geodetics-0.0.5: Terrestrial coordinate systems and geodetic calculations.

Geodetics.Ellipsoids

Description

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.

Synopsis

## Helmert transform between geodetic reference systems

data Helmert Source #

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

Constructors

 Helmert FieldscX, cY, cZ :: Length Double helmertScale :: Dimensionless DoubleParts per millionrX, rY, rZ :: Dimensionless Double

Instances

 Source # Methods(==) :: Helmert -> Helmert -> Bool #(/=) :: Helmert -> Helmert -> Bool # Source # MethodsshowList :: [Helmert] -> ShowS # Source # Methodsstimes :: Integral b => b -> Helmert -> Helmert # Source # Methodsmconcat :: [Helmert] -> Helmert #

The inverse of a Helmert transformation.

type ECEF = Vec3 (Length Double) Source #

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

Apply a Helmert transformation to earth-centered coordinates.

## Ellipsoid models of the Geoid

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

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

Methods

Arguments

 :: a -> Dimensionless Double Inverse of the flattening.

helmert :: a -> Helmert Source #

Arguments

 :: a -> ECEF -> ECEF The Helmert transform that will convert a position wrt this ellipsoid into a position wrt WGS84.

Arguments

 :: a -> ECEF -> ECEF And its inverse.

Instances

 Source # Methods Source # Methods Source # Methods

data WGS84 Source #

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

 Source # Methods(==) :: WGS84 -> WGS84 -> Bool #(/=) :: WGS84 -> WGS84 -> Bool # Source # MethodsshowsPrec :: Int -> WGS84 -> ShowS #show :: WGS84 -> String #showList :: [WGS84] -> ShowS # Source # Methods

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

Instances

 Source # Methods Source # MethodsshowList :: [LocalEllipsoid] -> ShowS # Source # Methods

Flattening (f) of an ellipsoid.

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

The minor radius of an ellipsoid.

The eccentricity squared of an ellipsoid.

The second eccentricity squared of an ellipsoid.

## Auxiliary latitudes and related Values

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

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.

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

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

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

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) Source #

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

type Matrix3 a = Vec3 (Vec3 a) Source #

3x3 transform matrix for Vec3.

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

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

Multiply a vector by a scalar.

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

Negation of a vector.

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

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) Source #

Inverse of a 3x3 matrix.

trans3 :: Matrix3 a -> Matrix3 a Source #

Transpose of a 3x3 matrix.

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

Dot product of two vectors

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

Cross product of two vectors