Geodetics.Ellipsoids

An Ellipsoid is a reasonable best fit for the surface of the Earth over some defined area. WGS84 is the standard used for the whole of the Earth. Other Ellipsoids are considered a best fit for some specific area.

Helmert transform between geodetic reference systems

data Helmert

The 7 parameter Helmert transformation. The monoid instance allows composition.

Constructors

Helmert

Fields

• cX, cY, cZ :: Length Double
• helmertScale :: Dimensionless Double

  Parts per million

• rX, rY, rZ :: Dimensionless Double

Instances

Eq Helmert

Defined in Geodetics.Ellipsoids

Methods

(==) :: Helmert -> Helmert -> Bool

(/=) :: Helmert -> Helmert -> Bool

Show Helmert

Defined in Geodetics.Ellipsoids

Methods

showsPrec :: Int -> Helmert -> ShowS

show :: Helmert -> String

showList :: [Helmert] -> ShowS

Semigroup Helmert

Defined in Geodetics.Ellipsoids

Methods

(<>) :: Helmert -> Helmert -> Helmert

sconcat :: NonEmpty Helmert -> Helmert

stimes :: Integral b => b -> Helmert -> Helmert

Monoid Helmert

Defined in Geodetics.Ellipsoids

Methods

mempty :: Helmert

mappend :: Helmert -> Helmert -> Helmert

mconcat :: [Helmert] -> Helmert

inverseHelmert :: Helmert -> Helmert

The inverse of a Helmert transformation.

type ECEF = Vec3 (Length Double)

Earth-centred, Earth-fixed coordinates as a vector. The origin and axes are not defined: use with caution.

applyHelmert :: Helmert -> ECEF -> ECEF

Apply a Helmert transformation to earth-centered coordinates.

Ellipsoid models of the Geoid

class (Show a, Eq a) => Ellipsoid a where

An Ellipsoid is defined by the major radius and the inverse flattening (which define its shape), and its Helmert transform relative to WGS84 (which defines its position and orientation).

The inclusion of the Helmert parameters relative to WGS84 actually make this a Terrestrial Reference Frame (TRF), but the term Ellipsoid will be used in this library for readability.

Minimum definition: majorRadius, flatR & helmert.

Laws:

helmertToWGS84 = applyHelmert . helmert
helmertFromWGS84 e . helmertToWGS84 e = id

Minimal complete definition

majorRadius, flatR, helmert

Methods

majorRadius :: a -> Length Double

flatR

Arguments

:: a

-> Dimensionless Double

Inverse of the flattening.

helmert :: a -> Helmert

helmertToWSG84

Arguments

:: a

-> ECEF

-> ECEF

The Helmert transform that will convert a position wrt this ellipsoid into a position wrt WGS84.

helmertFromWSG84

Arguments

:: a

-> ECEF

-> ECEF

And its inverse.

Instances

Ellipsoid LocalEllipsoid

Defined in Geodetics.Ellipsoids

Methods

majorRadius :: LocalEllipsoid -> Length Double

flatR :: LocalEllipsoid -> Dimensionless Double

helmert :: LocalEllipsoid -> Helmert

helmertToWSG84 :: LocalEllipsoid -> ECEF -> ECEF

helmertFromWSG84 :: LocalEllipsoid -> ECEF -> ECEF

Ellipsoid WGS84

Defined in Geodetics.Ellipsoids

Methods

majorRadius :: WGS84 -> Length Double

flatR :: WGS84 -> Dimensionless Double

helmert :: WGS84 -> Helmert

helmertToWSG84 :: WGS84 -> ECEF -> ECEF

helmertFromWSG84 :: WGS84 -> ECEF -> ECEF

Ellipsoid OSGB36

Defined in Geodetics.UK

Methods

majorRadius :: OSGB36 -> Length Double

flatR :: OSGB36 -> Dimensionless Double

helmert :: OSGB36 -> Helmert

helmertToWSG84 :: OSGB36 -> ECEF -> ECEF

helmertFromWSG84 :: OSGB36 -> ECEF -> ECEF

data WGS84

The WGS84 geoid, major radius 6378137.0 meters, flattening = 1 / 298.257223563 as defined in "Technical Manual DMA TM 8358.1 - Datums, Ellipsoids, Grids, and Grid Reference Systems" at the National Geospatial-Intelligence Agency (NGA).

The WGS84 has a special place in this library as the standard Ellipsoid against which all others are defined.

Constructors

WGS84

Instances

Eq WGS84

Defined in Geodetics.Ellipsoids

Methods

(==) :: WGS84 -> WGS84 -> Bool

(/=) :: WGS84 -> WGS84 -> Bool

Show WGS84

Defined in Geodetics.Ellipsoids

Methods

showsPrec :: Int -> WGS84 -> ShowS

show :: WGS84 -> String

showList :: [WGS84] -> ShowS

Ellipsoid WGS84

Defined in Geodetics.Ellipsoids

Methods

majorRadius :: WGS84 -> Length Double

flatR :: WGS84 -> Dimensionless Double

helmert :: WGS84 -> Helmert

helmertToWSG84 :: WGS84 -> ECEF -> ECEF

helmertFromWSG84 :: WGS84 -> ECEF -> ECEF

data LocalEllipsoid

Ellipsoids other than WGS84, used within a defined geographical area where they are a better fit to the local geoid. Can also be used for historical ellipsoids.

The Show instance just returns the name. Creating two different local ellipsoids with the same name is a Bad Thing.

Constructors

LocalEllipsoid

Fields

• nameLocal :: String
• majorRadiusLocal :: Length Double
• flatRLocal :: Dimensionless Double
• helmertLocal :: Helmert

Instances

Eq LocalEllipsoid

Defined in Geodetics.Ellipsoids

Methods

(==) :: LocalEllipsoid -> LocalEllipsoid -> Bool

(/=) :: LocalEllipsoid -> LocalEllipsoid -> Bool

Show LocalEllipsoid

Defined in Geodetics.Ellipsoids

Methods

showsPrec :: Int -> LocalEllipsoid -> ShowS

show :: LocalEllipsoid -> String

showList :: [LocalEllipsoid] -> ShowS

Ellipsoid LocalEllipsoid

Defined in Geodetics.Ellipsoids

Methods

majorRadius :: LocalEllipsoid -> Length Double

flatR :: LocalEllipsoid -> Dimensionless Double

helmert :: LocalEllipsoid -> Helmert

helmertToWSG84 :: LocalEllipsoid -> ECEF -> ECEF

helmertFromWSG84 :: LocalEllipsoid -> ECEF -> ECEF

flattening :: Ellipsoid e => e -> Dimensionless Double

Flattening (f) of an ellipsoid.

minorRadius :: Ellipsoid e => e -> Length Double

The minor radius of an ellipsoid.

eccentricity2 :: Ellipsoid e => e -> Dimensionless Double

The eccentricity squared of an ellipsoid.

eccentricity'2 :: Ellipsoid e => e -> Dimensionless Double

The second eccentricity squared of an ellipsoid.

Auxiliary latitudes and related Values

normal :: Ellipsoid e => e -> Angle Double -> Length Double

Distance from the surface at the specified latitude to the axis of the Earth straight down. Also known as the radius of curvature in the prime vertical, and often denoted N.

latitudeRadius :: Ellipsoid e => e -> Angle Double -> Length Double

Radius of the circle of latitude: the distance from a point at that latitude to the axis of the Earth.

meridianRadius :: Ellipsoid e => e -> Angle Double -> Length Double

Radius of curvature in the meridian at the specified latitude. Often denoted M.

primeVerticalRadius :: Ellipsoid e => e -> Angle Double -> Length Double

Radius of curvature of the ellipsoid perpendicular to the meridian at the specified latitude.

isometricLatitude :: Ellipsoid e => e -> Angle Double -> Angle Double

The isometric latitude. The isometric latitude is conventionally denoted by ψ (not to be confused with the geocentric latitude): it is used in the development of the ellipsoidal versions of the normal Mercator projection and the Transverse Mercator projection. The name "isometric" arises from the fact that at any point on the ellipsoid equal increments of ψ and longitude λ give rise to equal distance displacements along the meridians and parallels respectively.

Tiny linear algebra library for 3D vectors

type Vec3 a = (a, a, a)

3d vector as (X,Y,Z).

type Matrix3 a = Vec3 (Vec3 a)

3x3 transform matrix for Vec3.

add3 :: Num a => Vec3 (Quantity d a) -> Vec3 (Quantity d a) -> Vec3 (Quantity d a)

Add two vectors

scale3 :: Num a => Vec3 (Quantity d a) -> Quantity d' a -> Vec3 (Quantity (d * d') a)

Multiply a vector by a scalar.

negate3 :: Num a => Vec3 (Quantity d a) -> Vec3 (Quantity d a)

Negation of a vector.

transform3 :: Num a => Matrix3 (Quantity d a) -> Vec3 (Quantity d' a) -> Vec3 (Quantity (d * d') a)

Multiply a matrix by a vector in the Dimensional type system.

invert3 :: Fractional a => Matrix3 (Quantity d a) -> Matrix3 (Quantity ((d * d) / ((d * d) * d)) a)

Inverse of a 3x3 matrix.

trans3 :: Matrix3 a -> Matrix3 a

Transpose of a 3x3 matrix.

dot3 :: Num a => Vec3 (Quantity d1 a) -> Vec3 (Quantity d2 a) -> Quantity (d1 * d2) a

Dot product of two vectors

cross3 :: Num a => Vec3 (Quantity d1 a) -> Vec3 (Quantity d2 a) -> Vec3 (Quantity (d1 * d2) a)

Cross product of two vectors