@woosh/meep-engine/src/core/math/spline/spline_hermite3_bounds.js

Pure JavaScript game engine. Fully featured and production ready.

import { assert } from "../../assert.js";
import { max2 } from "../max2.js";
import { min2 } from "../min2.js";
import { spline_hermite3 } from "./spline_hermite3.js";

/**
 * Compute bounds of a 3-rd degree hermite curve
 * Note that this is a 1d case solver
 * Lower bound will be written into result[offset], upper bounds will be written into result[offset+result_stride]
 * Solution is based on https://stackoverflow.com/questions/24809978/calculating-the-bounding-box-of-cubic-bezier-curve
 * Differentiation of hermite polynomial is done in WolframAlpha
 * 0 = 3 t^2 (m0 + m1 + 2 p0 - 2 p1) - 2 t (2 m0 + m1 + 3 p0 - 3 p1) + m0
 * @param {number[]|Float32Array} result
 * @param {number} result_offset offset into the result array
 * @param {number} result_stride
 * @param {number} p0
 * @param {number} p1
 * @param {number} m0
 * @param {number} m1
 */
export function spline_hermite3_bounds(
    result,
    result_offset,
    result_stride,
    p0, p1, m0, m1) {

    assert.greaterThan(result_stride, 0, 'result_stride must be greater than 0');
    assert.isInteger(result_stride, 'result_stride');

    const a = 3 * (m0 + m1 + 2 * p0 - 2 * p1);
    const b = -2 * (2 * m0 + m1 + 3 * p0 - 3 * p1);
    const c = m0;

    let min = min2(p0, p1);
    let max = max2(p0, p1);

    if (Math.abs(a) < 1e-12) {

        if (Math.abs(b) >= 1e-12) {
            const t = -c / b;

            if (0 < t && t < 1) {
                const value = spline_hermite3(t, p0, p1, m0, m1);

                if (value < min) {
                    min = value;
                }
                if (value > max) {
                    max = value;
                }

            }

        }

    } else {

        const b2ac = b * b - 4 * c * a;
        const sqrtb2ac = Math.sqrt(b2ac);

        if (b2ac >= 0) {

            const t1 = (-b + sqrtb2ac) / (2 * a);

            if (0 < t1 && t1 < 1) {
                const value = spline_hermite3(t1, p0, p1, m0, m1);

                if (value < min) {
                    min = value;
                }
                if (value > max) {
                    max = value;
                }
            }

            const t2 = (-b - sqrtb2ac) / (2 * a);

            if (0 < t2 && t2 < 1) {
                const value = spline_hermite3(t2, p0, p1, m0, m1);

                if (value < min) {
                    min = value;
                }
                if (value > max) {
                    max = value;
                }
            }

        }

    }

    result[result_offset] = min;
    result[result_offset + result_stride] = max;
}