Math.Geometry.Spherical

Computations

areaTriangle

Arguments

:: Floating a

=> a

Radius of the sphere

-> (a, a)

A point given in radians

-> (a, a)

-> (a, a)

-> a

Compute the area of a triangle using L'Huillier's formula

compactness

Arguments

:: Floating a

=> [(a, a)]

Polygons on surface of the sphere, given in degrees

-> a

Take the area of the polygon and divide by the perimeter squared. Dimensionless.

relativeCompactness :: Floating a => [(a, a)] -> a

Relative compactness. Dimensionless.

areaConvex

Arguments

:: Floating a

=> a

Radius of a sphere

-> [(a, a)]

Polygon on the surface of the sphere

-> a

Compute the area of a convex polygon on the surface of a sphere.

perimeterPolygon

Arguments

:: Floating a

=> a

Radius of sphere

-> [(a, a)]

Polygon on sphere given in degrees

-> a

areaPolygon

Arguments

:: Floating a

=> a

Radius of sphere

-> [(a, a)]

Polygon on the sphere, with points given in degrees.

-> a

Uses areal projection; then finds area of the polygon by the shoelace method.

This is morally dubious in that it uses the Bonne projection centered around DC, so it will blow up in some cases.

distance

Arguments

:: Floating a

=> a

Radius of sphere

-> (a, a)

Point on sphere given in degrees

-> (a, a)

Point on sphere given in degrees

-> a

Distance in kilometers between two points given in degrees.

Projections

albers

Arguments

:: Floating a

=> (a, a)

A reference point on the sphere

-> (a, a) -> (a, a)

Albers projection for a given reference point.

ablers washingtonDC

littow :: Floating a => (a, a) -> (a, a)

Littow retroazimuthal + conformal projection

craig

Arguments

:: (Floating a, Eq a)

=> (a, a)

Reference point given in radians

-> (a, a) -> (a, a)

Craig retroazimuthal projection

winkel3 :: (Eq a, Floating a) => (a, a) -> (a, a)

Winkel Tripel projection

mercator :: Floating a => (a, a) -> (a, a)

Mercator projection.

bonne

Arguments

:: Floating a

=> a

Standard Parallel. If you are unsure of what to put, try radians 45.

-> a

Central meridian. If you are unsure of what to put, try snd washingtonDC.

-> (a, a)

-> (a, a)

Bonne projection.

Reference points

washingtonDC :: Floating a => (a, a)

For use as a reference point

mecca :: Floating a => (a, a)

For use as a reference point

Helper functions

radians :: Floating a => a -> a

Convert from degrees to radians.

toRadians :: Floating a => (a, a) -> (a, a)

Convert both coördinates to radians.

project

Arguments

:: (Floating a, Functor f)

=> ((a, a) -> (a, a))

A projection

-> f (a, a)

A polygon defined by points on the sphere, in degrees

-> f (a, a)

Project a given polygon