Safe Haskell	None
Language	Haskell2010

Naqsha.Geometry

Contents

Basics
Geometric hashing.
Distance calculation.
Internal details

Description

The geometric types and values exposed by naqsha.

Synopsis

Basics

A point on the globe is specified by giving its geo coordinates represented by the type Geo. It is essentially a pair of the Latitude and Longitude of the point.

Examples

kanpurLatitude  :: Latitude
kanpurLatitude  = lat $ degree 26.4477777
kanpurLongitude :: Longitude
kanpurLongitude = lon $ degree 80.3461111
kanpurGeo       :: Geo
kanpurGeo       = Geo kanpurLatitude kanpurLongitude

You can also specify the latitude and longitude in units of degree, minute and seconds.

kanpurLatitude  = lat $ degree 26 <> minute 26 <> second 52
kanpurLongitude = lon $ degree 80 <> minute 20 <> second 46

The show and read instance of the Latitude and Longitude types uses degrees for displaying and reading respectively. Show and Read instances can express these quantities up to Nano degree precision.

Convention on sign.

For latitudes, positive means north of the equator and negative means south. In the case of longitudes, positive means east of the longitude zero and negative means west. However, if you find these conventions confusing you can use the combinators north, south, east, and west when constructing latitudes or longitudes.

data Geo Source #

The coordinates of a point on the earth's surface.

Constructors

Geo !Latitude !Longitude

Instances

Eq Geo Source #
Methods (==) :: Geo -> Geo -> Bool # (/=) :: Geo -> Geo -> Bool #
Show Geo Source #
Methods showsPrec :: Int -> Geo -> ShowS # show :: Geo -> String # showList :: [Geo] -> ShowS #
Vector Vector Geo Source #
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Geo -> m (Vector Geo) # basicUnsafeThaw :: PrimMonad m => Vector Geo -> m (Mutable Vector (PrimState m) Geo) # basicLength :: Vector Geo -> Int # basicUnsafeSlice :: Int -> Int -> Vector Geo -> Vector Geo # basicUnsafeIndexM :: Monad m => Vector Geo -> Int -> m Geo # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Geo -> Vector Geo -> m () # elemseq :: Vector Geo -> Geo -> b -> b #
MVector MVector Geo Source #
Methods basicLength :: MVector s Geo -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Geo -> MVector s Geo # basicOverlaps :: MVector s Geo -> MVector s Geo -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Geo) # basicInitialize :: PrimMonad m => MVector (PrimState m) Geo -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Geo -> m (MVector (PrimState m) Geo) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Geo -> Int -> m Geo # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Geo -> Int -> Geo -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Geo -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Geo -> Geo -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Geo -> MVector (PrimState m) Geo -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Geo -> MVector (PrimState m) Geo -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Geo -> Int -> m (MVector (PrimState m) Geo) #
data Vector Geo Source #
data Vector Geo = GeoV (Vector (Angle, Angle))
data MVector s Geo Source #
data MVector s Geo = MGeoV (MVector s (Angle, Angle))

northPole :: Geo Source #

The North pole

southPole :: Geo Source #

The South pole

Latitudes

data Latitude Source #

The latitude of a point. Positive denotes North of Equator where as negative South.

Instances

Bounded Latitude Source #
Methods minBound :: Latitude # maxBound :: Latitude #
Eq Latitude Source #
Methods (==) :: Latitude -> Latitude -> Bool # (/=) :: Latitude -> Latitude -> Bool #
Ord Latitude Source #
Methods compare :: Latitude -> Latitude -> Ordering # (<) :: Latitude -> Latitude -> Bool # (<=) :: Latitude -> Latitude -> Bool # (>) :: Latitude -> Latitude -> Bool # (>=) :: Latitude -> Latitude -> Bool # max :: Latitude -> Latitude -> Latitude # min :: Latitude -> Latitude -> Latitude #
Read Latitude Source #
Methods readsPrec :: Int -> ReadS Latitude # readList :: ReadS [Latitude] # readPrec :: ReadPrec Latitude # readListPrec :: ReadPrec [Latitude] #
Show Latitude Source #
Methods showsPrec :: Int -> Latitude -> ShowS # show :: Latitude -> String # showList :: [Latitude] -> ShowS #
Bits Latitude Source #
Methods (.&.) :: Latitude -> Latitude -> Latitude # (.\|.) :: Latitude -> Latitude -> Latitude # xor :: Latitude -> Latitude -> Latitude # complement :: Latitude -> Latitude # shift :: Latitude -> Int -> Latitude # rotate :: Latitude -> Int -> Latitude # zeroBits :: Latitude # bit :: Int -> Latitude # setBit :: Latitude -> Int -> Latitude # clearBit :: Latitude -> Int -> Latitude # complementBit :: Latitude -> Int -> Latitude # testBit :: Latitude -> Int -> Bool # bitSizeMaybe :: Latitude -> Maybe Int # bitSize :: Latitude -> Int # isSigned :: Latitude -> Bool # shiftL :: Latitude -> Int -> Latitude # unsafeShiftL :: Latitude -> Int -> Latitude # shiftR :: Latitude -> Int -> Latitude # unsafeShiftR :: Latitude -> Int -> Latitude # rotateL :: Latitude -> Int -> Latitude # rotateR :: Latitude -> Int -> Latitude # popCount :: Latitude -> Int #
Angular Latitude Source #
Methods toAngle :: Latitude -> Angle Source #
Vector Vector Latitude Source #
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Latitude -> m (Vector Latitude) # basicUnsafeThaw :: PrimMonad m => Vector Latitude -> m (Mutable Vector (PrimState m) Latitude) # basicLength :: Vector Latitude -> Int # basicUnsafeSlice :: Int -> Int -> Vector Latitude -> Vector Latitude # basicUnsafeIndexM :: Monad m => Vector Latitude -> Int -> m Latitude # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Latitude -> Vector Latitude -> m () # elemseq :: Vector Latitude -> Latitude -> b -> b #
MVector MVector Latitude Source #
Methods basicLength :: MVector s Latitude -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Latitude -> MVector s Latitude # basicOverlaps :: MVector s Latitude -> MVector s Latitude -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Latitude) # basicInitialize :: PrimMonad m => MVector (PrimState m) Latitude -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Latitude -> m (MVector (PrimState m) Latitude) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Latitude -> Int -> m Latitude # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Latitude -> Int -> Latitude -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Latitude -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Latitude -> Latitude -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Latitude -> MVector (PrimState m) Latitude -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Latitude -> MVector (PrimState m) Latitude -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Latitude -> Int -> m (MVector (PrimState m) Latitude) #
data Vector Latitude Source #
data Vector Latitude = LatV (Vector Angle)
data MVector s Latitude Source #
data MVector s Latitude = MLatV (MVector s Angle)

lat :: Angle -> Latitude Source #

Construct latitude out of an angle.

north :: Angle -> Latitude Source #

Convert an angle to a northern latitude

tropicOfCancer = north $ degree 23.5

south :: Angle -> Latitude Source #

Convert an angle to a southern latitude.

 tropicOfCapricon = south $ degree 23.5

equator :: Latitude Source #

The latitude of equator.

tropicOfCancer :: Latitude Source #

The latitude corresponding to the Tropic of Cancer.

tropicOfCapricon :: Latitude Source #

The latitude corresponding to the Tropic of Capricon

Longitudes.

data Longitude Source #

The longitude of a point. Positive denotes East of the Greenwich meridian where as negative denotes West.

Instances

Bounded Longitude Source #
Methods minBound :: Longitude # maxBound :: Longitude #
Eq Longitude Source #
Methods (==) :: Longitude -> Longitude -> Bool # (/=) :: Longitude -> Longitude -> Bool #
Ord Longitude Source #
Methods compare :: Longitude -> Longitude -> Ordering # (<) :: Longitude -> Longitude -> Bool # (<=) :: Longitude -> Longitude -> Bool # (>) :: Longitude -> Longitude -> Bool # (>=) :: Longitude -> Longitude -> Bool # max :: Longitude -> Longitude -> Longitude # min :: Longitude -> Longitude -> Longitude #
Read Longitude Source #
Methods readsPrec :: Int -> ReadS Longitude # readList :: ReadS [Longitude] # readPrec :: ReadPrec Longitude # readListPrec :: ReadPrec [Longitude] #
Show Longitude Source #
Methods showsPrec :: Int -> Longitude -> ShowS # show :: Longitude -> String # showList :: [Longitude] -> ShowS #
Monoid Longitude Source #
Methods mempty :: Longitude # mappend :: Longitude -> Longitude -> Longitude # mconcat :: [Longitude] -> Longitude #
Bits Longitude Source #
Methods (.&.) :: Longitude -> Longitude -> Longitude # (.\|.) :: Longitude -> Longitude -> Longitude # xor :: Longitude -> Longitude -> Longitude # complement :: Longitude -> Longitude # shift :: Longitude -> Int -> Longitude # rotate :: Longitude -> Int -> Longitude # zeroBits :: Longitude # bit :: Int -> Longitude # setBit :: Longitude -> Int -> Longitude # clearBit :: Longitude -> Int -> Longitude # complementBit :: Longitude -> Int -> Longitude # testBit :: Longitude -> Int -> Bool # bitSizeMaybe :: Longitude -> Maybe Int # bitSize :: Longitude -> Int # isSigned :: Longitude -> Bool # shiftL :: Longitude -> Int -> Longitude # unsafeShiftL :: Longitude -> Int -> Longitude # shiftR :: Longitude -> Int -> Longitude # unsafeShiftR :: Longitude -> Int -> Longitude # rotateL :: Longitude -> Int -> Longitude # rotateR :: Longitude -> Int -> Longitude # popCount :: Longitude -> Int #
Group Longitude Source #
Methods invert :: Longitude -> Longitude # pow :: Integral x => Longitude -> x -> Longitude #
Angular Longitude Source #
Methods toAngle :: Longitude -> Angle Source #
Vector Vector Longitude Source #
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Longitude -> m (Vector Longitude) # basicUnsafeThaw :: PrimMonad m => Vector Longitude -> m (Mutable Vector (PrimState m) Longitude) # basicLength :: Vector Longitude -> Int # basicUnsafeSlice :: Int -> Int -> Vector Longitude -> Vector Longitude # basicUnsafeIndexM :: Monad m => Vector Longitude -> Int -> m Longitude # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Longitude -> Vector Longitude -> m () # elemseq :: Vector Longitude -> Longitude -> b -> b #
MVector MVector Longitude Source #
Methods basicLength :: MVector s Longitude -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Longitude -> MVector s Longitude # basicOverlaps :: MVector s Longitude -> MVector s Longitude -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Longitude) # basicInitialize :: PrimMonad m => MVector (PrimState m) Longitude -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Longitude -> m (MVector (PrimState m) Longitude) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Longitude -> Int -> m Longitude # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Longitude -> Int -> Longitude -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Longitude -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Longitude -> Longitude -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Longitude -> MVector (PrimState m) Longitude -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Longitude -> MVector (PrimState m) Longitude -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Longitude -> Int -> m (MVector (PrimState m) Longitude) #
data Vector Longitude Source #
data Vector Longitude = LongV (Vector Angle)
data MVector s Longitude Source #
data MVector s Longitude = MLongV (MVector s Angle)

lon :: Angle -> Longitude Source #

Convert angles to longitude.

east :: Angle -> Longitude Source #

Convert angle to an eastern longitude.

kanpurLongitude = east $ degree 80.3461

west :: Angle -> Longitude Source #

Convert angle to a western longitude

newyorkLongitude = west $ degree 74.0059

greenwich :: Longitude Source #

The zero longitude.

Angles and angular quantities.

data Angle Source #

An abstract angle. Internally, angles are represented as a 64-bit integer with each unit contribute 1/2^64 fraction of a complete circle. This means that angles are accurate up to a resolution of 2 π / 2^64 radians. Angles form a group under the angular addition and the fact that these are represented as integers means one can expect high speed accurate angle arithmetic.

When expressing angles one can use a more convenient notation:

myAngle   = degree 21.71167
yourAngle = degree 21 <> minute 42 <> second 42

Instances

Bounded Angle Source #
Methods minBound :: Angle # maxBound :: Angle #
Enum Angle Source #
Methods succ :: Angle -> Angle # pred :: Angle -> Angle # toEnum :: Int -> Angle # fromEnum :: Angle -> Int # enumFrom :: Angle -> [Angle] # enumFromThen :: Angle -> Angle -> [Angle] # enumFromTo :: Angle -> Angle -> [Angle] # enumFromThenTo :: Angle -> Angle -> Angle -> [Angle] #
Eq Angle Source #
Methods (==) :: Angle -> Angle -> Bool # (/=) :: Angle -> Angle -> Bool #
Ord Angle Source #
Methods compare :: Angle -> Angle -> Ordering # (<) :: Angle -> Angle -> Bool # (<=) :: Angle -> Angle -> Bool # (>) :: Angle -> Angle -> Bool # (>=) :: Angle -> Angle -> Bool # max :: Angle -> Angle -> Angle # min :: Angle -> Angle -> Angle #
Read Angle Source #
Methods readsPrec :: Int -> ReadS Angle # readList :: ReadS [Angle] # readPrec :: ReadPrec Angle # readListPrec :: ReadPrec [Angle] #
Show Angle Source #
Methods showsPrec :: Int -> Angle -> ShowS # show :: Angle -> String # showList :: [Angle] -> ShowS #
Monoid Angle Source #
Methods mempty :: Angle # mappend :: Angle -> Angle -> Angle # mconcat :: [Angle] -> Angle #
Bits Angle Source #
Methods (.&.) :: Angle -> Angle -> Angle # (.\|.) :: Angle -> Angle -> Angle # xor :: Angle -> Angle -> Angle # complement :: Angle -> Angle # shift :: Angle -> Int -> Angle # rotate :: Angle -> Int -> Angle # zeroBits :: Angle # bit :: Int -> Angle # setBit :: Angle -> Int -> Angle # clearBit :: Angle -> Int -> Angle # complementBit :: Angle -> Int -> Angle # testBit :: Angle -> Int -> Bool # bitSizeMaybe :: Angle -> Maybe Int # bitSize :: Angle -> Int # isSigned :: Angle -> Bool # shiftL :: Angle -> Int -> Angle # unsafeShiftL :: Angle -> Int -> Angle # shiftR :: Angle -> Int -> Angle # unsafeShiftR :: Angle -> Int -> Angle # rotateL :: Angle -> Int -> Angle # rotateR :: Angle -> Int -> Angle # popCount :: Angle -> Int #
Group Angle Source #
Methods invert :: Angle -> Angle # pow :: Integral x => Angle -> x -> Angle #
Unbox Angle Source #

Angular Angle Source #
Methods toAngle :: Angle -> Angle Source #
Vector Vector Angle Source #
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Angle -> m (Vector Angle) # basicUnsafeThaw :: PrimMonad m => Vector Angle -> m (Mutable Vector (PrimState m) Angle) # basicLength :: Vector Angle -> Int # basicUnsafeSlice :: Int -> Int -> Vector Angle -> Vector Angle # basicUnsafeIndexM :: Monad m => Vector Angle -> Int -> m Angle # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Angle -> Vector Angle -> m () # elemseq :: Vector Angle -> Angle -> b -> b #
MVector MVector Angle Source #
Methods basicLength :: MVector s Angle -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Angle -> MVector s Angle # basicOverlaps :: MVector s Angle -> MVector s Angle -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Angle) # basicInitialize :: PrimMonad m => MVector (PrimState m) Angle -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Angle -> m (MVector (PrimState m) Angle) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Angle -> Int -> m Angle # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Angle -> Int -> Angle -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Angle -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Angle -> Angle -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Angle -> MVector (PrimState m) Angle -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Angle -> MVector (PrimState m) Angle -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Angle -> Int -> m (MVector (PrimState m) Angle) #
data Vector Angle Source #
data Vector Angle = AngV (Vector Int64)
data MVector s Angle Source #
data MVector s Angle = MAngV (MVector s Int64)

degree :: Rational -> Angle Source #

Express angle in degrees.

minute :: Rational -> Angle Source #

Express angle in minutes.

second :: Rational -> Angle Source #

Express angle in seconds.

radian :: Double -> Angle Source #

Express angle in radians

toDegree :: Fractional r => Angle -> r Source #

Measure angle in degrees. This conversion may lead to loss of precision.

toRadian :: Angle -> Double Source #

Measure angle in radians. This conversion may lead to loss of precision.

class Angular a where Source #

Angular quantities.

Minimal complete definition

toAngle

Methods

toAngle :: a -> Angle Source #

Instances

Angular Longitude Source #
Methods toAngle :: Longitude -> Angle Source #
Angular Latitude Source #
Methods toAngle :: Latitude -> Angle Source #
Angular Angle Source #
Methods toAngle :: Angle -> Angle Source #

Geometric hashing.

Geometric hashing is a technique of converting geometric coordinates into 1-dimension strings. Often these hashes ensures that string with large common prefix are close by (although not the converse). Hence, these hashes can be used to stored geo-cordinates in database and build into it a sense of location awareness. We support the following geometric hashing:

Naqsha.Geometry.Coordinate.GeoHash:: The geohash standard (https://en.wikipedia.org/wiki/Geohash).

None of these modules are imported by default the user may import the one that is most desirable.

Distance calculation.

Calculating quantities like distance, bearing etc depends on the model of the globe that we choose. Even in a given model we might have different algorithms to compute the distance depending on speed-accuracy trade-offs. Choosing the correct model and algorithms is application dependent and hence we do not expose any default ones. The following modules can be imported depending on the need

Naqsha.Geometry.Spherical:: Assume a spherical model of the globe. Distance is calculated using the haversine formula.

Internal details

The basic types like Latitude or Longitude are exposed as opaque types from this module. For type safety, we encourage the users to use this module mostly when dealing with those times. For the rare case when some non-trivial operations need to be defined, we expose the internal module Naqsha.Geometry.Internal. However, use this interface with caution.