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JavaScript - Chebyshev Distance function

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Created by:

Blythe-F

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

The universal distance formula is:

Where:

x and y are points in the space,
i is a number of dimensions.

The two-dimensional formula is:

The three-dimensional formula is:

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:

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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

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More complicated examples

Edit

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

xxxxxxxxxx
 
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