naqsha-0.3.0.1: A library for working with anything map related.

Naqsha.Geometry

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

The North pole

The South pole

## Latitudes

data Latitude Source #

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

Instances

Construct latitude out of an angle.

Convert an angle to a northern latitude

tropicOfCancer = north $degree 23.5 Convert an angle to a southern latitude.  tropicOfCapricon = south$ degree 23.5

The latitude of equator.

The latitude corresponding to the Tropic of Cancer.

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
 Source # Instance detailsDefined in Naqsha.Geometry.Internal Methods Source # Instance detailsDefined in Naqsha.Geometry.Internal Methods Source # Instance detailsDefined in Naqsha.Geometry.Internal Methods Source # Instance detailsDefined in Naqsha.Geometry.Internal Methods Source # Instance detailsDefined in Naqsha.Geometry.Internal MethodsshowList :: [Longitude] -> ShowS # Source # Instance detailsDefined in Naqsha.Geometry.Internal Methodsstimes :: Integral b => b -> Longitude -> Longitude # Source # Instance detailsDefined in Naqsha.Geometry.Internal Methodsmconcat :: [Longitude] -> Longitude # Source # Instance detailsDefined in Naqsha.Geometry.Internal Methodsbit :: Int -> Longitude #testBit :: Longitude -> Int -> Bool # Source # Instance detailsDefined in Naqsha.Geometry.Internal Methodspow :: Integral x => Longitude -> x -> Longitude # Source # Instance detailsDefined in Naqsha.Geometry.Angle Methods Source # Instance detailsDefined in Naqsha.Geometry.Internal MethodsbasicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Longitude -> Vector Longitude -> m () #elemseq :: Vector Longitude -> Longitude -> b -> b # Source # Instance detailsDefined in Naqsha.Geometry.Internal MethodsbasicUnsafeNew :: 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) #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) # newtype Vector Longitude Source # Instance detailsDefined in Naqsha.Geometry.Internal newtype Vector Longitude = LongV (Vector Angle) newtype MVector s Longitude Source # Instance detailsDefined in Naqsha.Geometry.Internal newtype MVector s Longitude = MLongV (MVector s Angle)

Convert angles to longitude.

Convert angle to an eastern longitude.

kanpurLongitude = east $degree 80.3461 Convert angle to a western longitude newyorkLongitude = west$ degree 74.0059

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

Express angle in degrees.

Express angle in minutes.

Express angle in seconds.

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

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

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

class Angular a where Source #

Angular quantities.

Methods

toAngle :: a -> Angle Source #

Instances
 Source # Instance detailsDefined in Naqsha.Geometry.Angle Methods Source # Instance detailsDefined in Naqsha.Geometry.Angle Methods Source # Instance detailsDefined in Naqsha.Geometry.Angle Methods

# 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. This gives a certain amount of type safety when working with these quantities. A user should, whenever possible, only use this module. 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.