Copyright  (c) 2018 Cedric Liegeois 

License  BSD3 
Maintainer  Cedric Liegeois <ofmooseandmen@yahoo.fr> 
Stability  experimental 
Portability  portable 
Safe Haskell  Safe 
Language  Haskell2010 
Geodetic calculations assuming a spherical earth model.
All functions are implemented using the vectorbased approached described in Gade, K. (2010). A Nonsingular Horizontal Position Representation
Synopsis
 data GreatCircle
 class Show a => IsGreatCircle a where
 angularDistance :: NTransform a => a > a > Maybe a > Angle
 antipode :: NTransform a => a > a
 crossTrackDistance :: NTransform a => a > GreatCircle > Length > Length
 crossTrackDistance84 :: NTransform a => a > GreatCircle > Length
 destination :: NTransform a => a > Angle > Length > Length > a
 destination84 :: NTransform a => a > Angle > Length > a
 finalBearing :: (Eq a, NTransform a) => a > a > Maybe Angle
 initialBearing :: (Eq a, NTransform a) => a > a > Maybe Angle
 interpolate :: NTransform a => a > a > Double > a
 intersections :: NTransform a => GreatCircle > GreatCircle > Maybe (a, a)
 insideSurface :: (Eq a, NTransform a) => a > [a] > Bool
 mean :: NTransform a => [a] > Maybe a
 surfaceDistance :: NTransform a => a > a > Length > Length
 surfaceDistance84 :: NTransform a => a > a > Length
The
GreatCircle
type
data GreatCircle Source #
A circle on the surface of the Earth which lies in a plane passing through the Earth's centre. Every two distinct and nonantipodal points on the surface of the Earth define a Great Circle.
It is internally represented as its normal vector  i.e. the normal vector to the plane containing the great circle.
See greatCircle
, greatCircleE
, greatCircleF
or greatCircleBearing
constructors.
Instances
Eq GreatCircle Source #  
Defined in Data.Geo.Jord.Geodetics (==) :: GreatCircle > GreatCircle > Bool # (/=) :: GreatCircle > GreatCircle > Bool #  
Show GreatCircle Source #  
Defined in Data.Geo.Jord.Geodetics showsPrec :: Int > GreatCircle > ShowS # show :: GreatCircle > String # showList :: [GreatCircle] > ShowS # 
class Show a => IsGreatCircle a where Source #
Class for data from which a GreatCircle
can be computed.
:: a  
> GreatCircle 

:: a  
> Either String GreatCircle 

:: MonadFail m  
=> a  
> m GreatCircle 

Instances
(NTransform a, Show a) => IsGreatCircle (Track a) Source # 

Defined in Data.Geo.Jord.Kinematics greatCircle :: Track a > GreatCircle Source # greatCircleE :: Track a > Either String GreatCircle Source # greatCircleF :: MonadFail m => Track a > m GreatCircle Source #  
(NTransform a, Show a) => IsGreatCircle (a, Angle) Source # 
greatCircle (readLatLong "283321N0290700W", decimalDegrees 33.0) 
Defined in Data.Geo.Jord.Geodetics greatCircle :: (a, Angle) > GreatCircle Source # greatCircleE :: (a, Angle) > Either String GreatCircle Source # greatCircleF :: MonadFail m => (a, Angle) > m GreatCircle Source #  
(NTransform a, Show a) => IsGreatCircle (a, a) Source # 
let p1 = decimalLatLongHeight 45.0 (143.5) (metres 1500) let p2 = decimalLatLongHeight 46.0 14.5 (metres 3000) greatCircle (p1, p2)  heights are ignored, great circle are always at earth surface. 
Defined in Data.Geo.Jord.Geodetics greatCircle :: (a, a) > GreatCircle Source # greatCircleE :: (a, a) > Either String GreatCircle Source # greatCircleF :: MonadFail m => (a, a) > m GreatCircle Source # 
Calculations
angularDistance :: NTransform a => a > a > Maybe a > Angle Source #
angularDistance p1 p2 n
computes the angle between the horizontal positions 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.
antipode :: NTransform a => a > a Source #
antipode p
computes the antipodal horizontal position of p
:
the horizontal position on the surface of the Earth which is diametrically opposite to p
.
crossTrackDistance :: NTransform a => a > GreatCircle > Length > Length Source #
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:
let gc1 = greatCircle (decimalLatLong 51 0) (decimalLatLong 52 1) let gc2 = greatCircle (decimalLatLong 52 1) (decimalLatLong 51 0) crossTrackDistance p gc1 = ( crossTrackDistance p gc2) let p = decimalLatLong 53.2611 (0.7972) let gc = greatCircleBearing (decimalLatLong 53.3206 (1.7297)) (decimalDegrees 96.0) crossTrackDistance p gc r84  305.663 metres
crossTrackDistance84 :: NTransform a => a > GreatCircle > Length Source #
crossTrackDistance
using the mean radius of the WGS84 reference ellipsoid.
destination :: NTransform a => a > Angle > Length > Length > a Source #
destination p b d r
computes the destination position from position p
having
travelled the distance d
on the initial bearing (compass angle) b
(bearing will normally vary
before destination is reached) and using the earth radius r
.
let p0 = ecefToNVector (ecefMetres 3812864.094 (115142.863) 5121515.161) s84 let p1 = ecefMetres 3826406.4710518294 8900.536398998282 5112694.233184049 let p = destination p0 (decimalDegrees 96.0217) (metres 124800) r84 nvectorToEcef p s84 = p1
destination84 :: NTransform a => a > Angle > Length > a Source #
destination
using the mean radius of the WGS84 reference ellipsoid.
finalBearing :: (Eq a, NTransform a) => a > a > Maybe Angle Source #
finalBearing p1 p2
computes the final bearing arriving at p2
from p1
in compass angle.
Compass angles are clockwise angles from true north: 0 = north, 90 = east, 180 = south, 270 = west.
The final bearing will differ from the initialBearing
by varying degrees according to distance and latitude.
Returns Nothing
if both horizontal positions are equals.
initialBearing :: (Eq a, NTransform a) => a > a > Maybe Angle Source #
initialBearing p1 p2
computes the initial bearing from p1
to p2
in compass angle.
Compass angles are clockwise angles from true north: 0 = north, 90 = east, 180 = south, 270 = west.
Returns Nothing
if both horizontal positions are equals.
interpolate :: NTransform a => a > a > Double > a Source #
interpolate p0 p1 f# computes the horizontal position at fraction
f between the
p0 and
p1@.
Special conditions:
interpolate p0 p1 0.0 = p0 interpolate p0 p1 1.0 = p1
let p1 = latLongHeight (readLatLong "53°28'46''N 2°14'43''W") (metres 10000) let p2 = latLongHeight (readLatLong "55°36'21''N 13°02'09''E") (metres 20000) interpolate p1 p2 0.5 = decimalLatLongHeight 54.7835574 5.1949856 (metres 15000)
intersections :: NTransform a => GreatCircle > GreatCircle > Maybe (a, a) Source #
Computes the intersections between the two given GreatCircle
s.
Two GreatCircle
s intersect exactly twice unless there are equal (regardless of orientation),
in which case Nothing
is returned.
let gc1 = greatCircleBearing (decimalLatLong 51.885 0.235) (decimalDegrees 108.63) let gc2 = greatCircleBearing (decimalLatLong 49.008 2.549) (decimalDegrees 32.72) let (i1, i2) = fromJust (intersections gc1 gc2) i1 = decimalLatLong 50.9017226 4.4942782 i2 = antipode i1
insideSurface :: (Eq a, NTransform a) => a > [a] > Bool Source #
insideSurface p ps
determines whether the p
is inside the polygon defined by the list of positions ps
.
The polygon is closed if needed (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 nonzero.
Always returns False
if ps
does not at least defines a triangle.
let malmo = decimalLatLong 55.6050 13.0038 let ystad = decimalLatLong 55.4295 13.82 let lund = decimalLatLong 55.7047 13.1910 let helsingborg = decimalLatLong 56.0465 12.6945 let kristianstad = decimalLatLong 56.0294 14.1567 let polygon = [malmo, ystad, kristianstad, helsingborg, lund] let hoor = decimalLatLong 55.9295 13.5297 let hassleholm = decimalLatLong 56.1589 13.7668 insideSurface hoor polygon = True insideSurface hassleholm polygon = False
mean :: NTransform a => [a] > Maybe a Source #
mean ps
computes the mean geographic horitzontal position of ps
, if it is defined.
The geographic mean is not defined for antipodals position (since they cancel each other).
Special conditions:
mean [] = Nothing mean [p] = Just p mean [p1, p2, p3] = Just circumcentre mean [p1, .., antipode p1] = Nothing
surfaceDistance :: NTransform a => a > a > Length > Length Source #
surfaceDistance p1 p2
computes the surface distance (length of geodesic) between the positions p1
and p2
.
surfaceDistance84 :: NTransform a => a > a > Length Source #
surfaceDistance
using the mean radius of the WGS84 reference ellipsoid.