# Distance
[](https://github.com/pkinney/distance/actions/workflows/ci.yaml)
[](https://hex.pm/packages/distance)
Provides a set of distance functions for use in GIS or graphic applications.
## Installation
```elixir
defp deps do
[{:distance, "~> 1.0"}]
end
```
## Functions
### Point-Point Distance
Calculate geometric distance between two or more points (two- or three-dimensional):
```elixir
Distance.distance({2, -1}, {-1, 3}) # => 5
Distance.distance({2, -1, 4}, {-1, 3, 2}) # => 5.385...
Distance.distance([{2.5, 2.5}, {4, 0.8}, {2.5, 3.1}, {2.5, 3.1}]) # => 5.013...
```
Calculate the square of the geometric distance between two points (useful as
a faster way to compare distances between points without the need for an
expensive square root operation):
```elixir
Distance.distance_squared({2, -1}, {-1, 3}) # => 25
Distance.distance_squared({2, -1, 4}, {-1, 3, 2}) # => 29
```
### Point-Segment Distance
Calculate geometric distance between a point and the closest point on a line
segment. For instance the distance between the point (3, 3) and the line
segment between (-2, 1) and (5, 3).
```elixir
Distance.segment_distance({3, 2}, {-2, 1}, {5, 3}) # => 0.412...
```
Similar to the distance function, there is a squared version for faster
calculations when needed:
```elixir
Distance.segment_distance_squared({3, 2}, {-2, 1}, {5, 3}) # => 0.170...
```
### Angular Functions
Get bearing from one point to another and project from one point a given
distance along a direction. Additionally, there are useful methods for
simplifying angles to coterminal angles and measuring differences between
directions.
Angles are measured as radians off of the positive x-axis in the direction of
the positive y-axis.
### Great Circle Distance
Calculate great circle distances (shortest travel distance on the surface of
a spherical Earth) given a two longitude-latitude pairs. This is an implementation
of the [Haversine formula](https://en.wikipedia.org/wiki/Haversine_formula)
and approximates using a spherical (non-ellipsoid) Earth with a
mean radius of 6,371,008.8 meters derived from the WGS84 datum.
The function accepts two tuples in the form of `{longitude, latitude}` and
returns the distance in meters. It will also accept a List of tuples.
```elixir
Distance.GreatCircle.distance({-96.796667, 32.775833}, {126.967583, 37.566776}) # => 10974882.74...
Distance.GreatCircle.distance([
{-96.796667, 32.775833},
{126.967583, 37.566776},
{151.215158, -33.857406},
{55.274180, 25.197229},
{6.942661, 50.334057},
{-97.635926, 30.134442}
]) # => 44728827.849...
```
### Vincenty's Inverse Formula Distance
Calculate distance per [Vincenty's inverse formula](https://en.wikipedia.org/wiki/Vincenty%27s_formulae)
(shortest travel distance on the surface of an [oblate spheroid](https://en.wikipedia.org/wiki/Spheroid#Oblate_spheroids) Earth) given two longitude-latitude pairs.
This method is iterative and more costly than other methods, such as the [great circle](lib/distance/great_circle.ex) method, but also potentially more accurate.
It is important to note that [nearly antipodal points](https://en.wikipedia.org/wiki/Vincenty%27s_formulae#Nearly_antipodal_points) can cause convergence issues with this method.
The function accepts two tuples in the form of `{longitude, latitude}` and
returns the distance in meters. It will also accept a List of tuples.
```elixir
Distance.Vincenty.distance({-96.796667, 32.775833}, {126.967583, 37.566776}) # => 10997423.55...
Distance.Vincenty.distance([
{-96.796667, 32.775833},
{126.967583, 37.566776},
{151.215158, -33.857406},
{55.274180, 25.197229},
{6.942661, 50.334057},
{-97.635926, 30.134442}
]) # => 44737835.514...
```
