Topo (topo v1.0.2)

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

Point
LineString
Polygon
MultiPoint
MultiLineString
MultiPolygon

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 (https://github.com/bryanjos/geo). 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.

Summary

Types

geometry()

Functions

contains?(a, b)

Returns true if all points of geometry B lie within A.

disjoint?(a, b)

Returns true if geometries A and B do not have any points in common.

equals?(a, b)

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.

intersects?(a, b)

Returns true if geometries A and B share at least one point in common.

within?(a, b)

This is the direct converse of contains?. All points of geometry A lie within geometry B.

Types

geometry()

@type geometry() ::
  {number(), number()}
  | %{type: String.t(), coordinates: list()}
  | %Geo.Point{coordinates: term(), properties: term(), srid: term()}
  | %Geo.MultiPoint{coordinates: term(), properties: term(), srid: term()}
  | %Geo.LineString{coordinates: term(), properties: term(), srid: term()}
  | %Geo.MultiLineString{coordinates: term(), properties: term(), srid: term()}
  | %Geo.Polygon{coordinates: term(), properties: term(), srid: term()}
  | %Geo.MultiPolygon{coordinates: term(), properties: term(), srid: term()}

Functions

contains?(a, b)

@spec contains?(geometry(), geometry()) :: boolean()

Returns true if all points of geometry B lie within A.

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

Examples

iex> Topo.contains?(
...>   %{type: "Polygon", coordinates: [[{20, 20}, {20, 180}, {220, 180}, {220, 20}, {20, 20}]]},
...>   %{type: "Polygon", coordinates: [[{160, 60}, {20, 20}, {100, 140}, {160, 60}]]}
...> )
true

iex> Topo.contains?(
...>   %{type: "Polygon", coordinates: [[{160, 60}, {20, 20}, {100, 140}, {160, 60}]]},
...>   %{type: "Polygon", coordinates: [[{20, 20}, {20, 180}, {220, 180}, {220, 20}, {20, 20}]]}
...> )
false

disjoint?(a, b)

@spec disjoint?(geometry(), geometry()) :: boolean()

Returns true if geometries A and B do not have any points in common.

Examples

iex> Topo.disjoint?({1, -3}, %{type: "MultiPoint", coordinates: [{70, 35}, {100, 80}]})
true

iex> Topo.disjoint?(
...>   %{type: "Polygon", coordinates: [
...>     [{60, 120}, {60, 40}, {160, 40}, {160, 120}, {60, 120}],
...>     [{140, 100}, {80, 100}, {80, 60}, {140, 60}, {140, 100}]]},
...>   %Geo.MultiPoint{coordinates: [{70, 35}, {100, 80}]}
...> )
true

equals?(a, b)

@spec equals?(geometry(), geometry()) :: boolean()

Examples

iex> Topo.equals?(
...>   %{type: "Point", coordinates: {2, -3}},
...>   %{type: "MultiPoint", coordinates: [{2, -3}]}
...> )
true

iex> Topo.equals?(
...>   %{type: "Polygon", coordinates: [[{160, 60}, {20, 20}, {100, 140}, {160, 60}]]},
...>   %{type: "Polygon", coordinates: [[{20, 20}, {20, 180}, {220, 180}, {220, 20}, {20, 20}]]}
...> )
false

intersects?(a, b)

@spec intersects?(geometry(), geometry()) :: boolean()

Returns true if geometries A and B share at least one point in common.

Examples

iex> Topo.intersects?(
...>   %{type: "Polygon", coordinates: [[{2, 2}, {20, 2}, {11, 11}, {2, 2}]]},
...>   %{type: "LineString", coordinates: [{11, 10}, {4, 2.5}, {16, 2.5}, {11, 10}]}
...> )
true

iex> Topo.intersects?(
...>   %{type: "Polygon", coordinates: [
...>     [{60, 120}, {60, 40}, {160, 40}, {160, 120}, {60, 120}],
...>     [{140, 100}, {80, 100}, {80, 60}, {140, 60}, {140, 100}]]},
...>   %{type: "MultiPoint", coordinates: [{70, 35}, {100, 80}]}
...> )
false

within?(a, b)

@spec within?(geometry(), geometry()) :: boolean()

This is the direct converse of contains?. All points of geometry A lie within geometry B.

Examples

iex> Topo.within?(
...>   %{type: "Polygon", coordinates: [[{20, 20}, {20, 180}, {220, 180}, {220, 20}, {20, 20}]]},
...>   %{type: "Polygon", coordinates: [[{160, 60}, {20, 20}, {100, 140}, {160, 60}]]}
...> )
false

iex> Topo.within?(
...>   %{type: "Polygon", coordinates: [[{160, 60}, {20, 20}, {100, 140}, {160, 60}]]},
...>   %{type: "Polygon", coordinates: [[{20, 20}, {20, 180}, {220, 180}, {220, 20}, {20, 20}]]}
...> )
true