Geometry Library for Elixir

A Geometry library for Elixir that calculates spatial relationships between two
geometries. Geometries can be of any of the following types:

• Point
• LineString
• Polygon
• MultiPoint
• MultiLineString
• MultiPolygon

Installation

defp deps do
  [{:topo, "~> 1.0"}]
end

Usage

Full Documentation

The Topo module provides functions for determining the relationship between
two geometries. Each function returns a boolean and accepts any combination of
Point, LineString, Polygon, MultiPoint, MultiLineString, or MultiPolygon.

• intersects? - Geometries A and B share at least one point in
  common.
• disjoint? - Disjoint geometries share no points in common. This is the
  direct opposite of the intersects? result.
• contains? - All points of geometry B lie within A. See section
  below on [Contains].
• within? - This is the direct inverse of contains?. All points of
  geometry A lie within geometry B.
• equals? - Geometries A and B are equivalent and cover the exact
  same set of points. By definition, A and B are equal if A contains
  B and B contains A. Equality does not necessarily mean that the
  geometries are of the same type. A Point A is equal to a MultiPoint that
  contains only the same Point A.

Each of these functions can be passed any two Geometries in either a Map with a
:type and :coordinates keys or as a struct generated via the Geo library. Coordinates are represented as atoms {x, y}
and multiple coordinates as Lists.

a = %{type: "Polygon", coordinates: [[{2, 2}, {20, 2}, {11, 11}, {2, 2}]]}
b = %Geo.Polygon{coordinates: [[{2, 2}, {20, 2}, {11, 11}, {2, 2}]]}
Topo.equals? a, b # => true

Instead of a Point geometry, just a single coordinate can be used.

a = %{type: "Polygon", coordinates: [[{2, 2}, {20, 2}, {11, 11}, {2, 2}]]}
Topo.intersects? a, {4, 6} # => true

The Topo library’s functions will automatically attempt to “clean” geometries
passed to them:

• Linear Rings (including Polygons) will be reordered to a counter-clockwise
  direction.
• Polygon’s Linear Rings will automatically be closed if the first point is not
  repeated as the last point.
• Points that are equal or collinear with surrounding points are removed from
  LineStrings or Polygons.

A note on contains?

There are a few non-obvious special cases that are worth mentioning:

• A Polygon does not contain its own boundary. Specifically a LineString that
  is the exact same as a Polygon’s exterior Linear ring is not contained within a
  that Polygon.

a = %Geo.Polygon{coordinates: [[{2, 2}, {20, 2}, {11, 11}, {2, 2}]]}
b = %Geo.LineString{coordinates: [{2, 2}, {20, 2}, {11, 11}, {2, 2}]}
Topo.contains? a, b # => false
Topo.intersects? a, b  # => true

• A LineString does not contain it’s own first and last point (unless those
  points are the same, as in a LinearRing)

a = %Geo.LineString{coordinates: [{1, 3}, {2, -1}, {0, -1}]}
b = %Geo.LineString{coordinates: [{1, 3}, {2, -1}, {0, -1}, {1, 3}]}
Topo.contains? a, {1, 3} # => false
Topo.intersects? a, {1, 3} # => true
Topo.contains? b, {1, 3} # => true

Float Precision Issues

It is possible that floating point math imprecision can cause incorrect results for certain inputs. This is often encountered during the line segment comparison (see LineStringPolygonTest for an example). By default, Topo is strict on intersection math; however, if you with to allow a less strict requirement for line segment intersection, you can set an :epsilon value at compile time, which will be passed to the SegSeg library (see here for a more detailed explanation).

In your application’s config file add

config :topo, epsilon: true

Topo uses the Application.config_env/3 function to avoid querying the value on each computation, so you may have to clean and recompile the dependencies of your application after changing. The default value is false will will apply strict comparison to the resulting floating point numbers used in calculating line segment relationships.

Tests

> mix test