jord-1.0.0.0: Geographical Position Calculations

Copyright (c) 2020 Cedric Liegeois BSD3 Cedric Liegeois experimental portable Safe Haskell2010

Data.Geo.Jord

Description

Convience module re-exporting all of Jord API while resolving function name clashes. You'll probably rather want to import Data.Geo.Jord.Position and only the core module(s) that suit your problem:

Synopsis

# Core modules

data Geodesic a Source #

Geodesic line: shortest route between two positions on the surface of a model.

Instances
 Model a => Eq (Geodesic a) Source # Instance detailsDefined in Data.Geo.Jord.Geodesic Methods(==) :: Geodesic a -> Geodesic a -> Bool #(/=) :: Geodesic a -> Geodesic a -> Bool # Model a => Show (Geodesic a) Source # Instance detailsDefined in Data.Geo.Jord.Geodesic MethodsshowsPrec :: Int -> Geodesic a -> ShowS #show :: Geodesic a -> String #showList :: [Geodesic a] -> ShowS #

directGeodesic :: Ellipsoidal a => Position a -> Angle -> Length -> Maybe (Geodesic a) Source #

directGeodesic p1 b1 d solves the direct geodesic problem using Vicenty formula: position along the geodesic, reached from position p1 having travelled the surface distance d on the initial bearing (compass angle) b1 at constant height; it also returns the final bearing at the reached position. The Vincenty formula for the direct problem should always converge, however this function returns Nothing if it would ever fail to do so (probably thus indicating a bug in the implementation).

#### Examples

Expand
>>> import Data.Geo.Jord.Geodesic
>>> import Data.Geo.Jord.Position
>>> 
>>> directGeodesic (northPole WGS84) zero (kilometres 20003.931458623)
Just (Geodesic {geodesicPos1 = 90°0'0.000"N,0°0'0.000"E 0.0m (WGS84)
, geodesicPos2 = 90°0'0.000"S,180°0'0.000"E 0.0m (WGS84)
, geodesicBearing1 = Just 0°0'0.000"
, geodesicBearing2 = Just 180°0'0.000"
, geodesicLength = 20003.931458623km})


inverseGeodesic :: Ellipsoidal a => Position a -> Position a -> Maybe (Geodesic a) Source #

inverseGeodesic p1 p2 solves the inverse geodesic problem using Vicenty formula: surface distance, and initial/final bearing between the geodesic line between positions p1 and p2. The Vincenty formula for the inverse problem can fail to converge for nearly antipodal points in which case this function returns Nothing.

#### Examples

Expand
>>> import Data.Geo.Jord.Geodesic
>>> import Data.Geo.Jord.Position
>>> 
>>> inverseGeodesic (latLongPos 0 0 WGS84) (latLongPos 0.5 179.5 WGS84)
Just (Geodesic {geodesicPos1 = 0°0'0.000"N,0°0'0.000"E 0.0m (WGS84)
, geodesicPos2 = 0°30'0.000"N,179°30'0.000"E 0.0m (WGS84)
, geodesicBearing1 = Just 25°40'18.742"
, geodesicBearing2 = Just 154°19'37.507"
, geodesicLength = 19936.288578981km})
>>> 
>>> inverseGeodesic (latLongPos 0 0 WGS84) (latLongPos 0.5 179.7 WGS84)
Nothing


data MinorArc a Source #

Oriented minor arc of a great circle between two positions: shortest path between positions on a great circle.

Instances
 Model a => Eq (MinorArc a) Source # Instance detailsDefined in Data.Geo.Jord.GreatCircle Methods(==) :: MinorArc a -> MinorArc a -> Bool #(/=) :: MinorArc a -> MinorArc a -> Bool # Model a => Show (MinorArc a) Source # Instance detailsDefined in Data.Geo.Jord.GreatCircle MethodsshowsPrec :: Int -> MinorArc a -> ShowS #show :: MinorArc a -> String #showList :: [MinorArc a] -> ShowS #

data GreatCircle a Source #

A circle on the surface of a sphere which lies in a plane passing through the sphere centre. Every two distinct and non-antipodal points define a unique Great Circle.

It is internally represented as its normal vector - i.e. the normal vector to the plane containing the great circle.

Instances
 Eq a => Eq (GreatCircle a) Source # Instance detailsDefined in Data.Geo.Jord.GreatCircle Methods(==) :: GreatCircle a -> GreatCircle a -> Bool #(/=) :: GreatCircle a -> GreatCircle a -> Bool # Model a => Show (GreatCircle a) Source # Instance detailsDefined in Data.Geo.Jord.GreatCircle MethodsshowsPrec :: Int -> GreatCircle a -> ShowS #show :: GreatCircle a -> String #showList :: [GreatCircle a] -> ShowS #

greatCircleThrough :: Spherical a => Position a -> Position a -> Maybe (GreatCircle a) Source #

greatCircleThrough p1 p2 returns the GreatCircle passing by both positions p1 and p2. If positions are antipodal, any great circle passing through those positions will be returned. Returns Nothing if given positions are equal.

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let p1 = latLongHeightPos 45.0 (-143.5) (metres 1500) S84
>>> let p2 = latLongHeightPos 46.0 14.5 (metres 3000) S84
>>> greatCircleThrough p1 p2 -- heights are ignored, great circle is always at surface.
Just Great Circle { through 45°0'0.000"N,143°30'0.000"W 1500.0m (S84) & 46°0'0.000"N,14°30'0.000"E 3000.0m (S84) }


greatCircleHeadingOn p b returns the GreatCircle passing by position p and heading on bearing b.

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let p = latLongPos 45.0 (-143.5) S84
>>> let b = decimalDegrees 33.0
>>> greatCircleHeadingOn p b
Great Circle { by 45°0'0.000"N,143°30'0.000"W 0.0m (S84) & heading on 33°0'0.000" }


minorArc :: Spherical a => Position a -> Position a -> Maybe (MinorArc a) Source #

minorArc p1 p2 returns the MinorArc from p1 to p2. Returns Nothing if given positions are equal.

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let p1 = latLongHeightPos 45.0 (-143.5) (metres 1500) S84
>>> let p2 = latLongHeightPos 46.0 14.5 (metres 3000) S84
Just Minor Arc { from: 45°0'0.000"N,143°30'0.000"W 1500.0m (S84), to: 46°0'0.000"N,14°30'0.000"E 3000.0m (S84) }


alongTrackDistance :: Spherical a => Position a -> MinorArc a -> Length Source #

alongTrackDistance p a computes how far Position p is along a path described by the minor arc a: if a perpendicular is drawn from p to the path, the along-track distance is the signed distance from the start point to where the perpendicular crosses the path.

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let p = s84Pos 53.2611 (-0.7972) zero
>>> let g = minorArcBetween (s84Pos 53.3206 (-1.7297) zero) (s84Pos 53.1887 0.1334 zero)
>>> fmap (alongTrackDistance p) a
Right 62.3315757km


alongTrackDistance' :: Spherical a => Position a -> Position a -> Angle -> Length Source #

alongTrackDistance' p s b computes how far Position p is along a path starting at s and heading on bearing b: if a perpendicular is drawn from p to the path, the along-track distance is the signed distance from the start point to where the perpendicular crosses the path.

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let p = s84Pos 53.2611 (-0.7972) zero
>>> let s = s84Pos 53.3206 (-1.7297) zero
>>> let b = decimalDegrees 96.0017325
>>> alongTrackDistance' p s b
62.3315757km


angularDistance :: Spherical a => Position a -> Position a -> Maybe (Position a) -> Angle Source #

angularDistance p1 p2 n computes the angle between the horizontal Points p1 and p2. If n is Nothing, the angle is always in [0..180], otherwise it is in [-180, +180], signed + if p1 is clockwise looking along n, - in opposite direction.

crossTrackDistance p gc computes the signed distance from horizontal Position p to great circle gc. Returns a negative Length if Position if left of great circle, positive Length if Position if right of great circle; the orientation of the great circle is therefore important:

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let gc1 = greatCircleThrough (s84Pos 51 0 zero) (s84Pos 52 1 zero)
>>> fmap (crossTrackDistance p) gc1
Right -176.7568725km
>>> 
>>> let gc2 = greatCircleThrough (s84Pos 52 1 zero) (s84Pos 51 0 zero)
>>> fmap (crossTrackDistance p) gc2
Right 176.7568725km
>>> 
>>> let p = s84Pos 53.2611 (-0.7972) zero
>>> let gc = greatCircleHeadingOn (s84Pos 53.3206 (-1.7297) zero) (decimalDegrees 96.0)
>>> crossTrackDistance p gc
-305.6629 metres


crossTrackDistance' :: Spherical a => Position a -> Position a -> Angle -> Length Source #

crossTrackDistance' p s b computes the signed distance from horizontal Position p to the great circle passing by s and heading on bearing b.

This is equivalent to:

    crossTrackDistance p (greatCircleHeadingOn s b)


interpolate :: Spherical a => Position a -> Position a -> Double -> Position a Source #

interpolate p0 p1 f# computes the position at fraction f between the p0 and p1@.

Special conditions:

    interpolate p0 p1 0.0 = p0
interpolate p0 p1 1.0 = p1


errors if f || f 1

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let p1 = s84Pos 53.479444 (-2.245278) (metres 10000)
>>> let p2 = s84Pos 55.605833 13.035833 (metres 20000)
>>> interpolate p1 p2 0.5
54°47'0.805"N,5°11'41.947"E 15.0km (S84)


intersection :: Spherical a => MinorArc a -> MinorArc a -> Maybe (Position a) Source #

Computes the intersection between the two given minor arcs of great circle.

see also intersections

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let a1 = minorArcBetween (s84Pos 51.885 0.235 zero) (s84Pos 48.269 13.093 zero)
>>> let a2 = minorArcBetween (s84Pos 49.008 2.549 zero) (s84Pos 56.283 11.304 zero)
>>> join (intersection <\$> a1 <*> a2)
Just 50°54'6.260"N,4°29'39.052"E 0.0m (S84)


intersections :: Spherical a => GreatCircle a -> GreatCircle a -> Maybe (Position a, Position a) Source #

Computes the intersections between the two given GreatCircles. Two great circles intersect exactly twice unless there are equal (regardless of orientation), in which case Nothing is returned.

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let gc1 = greatCircleHeadingOn (s84Pos 51.885 0.235 zero) (decimalDegrees 108.63)
>>> let gc2 = greatCircleHeadingOn (s84Pos 49.008 2.549 zero) (decimalDegrees 32.72)
>>> intersections gc1 gc2
Just (50°54'6.201"N,4°29'39.402"E 0.0m (S84),50°54'6.201"S,175°30'20.598"W 0.0m (S84))
>>> let i = intersections gc1 gc2
fmap fst i == fmap (antipode . snd) i
>>> True


isBetween :: Spherical a => Position a -> MinorArc a -> Bool Source #

isBetween p a determines whether position p is within the minor arc of great circle a.

If p is not on the arc, returns whether p is within the area bound by perpendiculars to the arc at each point (in the same hemisphere).

isInsideSurface :: Spherical a => Position a -> [Position a] -> Bool Source #

isInsideSurface p ps determines whether position p is inside the surface polygon defined by positions ps (i.e. ignoring the height of the positions). The polygon can be opened or closed (i.e. if head ps /= last ps).

Uses the angle summation test: on a sphere, due to spherical excess, enclosed point angles will sum to less than 360°, and exterior point angles will be small but non-zero.

Always returns False if ps does not at least defines a triangle.

#### Examples

Expand
>>> import Data.Geo.Jord.GreatCircle
>>> import Data.Geo.Jord.Position
>>> 
>>> let malmo = s84Pos 55.6050 13.0038 zero
>>> let ystad = s84Pos 55.4295 13.82 zero
>>> let lund = s84Pos 55.7047 13.1910 zero
>>> let helsingborg = s84Pos 56.0465 12.6945 zero
>>> let kristianstad = s84Pos 56.0294 14.1567 zero
>>> let polygon = [malmo, ystad, kristianstad, helsingborg, lund]
>>> let hoor = s84Pos 55.9295 13.5297 zero
>>> let hassleholm = s84Pos 56.1589 13.7668 zero
>>> isInsideSurface hoor polygon
True
>>> isInsideSurface hassleholm polygon
False


mean :: Spherical a => [Position a] -> Maybe (Position a) Source #

mean ps computes the geographic mean surface position of ps, if it is defined.

The geographic mean is not defined for antipodals positions (since they cancel each other).

Special conditions:

    mean [] = Nothing
mean [p] = Just p
mean [p1, p2, p3] = Just circumcentre
mean [p1, .., antipode p1] = Nothing


# Aliases for name-clashing functions

destinationE :: Ellipsoidal a => Position a -> Angle -> Length -> Maybe (Position a) Source #

alias for destination.

alias for finalBearing.

alias for initialBearing.

alias for surfaceDistance.

destinationS :: Spherical a => Position a -> Angle -> Length -> Position a Source #

alias for destination.

finalBearingS :: Spherical a => Position a -> Position a -> Maybe Angle Source #

alias for finalBearing.

alias for initialBearing.

surfaceDistanceS :: Spherical a => Position a -> Position a -> Length Source #

alias for surfaceDistance.