QuadraticRealPolynomial.js

/*global define*/
define([
        './DeveloperError',
        './Math'
    ], function(
        DeveloperError,
        CesiumMath) {
    'use strict';

    /**
     * Defines functions for 2nd order polynomial functions of one variable with only real coefficients.
     *
     * @exports QuadraticRealPolynomial
     */
    var QuadraticRealPolynomial = {};

    /**
     * Provides the discriminant of the quadratic equation from the supplied coefficients.
     *
     * @param {Number} a The coefficient of the 2nd order monomial.
     * @param {Number} b The coefficient of the 1st order monomial.
     * @param {Number} c The coefficient of the 0th order monomial.
     * @returns {Number} The value of the discriminant.
     */
    QuadraticRealPolynomial.computeDiscriminant = function(a, b, c) {
        //>>includeStart('debug', pragmas.debug);
        if (typeof a !== 'number') {
            throw new DeveloperError('a is a required number.');
        }
        if (typeof b !== 'number') {
            throw new DeveloperError('b is a required number.');
        }
        if (typeof c !== 'number') {
            throw new DeveloperError('c is a required number.');
        }
        //>>includeEnd('debug');

        var discriminant = b * b - 4.0 * a * c;
        return discriminant;
    };

    function addWithCancellationCheck(left, right, tolerance) {
        var difference = left + right;
        if ((CesiumMath.sign(left) !== CesiumMath.sign(right)) &&
                Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance) {
            return 0.0;
        }

        return difference;
    }

    /**
     * Provides the real valued roots of the quadratic polynomial with the provided coefficients.
     *
     * @param {Number} a The coefficient of the 2nd order monomial.
     * @param {Number} b The coefficient of the 1st order monomial.
     * @param {Number} c The coefficient of the 0th order monomial.
     * @returns {Number[]} The real valued roots.
     */
    QuadraticRealPolynomial.computeRealRoots = function(a, b, c) {
        //>>includeStart('debug', pragmas.debug);
        if (typeof a !== 'number') {
            throw new DeveloperError('a is a required number.');
        }
        if (typeof b !== 'number') {
            throw new DeveloperError('b is a required number.');
        }
        if (typeof c !== 'number') {
            throw new DeveloperError('c is a required number.');
        }
        //>>includeEnd('debug');

        var ratio;
        if (a === 0.0) {
            if (b === 0.0) {
                // Constant function: c = 0.
                return [];
            }

            // Linear function: b * x + c = 0.
            return [-c / b];
        } else if (b === 0.0) {
            if (c === 0.0) {
                // 2nd order monomial: a * x^2 = 0.
                return [0.0, 0.0];
            }

            var cMagnitude = Math.abs(c);
            var aMagnitude = Math.abs(a);

            if ((cMagnitude < aMagnitude) && (cMagnitude / aMagnitude < CesiumMath.EPSILON14)) { // c ~= 0.0.
                // 2nd order monomial: a * x^2 = 0.
                return [0.0, 0.0];
            } else if ((cMagnitude > aMagnitude) && (aMagnitude / cMagnitude < CesiumMath.EPSILON14)) { // a ~= 0.0.
                // Constant function: c = 0.
                return [];
            }

            // a * x^2 + c = 0
            ratio = -c / a;

            if (ratio < 0.0) {
                // Both roots are complex.
                return [];
            }

            // Both roots are real.
            var root = Math.sqrt(ratio);
            return [-root, root];
        } else if (c === 0.0) {
            // a * x^2 + b * x = 0
            ratio = -b / a;
            if (ratio < 0.0) {
                return [ratio, 0.0];
            }

            return [0.0, ratio];
        }

        // a * x^2 + b * x + c = 0
        var b2 = b * b;
        var four_ac = 4.0 * a * c;
        var radicand = addWithCancellationCheck(b2, -four_ac, CesiumMath.EPSILON14);

        if (radicand < 0.0) {
            // Both roots are complex.
            return [];
        }

        var q = -0.5 * addWithCancellationCheck(b, CesiumMath.sign(b) * Math.sqrt(radicand), CesiumMath.EPSILON14);
        if (b > 0.0) {
            return [q / a, c / q];
        }

        return [c / q, q / a];
    };

    return QuadraticRealPolynomial;
});