2016-08-25-different-distances.md 865 B
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
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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 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.