jord-0.3.1.0: Geographical Position Calculations

Copyright (c) 2018 Cedric Liegeois BSD3 Cedric Liegeois experimental portable Safe Haskell2010

Data.Geo.Jord.Geodetics

Description

Geodetic calculations assuming a spherical earth model.

All functions are implemented using the vector-based approached described in Gade, K. (2010). A Non-singular Horizontal Position Representation

Synopsis

# The GreatCircle type

A circle on the surface of the Earth which lies in a plane passing through the Earth's centre. Every two distinct and non-antipodal 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
 Source # Instance detailsDefined in Data.Geo.Jord.Geodetics Methods Source # Instance detailsDefined in Data.Geo.Jord.Geodetics MethodsshowList :: [GreatCircle] -> ShowS #

# Smart constructors

greatCircle :: (NTransform a, Show a) => a -> a -> GreatCircle Source #

GreatCircle passing by both given positions. errors if given positions are equal or antipodal.

greatCircleE :: NTransform a => a -> a -> Either String GreatCircle Source #

GreatCircle passing by both given positions. A Left indicates that given positions are equal or antipodal.

greatCircleF :: (NTransform a, MonadFail m) => a -> a -> m GreatCircle Source #

GreatCircle passing by both given positions. fails if given positions are equal or antipodal.

greatCircleBearing :: NTransform a => a -> Angle -> GreatCircle Source #

GreatCircle passing by the given position and heading on given bearing.

# 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 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)


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.

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


errors if f || f 1.0

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

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

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 non-zero.

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

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.