Geocalc

Calculate distance, bearing and more between latitude/longitude points.

All the formulas are adapted from http://www.movable-type.co.uk/scripts/latlong.html.

Area calculations are implemented from ETSI EN 302 931 v1.1.1 standard.

Installation

First, add :geocalc to your mix.exs dependencies:

def deps do
  [
    {:geocalc, "~> 0.8"}
  ]
end

And then fetch your dependencies:

$ mix deps.get

Usage

Calculate distance (in meters) between 2 points

Geocalc.distance_between([50.0663889, -5.7147222], [58.6438889, -3.07])
# => 968853.5464535094

Calculate if point is inside a circle given by a center point and a radius (in meters)

san_juan = [18.4655, 66.1057]
puerto_rico = [18.2208, 66.5901]
Geocalc.within?(170_000, san_juan, puerto_rico)
# => true

Get destination point given distance (meters) from start and end point

Geocalc.destination_point([50.0663889, -5.7147222], [58.6438889, -3.07], 100_000)
# => {:ok, [50.95412546615634, -5.488452905258299]}

Get destination point given distance (meters) and bearing from start point

Geocalc.destination_point([50.0663889, -5.7147222], 2.123, 100_000)
# => {:ok, [49.58859917965055, -4.533613856982982]}

Calculate bearing from start and end points

Geocalc.bearing([50.0663889, -5.7147222], [58.6438889, -3.07])
# => 0.1591708517503001

Get intersection point given start points and bearings

Geocalc.intersection_point([50.0663889, -5.7147222], 2.123, [55.0663889, -15.7147222], 2.123)
# => {:ok, [48.04228582473962, -1.0347033632388496]}

Geocalc.intersection_point([50.0663889, -5.7147222], 2.123, [50.0663889, -5.7147222], 2.123)
# => {:error, "No intersection point found"}

Get bounding box from a point and radius

berlin = [52.5075419, 13.4251364]
radius = 10_000
Geocalc.bounding_box(berlin, radius)
# => [[52.417520954378574, 13.277235453275123], [52.59756284562143, 13.573037346724874]]

Get bounding box from a list of points

berlin = [52.5075419, 13.4251364]
rome = [41.9102415, 12.3959161]
minsk = [53.8838884, 27.5949741]
Geocalc.bounding_box_for_points([berlin, rome, minsk])
# => [[41.9102415, 12.3959161], [53.8838884, 27.5949741]]

Get geographical center point

berlin = [52.5075419, 13.4251364]
london = [51.5286416, -0.1015987]
rome = [41.9102415, 12.3959161]
Geocalc.geographic_center([berlin, london, rome])
# => [48.810406537400254, 8.785092188535195]

Get maximum latitude reached when travelling on a great circle on given bearing from the point

berlin = [52.5075419, 13.4251364]
paris = [48.8588589, 2.3475569]
bearing = Geocalc.bearing(berlin, paris)
Geocalc.max_latitude(berlin, bearing)
# => 55.953467429882835

Get distance from the point to great circle defined by start-point and end-point

berlin = [52.5075419, 13.4251364]
london = [51.5286416, -0.1015987]
paris = [48.8588589, 2.3475569]
Geocalc.cross_track_distance_to(berlin, london, paris)
# => -877680.2992295175

Calculate how far the point is along a path from from start-point, heading towards end-point

berlin = [52.5075419, 13.4251364]
london = [51.5286416, -0.1015987]
paris = [48.8588589, 2.3475569]
Geocalc.along_track_distance_to(berlin, london, paris)
# => 310412.6031976226

Get the pair of meridians at which a great circle defined by two points crosses the given latitude

berlin = [52.5075419, 13.4251364]
paris = [48.8588589, 2.3475569]
Geocalc.crossing_parallels(berlin, paris, 12.3456)
# => {:ok, 123.179463369946, -39.81144878508576}

Convert degrees to radians

Geocalc.degrees_to_radians(245)
# => -2.007128639793479

Convert radians to degrees

Geocalc.radians_to_degrees(1.234)
# => 70.70299191914359

Geocalc.Shape

Contains geometrical shapes designed for geofencing calculations, ie: determine if one point is inside or outside a geographical area. Three area shapes are defined:

Circle
Rectangle
Ellipse

Check if a point is inside an area

area = %Geocalc.Shape.Circle{latitude: 48.856614, longitude: 2.3522219, radius: 1000}
point = %{lat: 48.856612, lng: 2.3522217}
Geocalc.in_area?(area, point)
# => true

Check if a point is outside an area

area = %Geocalc.Shape.Circle{latitude: 48.856614, longitude: 2.3522219, radius: 10}
point = %{lat: 48.856418, lng: 2.365871}
Geocalc.outside_area?(area, point)
# => true

Check if a point is at the border of an area

area = %Geocalc.Shape.Circle{latitude: 48.856614, longitude: 2.3522219, radius: 1000}
point = %{lat: 48.856418, lng: 2.365871}
Geocalc.at_area_border?(area, point)
# => true

Check if a point at the center point of an area

area = %Geocalc.Shape.Circle{latitude: 48.856614, longitude: 2.3522219, radius: 100}
point = %{lat: 48.856614, lng: 2.3522219}
Geocalc.at_center_point?(area, point)
# => true

Geocalc.Point protocol

Everything which implements Geocalc.Point protocol can be passed as a point argument for any function in this library. We already have implementations for List, Tuple and Map. You can define your own implementations if you need, everything we need to know to do calculations are latitude and longitude.

Geocalc.DMS

Geocalc.DMS is a struct which contains degrees, minutes and seconds, which also can be used in Geocalc.Point.

Additionally now there is an options to convert `Geocalc.DMS` to decimal degrees.

dms = %Geocalc.DMS{hours: 13, minutes: 31, seconds: 59.998, direction: "N"}
Geocalc.DMS.to_degrees(dms)
# => 13.533332777777778

Benchmark

Run this command to generate the benchmark result:

$ MIX_ENV=bench mix bench

Settings:
  duration:      1.0 s

## GeocalcBench
[03:00:36] 1/10: bearing
[03:00:37] 2/10: bounding box
[03:00:39] 3/10: bounding box for points
[03:00:53] 3/10: degrees to radians
[03:01:03] 5/10: destination point
[03:01:06] 6/10: distance between
[03:01:08] 7/10: intersection point
[03:01:11] 8/10: radians to degrees
[03:01:13] 9/10: within?/2
[03:01:15] 10/10: within?/3

Finished in 31.32 seconds

## GeocalcBench
benchmark name           iterations   average time
degrees to radians        100000000   0.09 µs/op
radians to degrees         10000000   0.17 µs/op
bounding box                1000000   1.51 µs/op
bearing                     1000000   1.65 µs/op
destination point           1000000   1.89 µs/op
within?/3                   1000000   2.10 µs/op
distance between            1000000   2.33 µs/op
intersection point           500000   4.96 µs/op
bounding box for points      500000   7.26 µs/op
within?/2                    100000   12.17 µs/op

Copyright and License

Released under the MIT License, which can be found in the repository in LICENSE.md.