow(Y2, this.ONE_THIRD);
                }
                let t1 = (-b - (Y1 + Y2)) / (3 * a);
                if (t1 >= 0 && t1 <= 1) {
                    roots[n++] = t1;
                }
            } else {
                var T = (2 * A * b - 3 * a * B) / (2 * Math.sqrt(A * A * A));
                var theta = Math.acos(T) / 3;
                var ASqrt = Math.sqrt(A);
                var tmp = Math.cos(theta);