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AreaMethod

Bases: StrEnum

Ellipsoidal class-attribute instance-attribute 

Ellipsoidal = auto()

Use an ellipsoidal model of the Earth for area calculations.

This uses the geodesic measurement methods given by Karney (2013).

Assumptions
  • Polygons are assumed to be wound in a counter-clockwise direction for the exterior ring and a clockwise direction for interior rings. This is the standard winding for geometries that follow the Simple Feature standard. Alternative windings may result in a negative area. See "Interpreting negative area values" below.
  • Polygons are assumed to be smaller than half the size of the earth. If you expect to be dealing with polygons larger than this, please use the unsigned methods.
Units
  • return value: meter²
Interpreting negative area values

A negative value can mean one of two things:

  1. The winding of the polygon is in the clockwise direction (reverse winding). If this is the case, and you know the polygon is smaller than half the area of earth, you can take the absolute value of the reported area to get the correct area.
  2. The polygon is larger than half the planet. In this case, the returned area of the polygon is not correct. If you expect to be dealing with very large polygons, please use the unsigned methods.

Euclidean class-attribute instance-attribute 

Euclidean = auto()

Calculate planar area.

Spherical class-attribute instance-attribute 

Spherical = auto()

Use a spherical model of the Earth for area calculations.

Calculate the geodesic area of a geometry on a sphere using the algorithm presented in Some Algorithms for Polygons on a Sphere by Chamberlain and Duquette (2007).

Units
  • return value: meter²

LengthMethod

Bases: StrEnum

Ellipsoidal class-attribute instance-attribute 

Ellipsoidal = auto()

Determine the length of a geometry on an ellipsoidal model of the earth.

This uses the geodesic measurement methods given by Karney (2013). As opposed to older methods like Vincenty, this method is accurate to a few nanometers and always converges.

Euclidean class-attribute instance-attribute 

Euclidean = auto()

Determine the length of a geometry using planar calculations.

Haversine class-attribute instance-attribute 

Haversine = auto()

Determine the length of a geometry using the haversine formula.

Note: this implementation uses a mean earth radius of 6371.088 km, based on the recommendation of the IUGG

Vincenty class-attribute instance-attribute 

Vincenty = auto()

Determine the length of a geometry using Vincenty's formulae.

SimplifyMethod

Bases: StrEnum

RDP class-attribute instance-attribute 

RDP = auto()

Use the Ramer-Douglas-Peucker algorithm for LineString simplificatino.

Polygons are simplified by running the RDP algorithm on all their constituent rings. This may result in invalid Polygons, and has no guarantee of preserving topology.

Multi* objects are simplified by simplifying all their constituent geometries individually.

VW class-attribute instance-attribute 

VW = auto()

Use the Visvalingam-Whyatt algorithm for LineString simplification.

See here for a graphical explanation Polygons are simplified by running the algorithm on all their constituent rings.

This may result in invalid Polygons, and has no guarantee of preserving topology. Multi* objects are simplified by simplifying all their constituent geometries individually.

VW_Preserve class-attribute instance-attribute 

VW_Preserve = auto()

Use a topology-preserving variant of the Visvalingam-Whyatt algorithm for LineString simplification.

See here for a graphical explanation.

The topology-preserving algorithm uses an R* tree to efficiently find candidate line segments which are tested for intersection with a given triangle. If intersections are found, the previous point (i.e. the left component of the current triangle) is also removed, altering the geometry and removing the intersection.

Notes
  • It is possible for the simplification algorithm to displace a Polygon's interior ring outside its shell.
  • The algorithm does not guarantee a valid output geometry, especially on smaller geometries.
  • If removal of a point causes a self-intersection, but the geometry only has n + 1 points remaining (3 for a LineString, 5 for a Polygon), the point is retained and the simplification process ends. This is because there is no guarantee that removal of two points will remove the intersection, but removal of further points would leave too few points to form a valid geometry.
  • The tolerance used to remove a point is epsilon, in keeping with GEOS. JTS uses epsilon ^ 2