| Copyright | (c) 2018 Cedric Liegeois |
|---|---|
| License | BSD3 |
| Maintainer | Cedric Liegeois <ofmooseandmen@yahoo.fr> |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe |
| Language | Haskell2010 |
Data.Geo.Jord.GreatCircle
Description
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.
Synopsis
- data GreatCircle
- greatCircle :: (Eq a, Position a, Show a) => a -> a -> GreatCircle
- greatCircleE :: (Eq a, Position a) => a -> a -> Either String GreatCircle
- greatCircleF :: (Eq a, MonadFail m, Position a) => a -> a -> m GreatCircle
- greatCircleBearing :: Position a => a -> Angle -> GreatCircle
- crossTrackDistance :: Position a => a -> GreatCircle -> Length
- crossTrackDistance' :: Position a => a -> GreatCircle -> Length -> Length
- intersections :: Position a => GreatCircle -> GreatCircle -> Maybe (a, a)
- isInside :: (Eq a, Position a) => a -> [a] -> Bool
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 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 Source # | |
Defined in Data.Geo.Jord.GreatCircle | |
| Show GreatCircle Source # | |
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 Source #
greatCircleE :: (Eq a, Position a) => a -> a -> Either String GreatCircle Source #
greatCircleF :: (Eq a, MonadFail m, Position a) => a -> a -> m GreatCircle Source #
greatCircleBearing :: Position a => a -> Angle -> GreatCircle Source #
GreatCircle passing by the given Position and heading on given bearing.
Geodesic calculations
crossTrackDistance :: Position a => a -> GreatCircle -> Length Source #
crossTrackDistance' assuming a radius of meanEarthRadius.
crossTrackDistance' :: Position a => a -> GreatCircle -> Length -> Length Source #
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) 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.
isInside :: (Eq a, Position a) => a -> [a] -> Bool Source #
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.