JavaScript - Rectilinear Distance function

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

Rectilinear Distance is also known as taxicab metric, L1 distance or L1 norm, snake distance, city block distance, Manhattan distance, or Manhattan length.

It was used to measure the absolute distance needed to move from one place to the second one in taxicab city.

A practical example in 2D:

// ONLINE-RUNNER:browser;

const calculateRectilinearDistance = (a, b) => {
  	if (a.length === 0 || a.length !== b.length) {
      	return NaN;
    }
    let sum = 0.0;
    for (let i = 0; i < a.length; ++i) {
        sum += Math.abs(a[i] - b[i]);
    }
    return sum;
};


// Usage example:

const a = [1, 1];
const b = [4, 4];

const distance = calculateRectilinearDistance(a, b);

console.log(distance);  // 6

More complicated examples

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

// ONLINE-RUNNER:browser;

const calculateRectilinearDistance = (a, b) => {
  	if (a.length === 0 || a.length !== b.length) {
      	return NaN;
    }
    let sum = 0.0;
    for (let i = 0; i < a.length; ++i) {
        sum += Math.abs(a[i] - b[i]);
    }
    return sum;
};


// Usage example:


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

const distance1 = calculateRectilinearDistance(a1, b1);

console.log(distance1);  // 9


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

const distance2 = calculateRectilinearDistance(a2, b2);

console.log(distance2);  // 6

See also

1. JavaScript - Chebyshev Distance function

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

References

1. Rectilinear distance - Wikipedia