@woosh/meep-engine/src/core/math/solveQuadratic.js

Pure JavaScript game engine. Fully featured and production ready.

import { assert } from "../assert.js";
import { EPSILON } from "./EPSILON.js";

/**
 * Return solutions for a quadratic polynomial: ax² + bx + c
 * Typically there will be 2 solution, in some cases we will have 0, having 1 solution is impossible
 * This solver only deals with real numbers, so imaginary solution are not provided. In case solution would be imaginary - we return 0 roots
 * @param {number} a
 * @param {number} b
 * @param {number} c
 * @param {number[]} result solutions are written here
 * @param {number} result_offset offset into result array where solutions are written to
 * @returns {number} number of found solutions (roots)
 */
export function solveQuadratic(
    result, result_offset,
    a, b, c
) {

    assert.isNumber(a, 'a');
    assert.isNumber(b, 'b');
    assert.isNumber(c, 'c');


    if (Math.abs(a) < EPSILON) {

        if (Math.abs(b) < EPSILON) {

            if (Math.abs(c) < EPSILON) {
                // special case, all variables are close to 0

                result[result_offset] = 0;
                result[result_offset + 1] = 0;

                return 2;

            }

        } else {
            result[result_offset] = -c / b;
            result[result_offset + 1] = -c / b;

            return 2;
        }

    } else {
        // 2 root solution

        const disc_sqr = b * b - 4 * a * c;

        if (disc_sqr >= 0) {
            // if discriminant square is negative, solution can only be imaginary, we don't deal with that

            const disc = Math.sqrt(disc_sqr);
            const a2 = 2 * a;

            result[result_offset] = (-b - disc) / a2;
            result[result_offset + 1] = (-b + disc) / a2;

            return 2;
        }

    }

    // no roots
    return 0;
}