How to find the coordinate that is closest to the point of origin?

Question

I know there are many many questions about sorting javascript arrays by multiple values, but none of the answers solved my problem.

I have an array of coordinates like:

x  |  y
--------
10    20
12    18
20    30
5     40
100   2

How can I get the coordinate that is closest to the point of origin?

Solution 1

Calculate the distance of each point using

Math.sqrt( Math.pow(x, 2) + Math.pow(y, 2) );

Take the result that's the lowest

---

var points = [
  {x: 10, y: 20},
  {x: 12, y: 18},
  {x: 20, y: 30},
  {x: 5, y: 40},
  {x: 100, y: 2}
];

function d(point) {
  return Math.pow(point.x, 2) + Math.pow(point.y, 2);
}

var closest = points.slice(1).reduce(function(min, p) {
  if (d(p) < min.d) min.point = p;
  return min;
}, {point: points[0], d:d(points[0])}).point;

closest;
// {x: 12, y:18}

You'll notice that we're skipping the Math.sqrt step here. As Mark Setchell points out, calculating the square root is a sort of "lowest common denominator" operation; We can still determine the closest point by getting the smallest x^2 + y^2 value.

Solution 2

For each x,y pair, square x, square y and add together. Smallest number is nearest to the origin.

Comments

[Mark Setchell]

There's no need for the square root. If a^2 > b^2 it follows that a>b.

[Mulan]

True, thanks for the feedback. I will update my answer.

[Mark Setchell]

@naomik That is the Manhattan distance and it is used for some applications - I don't know if it is applicable here.

[Mark Setchell]

Thinking about it, the Manhattan distance is not applicable here because it will make the point 2,0 the same distance (2) from the origin as 1,1 which is obviously nearer at squareroot(2).

[Jaanus]

You are not setting the min.d if d(p) < min.d, you just update the point coordinates, but distance stays old.