Data.Geo.Jord.GreatCircle

Types and functions for working with Great Circle.

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

This module assumes a spherical earth.

The GreatCircle type

data GreatCircle

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

Eq GreatCircle

Defined in Data.Geo.Jord.GreatCircle

Methods

(==) :: GreatCircle -> GreatCircle -> Bool

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

Show GreatCircle

Defined in Data.Geo.Jord.GreatCircle

Methods

showsPrec :: Int -> GreatCircle -> ShowS

show :: GreatCircle -> String

showList :: [GreatCircle] -> ShowS

Smart constructors

greatCircle :: (Eq a, Position a, Show a) => a -> a -> GreatCircle

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

greatCircleE :: (Eq a, Position a) => a -> a -> Either String GreatCircle

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

greatCircleF :: (Eq a, MonadFail m, Position a) => a -> a -> m GreatCircle

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

greatCircleBearing :: Position a => a -> Angle -> GreatCircle

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

Geodesic calculations

crossTrackDistance :: Position a => a -> GreatCircle -> Length

crossTrackDistance' assuming a radius of meanEarthRadius.

crossTrackDistance' :: Position a => a -> GreatCircle -> Length -> Length

Signed distance from given Position to given GreatCircle. 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 (latLongDecimal 51 0) (latLongDecimal 52 1)
    let gc2 = greatCircle (latLongDecimal 52 1) (latLongDecimal 51 0)
    crossTrackDistance p gc1 == (- crossTrackDistance p gc2)

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

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.

isInside :: (Eq a, Position a) => a -> [a] -> Bool

Determines whether the given Position is inside the polygon defined by the given list of Positions. 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 positions does not at least defines a triangle.