@woosh/meep-engine/src/core/math/spline/spline3_hermite.js

Pure JavaScript game engine. Fully featured and production ready.

/**
 * Perform cubic Hermite interpolation
 * @see https://en.wikipedia.org/wiki/Cubic_Hermite_spline
 * @param {number} t normalized interpolation position in interval [0,1]
 * @param {number} p0 first value
 * @param {number} p1 second value
 * @param {number} m0 first tangent (tangent exiting from first value)
 * @param {number} m1 second tangent (tangent entering into second value)
 * @return {number}
 *
 * @author Alex Goldring
 * @copyright Company Named Limited (c) 2025
 */
export function spline3_hermite(t, p0, p1, m0, m1) {

    const t2 = t * t;
    const t3 = t2 * t;

    const a = 2 * t3 - 3 * t2 + 1;
    const b = t3 - 2 * t2 + t;
    const c = t3 - t2;
    const d = 3 * t2 - 2 * t3;

    return a * p0 + b * m0 + c * m1 + d * p1;
}