Adding NED coordinate system

README.md

@@ -47,8 +47,10 @@ trans = ENUfromLLA(origin_lla, wgs84)
 point_enu = trans(point_lla)
 
 # Equivalently
-point_enu = ENU(point_enu, point_origin, wgs84)
+point_enu = ENU(point_lla, origin_lla, wgs84)
 ```
+The `NED` coordinate system is also available as an alternative to `ENU`, with 
+the same interface.
 
 Similarly, we could convert to UTM/UPS coordinates, and two types are provided
 for this - `UTM` stores 3D coordinates `x`, `y`, and `z` in an unspecified zone,
@@ -252,7 +254,8 @@ as the geodetic coordinates mentioned above, it's common to see
   defining a terrestrial reference frame.
 * The east,north and up **ENU** components of a Cartesian coordinate frame at a
   particular point on the ellipsoid.  This coordinate system is useful as a
-  local frame for navigation.
+  local frame for navigation. It is also common for navigation systems to use
+  north,east and down (**NED**) coordinates.
 * Easting,northing and vertical components of a **projected coordinate system** or
   [**map projection**](http://www.icsm.gov.au/mapping/about_projections.html).
   There's an entire zoo of these, designed to represent the curved surface of an
@@ -325,10 +328,17 @@ projection about the corresponding pole, otherwise `zone` is an integer between
 
 ##### `ENU{T}` - east-north-up
 
-The `ENU` type is a local Cartesian coordinate that encodes a point's distance
+The `ENU` type stores local Cartesian coordinates that encode a point's distance
 towards east `e`, towards north `n` and upwards `u` with respect to an
 unspecified origin. Like `ECEF`, `ENU` is also a subtype of `StaticVector`.
 
+##### `NED{T}` - north-east-down
+
+The `NED` type is an alternative convention to `ENU`. It stores local Cartesian 
+coordinates that encode a point's distance towards north `n`, towards east `e` 
+and downwards `d` with respect to an unspecified origin. Like `ECEF`, `NED` is 
+also a subtype of `StaticVector`.
+
 ### Geodetic Datums
 
 Geodetic datums are modelled as subtypes of the abstract type `Datum`.  The
@@ -379,7 +389,7 @@ be pre-cached (for instance, the origin of an ENU transformation).
 
 The `LLAfromECEF` and `ECEFfromLLA` transformations require an ellipsoidal datum
 to perform the conversion. The exact transformation is performed in both directions,
-using a port the ECEF → LLA transformation from *GeographicLib*.
+using a port of the ECEF → LLA transformation from *GeographicLib*.
 
 Note that in some cases where points are very close to the centre of the ellipsoid,
 multiple equivalent `LLA` points are valid solutions to the transformation problem.
@@ -402,22 +412,24 @@ native Julia port of that used in *GeographicLib*, and is accurate to nanometers
 for up to several UTM zones away from the reference meridian. However, the
 series expansion diverges at ±90° from the reference meridian. While the `UTMZ`-methods
 will automatically choose the canonical zone and hemisphere for the input,
-extreme care must be taken to choose an appropriate zone for the `UTM` methods.
-(In the future, we implement the exact UTM transformation as a fallback —
-contributions welcome!)
+extreme care must be taken to choose an appropriate zone for the `UTM` methods
+(In the future, we will implement the exact UTM transformation as a fallback —
+contributions welcome!).
 
 There is also `UTMfromUTMZ` and `UTMZfromUTM` transformations that are helpful
 for converting between these two formats and putting data into the same `UTM`
 zone.
 
-#### To and from local `ENU` frames
+#### To and from local `ENU` and `NED` frames
 
 The `ECEFfromENU` and `ENUfromECEF` transformations define the transformation
 around a specific origin. Both the origin coordinates as an `ECEF` as well as
 its corresponding latitude and longitude are stored in the transformation for
 maximal efficiency when performing multiple `transform`s. The transformation can
 be inverted with `inv` to perform the reverse transformation with respect to the
-same origin.
+same origin. Moreover, the `ENUfromNED` transformation and its inverse `NEDfromENU` 
+can be used to change a local frame's orientation convention between `ENU` and `NED`, 
+while keeping the same origin.
 
 #### Web Mercator support
 
@@ -443,11 +455,17 @@ These include:
 * `ECEFfromUTM(zone, hemisphere, datum) = ECEFfromLLA(datum) ∘ LLAfromUTM(zone, hemisphere, datum)`
 * `ENUfromLLA(origin, datum) = ENUfromECEF(origin, datum) ∘ ECEFfromLLA(datum)`
 * `LLAfromENU(origin, datum) = LLAfromECEF(datum) ∘ ECEFfromENU(origin, datum)`
+* `NEDfromLLA(origin, datum) = NEDfromENU() ∘ ENUfromECEF(origin, datum) ∘ ECEFfromLLA(datum)`
+* `LLAfromNED(origin, datum) = LLAfromECEF(datum) ∘ ECEFfromENU(origin,datum) ∘ ENUfromNED()`
 * `ECEFfromUTMZ(datum) = ECEFfromLLA(datum) ∘ LLAfromUTMZ(datum)`
 * `ENUfromUTMZ(origin, datum)  = ENUfromLLA(origin, datum) ∘ LLAfromUTMZ(datum`
 * `UTMZfromENU(origin, datum)  = UTMZfromLLA(datum) ∘ LLAfromENU(origin, datum)`
+* `NEDfromUTMZ(origin, datum)  = NEDfromLLA(origin, datum) ∘ LLAfromUTMZ(datum`
+* `UTMZfromNED(origin, datum)  = UTMZfromLLA(datum) ∘ LLAfromNED(origin, datum)`
 * `UTMfromENU(origin, zone, hemisphere, datum) = UTMfromLLA(zone, hemisphere, datum) ∘ LLAfromENU(origin, datum)`
 * `ENUfromUTM(origin, zone, hemisphere, datum) = ENUfromLLA(origin, datum) ∘ LLAfromUTM(zone, hemisphere, datum)`
+* `UTMfromNED(origin, zone, hemisphere, datum) = UTMfromLLA(zone, hemisphere, datum) ∘ LLAfromNED(origin, datum)`
+* `NEDfromUTM(origin, zone, hemisphere, datum) = NEDfromLLA(origin, datum) ∘ LLAfromUTM(zone, hemisphere, datum)`
 
 Constructor-based transforms for these are also provided, such as `UTMZ(ecef, datum)`
 which converts to `LLA` as an intermediary, as above. When converting multiple

src/Geodesy.jl

@@ -13,6 +13,7 @@ export
     # Points
     ECEF,
     ENU,
+    NED,
     LLA,
     LatLon,
     UTM,
@@ -38,9 +39,10 @@ export
 
     # transformation methods
     transform_deriv, transform_deriv_params, compose, ∘,
-    ECEFfromLLA, LLAfromECEF, ENUfromECEF, ECEFfromENU, ENUfromLLA, LLAfromENU,
-    UTMfromLLA, LLAfromUTM, UTMfromECEF, ECEFfromUTM, ENUfromUTM, UTMfromENU,
-    UTMZfromLLA, LLAfromUTMZ, UTMZfromECEF, ECEFfromUTMZ, ENUfromUTMZ, UTMZfromENU,
+    ECEFfromLLA, LLAfromECEF, ENUfromECEF, ECEFfromENU, ENUfromLLA, LLAfromENU, 
+    ENUfromNED, NEDfromENU, NEDfromECEF, ECEFfromNED, NEDfromLLA, LLAfromNED,
+    UTMfromLLA, LLAfromUTM, UTMfromECEF, ECEFfromUTM, ENUfromUTM, UTMfromENU, NEDfromUTM, UTMfromNED,
+    UTMZfromLLA, LLAfromUTMZ, UTMZfromECEF, ECEFfromUTMZ, ENUfromUTMZ, UTMZfromENU, NEDfromUTMZ, UTMZfromNED,
     UTMZfromUTM, UTMfromUTMZ,
     WebMercatorfromLLA, LLAfromWebMercator,
 

src/conversion.jl

@@ -1,15 +1,23 @@
-
 ############################
 ### Identity conversions ###
 ############################
 
 ECEF(ecef::ECEF, datum) = ecef
 LLA(lla::LLA, datum) = lla
 ENU(enu::ENU, datum) = enu
+NED(ned::NED, datum) = ned
 UTM(utm::UTM, datum) = utm
 UTMZ(utmz::UTMZ, datum) = utmz
 
 
+################################
+### ENU <-> NED coordinates  ###
+################################
+
+ENU(ned::NED) = ENUfromNED()(ned)
+NED(enu::ENU) = NEDfromENU()(enu)
+
+
 ################################
 ### LLA <-> ECEF coordinates ###
 ################################
@@ -23,10 +31,17 @@ LLA(ecef::ECEF, datum) = LLAfromECEF(datum)(ecef)
 ################################
 
 ENU(ecef::ECEF, origin, datum) = ENUfromECEF(origin, datum)(ecef)
-
 ECEF(enu::ENU, origin, datum) = ECEFfromENU(origin, datum)(enu)
 
 
+################################
+### ECEF <-> NED coordinates ###
+################################
+
+NED(ecef::ECEF, origin, datum) = NEDfromECEF(origin, datum)(ecef)
+ECEF(ned::NED, origin, datum) = ECEFfromNED(origin, datum)(ned)
+
+
 ################################
 ### LLA <-> ENU coordinates ###
 ################################
@@ -35,6 +50,14 @@ ENU(lla::LLA, origin, datum) =  ENUfromLLA(origin, datum)(lla)
 LLA(enu::ENU, origin, datum) = LLAfromENU(origin, datum)(enu)
 
 
+################################
+### LLA <-> NED coordinates ###
+################################
+
+NED(lla::LLA, origin, datum) =  NEDfromLLA(origin, datum)(lla)
+LLA(ned::NED, origin, datum) = LLAfromNED(origin, datum)(ned)
+
+
 ################################
 ### LLA <-> UTMZ coordinates ###
 ################################
@@ -59,6 +82,14 @@ ENU(utm::UTMZ, origin, datum) = ENUfromUTMZ(origin, datum)(utm)
 UTMZ(enu::ENU, origin, datum) = UTMZfromENU(origin, datum)(enu)
 
 
+################################
+### NED <-> UTMZ coordinates ###
+################################
+
+NED(utm::UTMZ, origin, datum) = NEDfromUTMZ(origin, datum)(utm)
+UTMZ(ned::NED, origin, datum) = UTMZfromNED(origin, datum)(ned)
+
+
 ###############################
 ### LLA <-> UTM coordinates ###
 ###############################
@@ -82,6 +113,15 @@ UTM(ecef::ECEF, zone::Integer, hemisphere::Bool, datum) = UTMfromECEF(zone, hemi
 ENU(utm::UTM, zone::Integer, hemisphere::Bool, origin, datum) = ENUfromUTM(origin, zone, hemisphere, datum)(utm)
 UTM(enu::ENU, zone::Integer, hemisphere::Bool, origin, datum) = UTMfromENU(origin, zone, hemisphere, datum)(enu)
 
+
+###############################
+### NED <-> UTM coordinates ###
+###############################
+
+NED(utm::UTM, zone::Integer, hemisphere::Bool, origin, datum) = NEDfromUTM(origin, zone, hemisphere, datum)(utm)
+UTM(ned::NED, zone::Integer, hemisphere::Bool, origin, datum) = UTMfromNED(origin, zone, hemisphere, datum)(ned)
+
+
 ###############################
 ### UTMZ <-> UTM coordinates ###
 ###############################

src/points.jl

@@ -82,6 +82,24 @@ end
 Base.show(io::IO, ::MIME"text/plain", enu::ENU) = print(io, "ENU($(enu.e), $(enu.n), $(enu.u))")
 
 
+"""
+    NED(n, e, d = 0.0)
+
+North-East-Down (NED) coordinates. A local Cartesian coordinate system, linearized about a reference point.
+"""
+struct NED{T <: Number} <: FieldVector{T}
+    n::T
+    e::T
+    d::T
+end
+NED(x :: T, y :: T) where {T} = NED(x, y, zero(T))
+@inline function NED(x,y,z)
+    T = promote_type(promote_type(typeof(x),typeof(y)), typeof(z))
+    NED{T}(x,y,z)
+end
+Base.show(io::IO, ::MIME"text/plain", ned::NED) = print(io, "NED($(ned.n), $(ned.e), $(ned.d))")
+
+
 """
     UTM(x, y, z = 0.0)