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

Pure JavaScript game engine. Fully featured and production ready.

/**
 * Generalized bell function, also known as "Cauchy membership function"
 * @see "dbellmf" function from Matlab
 * @see https://codecrucks.com/what-is-fuzzy-membership-function-complete-guide/
 * @see https://researchhubs.com/post/maths/fundamentals/bell-shaped-function.html
 * @param {number} v value to be filtered (have membership adjustment applied to)
 * @param {number} a Controls window, larger value = larger window. Function will return exactly 0.5 at this distance away from center
 * @param {number} b Slope, larger slope makes function's tails sharper, meaning that values fall off faster away from center
 * @param {number} c Controls center of the bell curve
 * @returns {number}
 */
export function bell_membership_function(v, a, b, c) {
    if(a === 0){
        // avoid division by 0
        return 0;
    }

    const vc = v - c;
    const N = vc / a;

    const d = 1 + Math.pow(N, b * 2);

    return 1 / d;
}