---
title: Different Measures of Distance
tags: geometry
description: A few different ways of calculating distance in noncontinuous 2d spaces
---

How far is it from one place to another? How does that change if
you're on a flat plane? What if that plane has discrete distances
(like a checkerboard, or Civ map)?

### Euclidean Distance

![The shortest distance between two points](/images/post_2016_08_25/euclidean.png){width=150 height=150}

This is the go-to of distance calculations. If you're talking about
continuous, uniform planar (2d) space^[It holds for 3d and
higher-dimensional spaces, too.], [Euclidean
distance](https://en.wikipedia.org/wiki/Euclidean_distance) is the
shortest distance between two points.



$$d = \sqrt{ |x_1 - x_2|^2 + |y_1 - y_2|^2 }$$



### Manhattan Distance

### Civ Distance

### D&D Distance

This is a bit more complex.