JavaScript - Chebyshev Distance function

In this short article, we would like to show how to calculate Chebyshev Distance using JavaScript.

In simple words: Chebyshev Distance is the maximal positive distance between corresponding coordinates.

Chebyshev Distance has applications in different fields, e.g. Artificial Intelligence.

A practical example in 2D:

// ONLINE-RUNNER:browser;

const calculateChebyshevDistance = (a, b) => {
    if (a.length === 0 || a.length !== b.length) {
      	return NaN;
    }
    let max = Math.abs(a[0] - b[0]);
    for (let i = 1; i < a.length; ++i) {
        const distance = Math.abs(a[i] - b[i]);
        if (distance > max) {
          	max = distance;
        }
    }
    return max;
};


// Usage example:

const a = [2, 1];
const b = [3, 5];

const distance = calculateChebyshevDistance(a, b);

console.log(distance);  // 4

More complicated examples

In this section, you can find Chebyshev Distance examples for 3D and 4D.

// ONLINE-RUNNER:browser;

const calculateChebyshevDistance = (a, b) => {
    if (a.length === 0 || a.length !== b.length) {
      	return NaN;
    }
    let max = Math.abs(a[0] - b[0]);
    for (let i = 1; i < a.length; ++i) {
        const distance = Math.abs(a[i] - b[i]);
        if (distance > max) {
          	max = distance;
        }
    }
    return max;
};


// Usage example:

const a1 = [1, 2, 3];
const b1 = [5, 5, 5];

const distance1 = calculateChebyshevDistance(a1, b1);

console.log(distance1);  // 4


const a2 = [1, 2, 3, 4];
const b2 = [3, 4, 4, 3];

const distance2 = calculateChebyshevDistance(a2, b2);

console.log(distance2);  // 2

See also

1. JavaScript - Rectilinear Distance function

2. JavaScript - how to calculate distance between two points with Pythagorean equation?

References

1. Chebyshev distance - Wikipedia