--- title: "GeoPosition" language: "en" type: "Symbol" summary: "GeoPosition[{lat, lon}] represents a geodetic position with latitude lat and longitude lon. GeoPosition[{lat, lon, h}] represents a geodetic position with height h relative to the reference ellipsoid. GeoPosition[{lat, lon, h}, datum] represents a geodetic position referring to the specified datum. GeoPosition[{{lat1, lon1}, {lat2, lon2}, ...}, datum] represents an array of geodetic positions. GeoPosition[entity] returns the geodetic position of the specified geographical entity." keywords: - geo position - geodetic position - geo location - geodetic location - position on Earth - latitude longitude - lat lon - lat long - lat lng - GIS - geodesy - mapping - surveying - cartography - navigation - positioning - GPS - BLH - ITRF2000 - WGS84 - NGA - NGS - GEOTRANS - geographic translator - ecef2geodetic - enu2geodetic canonical_url: "https://reference.wolfram.com/language/ref/GeoPosition.html" source: "Wolfram Language Documentation" related_guides: - title: "Geodesy" link: "https://reference.wolfram.com/language/guide/Geodesy.en.md" - title: "Geographic Data & Entities" link: "https://reference.wolfram.com/language/guide/GeographicData.en.md" - title: "Maps & Cartography" link: "https://reference.wolfram.com/language/guide/MapsAndCartography.en.md" - title: "Weather Data" link: "https://reference.wolfram.com/language/guide/WeatherData.en.md" - title: "Free-Form & External Input" link: "https://reference.wolfram.com/language/guide/FreeFormAndExternalInput.en.md" - title: "Locations, Paths, and Routing" link: "https://reference.wolfram.com/language/guide/LocationsPathsAndRouting.en.md" - title: "Scientific Data Analysis" link: "https://reference.wolfram.com/language/guide/ScientificDataAnalysis.en.md" - title: "Angles and Polar Coordinates" link: "https://reference.wolfram.com/language/guide/AnglesAndPolarCoordinates.en.md" - title: "Knowledge Representation & Access" link: "https://reference.wolfram.com/language/guide/KnowledgeRepresentationAndAccess.en.md" - title: "Database Connectivity" link: "https://reference.wolfram.com/language/guide/DatabaseConnectivity.en.md" - title: "WDF (Wolfram Data Framework)" link: "https://reference.wolfram.com/language/guide/WDFWolframDataFramework.en.md" related_tutorials: - title: "GeoGraphics" link: "https://reference.wolfram.com/language/tutorial/GeoGraphics.en.md" --- # GeoPosition GeoPosition[{lat, lon}] represents a geodetic position with latitude lat and longitude lon. GeoPosition[{lat, lon, h}] represents a geodetic position with height h relative to the reference ellipsoid. GeoPosition[{lat, lon, h}, datum] represents a geodetic position referring to the specified datum. GeoPosition[{{lat1, lon1}, {lat2, lon2}, …}, datum] represents an array of geodetic positions. GeoPosition[entity] returns the geodetic position of the specified geographical entity. ## Details * Latitude and longitude values in ``GeoPosition[{lat, lon}]`` can be given as decimal degrees, DMS strings, or ``Quantity`` angles. * Height ``h`` in ``GeoPosition[{lat, lon, h}]`` can be given as a numeric object in meters or as a ``Quantity`` length. * Height ``h`` in ``GeoPosition[{lat, lon, h}]`` is geodetic height, measured with respect to the reference ellipsoid. * ``GeoPosition[{lat, lon, h, t}]`` includes a time ``t`` that can be given as a numeric object or as a ``DateObject`` specification. A numeric ``t`` represents GMT time measured in seconds since the beginning of January 1, 1900. * Valid latitude angles range from $-90$ to 90 degrees. Longitude angles, traditionally between $-180$ and 180 degrees, are unrestricted and interpreted modulo 360 degrees. * A ``GeoPosition`` object with no explicit height assumes height zero with respect to the reference ellipsoid. A ``GeoPosition`` object with no explicit time assumes the current date. * ``GeoPosition[{lat, lon}]`` assumes the default datum ``"ITRF00"``. * Standard datums can be specified by name. Typical named datums include: | | | | ------------- | ---------------------------------------------- | | "ITRF00" | International Terrestrial Reference Frame 2000 | | "NAD27" | North American Datum of 1927 | | "NAD83CORS96" | North American Datum of 1983 (CORS96) | * The complete list of named datums and reference ellipsoids is given by ``GeodesyData[]``. * ``GeoPosition[GeoPosition[{lat, lon}, datum1], datum2]`` converts between datums. * ``GeoPosition[pos, datum]`` converts from any type of geographic position. The following coordinate types can be given: ``GeoPosition``, ``GeoPositionXYZ``, ``GeoPositionENU``, ``GeoGridPosition``. * ``GeoPosition[pos]`` converts from any type of geographic position, keeping the same datum of ``pos``. * ``GeoPosition`` can represent a geodetic position on a body other than Earth using ``GeoPosition[coords, body]``, where ``body`` is an ``Entity`` object of domains ``"Planet"``, ``"MinorPlanet"``, or ``"PlanetaryMoon"``. * For an ``image`` with Exif location information, ``GeoPosition[image]`` returns that information as a ``GeoPosition`` object. * For extended entities, ``GeoPosition[entity]`` uses when possible the position of the geographic center of the entity. * ``GeoPosition[…][prop]`` gives the specified property of a geo position. * Possible properties include: | | | | ------------------- | ------------------------------------------------------------- | | "AbsoluteTime" | date as number of seconds since Jan 1, 1900, 00:00 GMT | | "Count" | number of positions in the GeoPosition object | | "Data" | first argument of the GeoPosition object | | "DateList" | date list {y, m, d, h, m, s} in GMT time | | "DateObject" | full date object | | "Datum" | datum of the GeoPosition object | | "Depth" | point depth: 0 for a single position, 1 for a list of them, … | | "Dimension" | number of coordinates for each position | | "Elevation" | numeric elevation in meters, with respect to the ellipsoid | | "Latitude" | numeric latitude in degrees | | "LatitudeLongitude" | numeric {lat, lon} pair in degrees | | "Longitude" | numeric longitude in degrees | | "LongitudeLatitude" | numeric {lon, lat} pair in degrees | | "PackingType" | Integer or Real if data is packed; None otherwise | ## Examples (39) ### Basic Examples (4) A geodetic position in the default reference frame: ```wl In[1]:= GeoPosition[{37, -109}] Out[1]= GeoPosition[{37, -109}] ``` --- The geo location of a city: ```wl In[1]:= GeoPosition[Entity["City", {"NewYork", "NewYork", "UnitedStates"}]] Out[1]= GeoPosition[{40.6643, -73.9385}] ``` --- The current position of the International Space Station, including height and time information: ```wl In[1]:= SatelliteData[Entity["Satellite", "25544"], "Position"] Out[1]= GeoPosition[{-47.9611, -124.661, 426753., 3.814198461806996`16.33397827010365*^9}] ``` --- A position that explicitly refers to the ITRF00 reference frame: ```wl In[1]:= GeoPosition[{40.112981, -88.261227, 192.868}, "ITRF00"] Out[1]= GeoPosition[{40.113, -88.2612, 192.868}, "ITRF00"] ``` Convert this position to NAD 83 (CORS96) coordinates: ```wl In[2]:= GeoPosition[ %, "NAD83CORS96"] Out[2]= GeoPosition[{40.113, -88.2612, 194.009}, "NAD83CORS96"] ``` Convert to Cartesian geocentric coordinates: ```wl In[3]:= GeoPositionXYZ[%] Out[3]= GeoPositionXYZ[{148218., -4.882534099628989*^6, 4.087711971432877*^6}, "NAD83CORS96"] ``` Convert back to geodetic coordinates: ```wl In[4]:= GeoPosition[%] Out[4]= GeoPosition[{40.113, -88.2612, 194.009}, "NAD83CORS96"] ``` Convert back to ITRF00: ```wl In[5]:= GeoPosition[%, "ITRF00"] Out[5]= GeoPosition[{40.113, -88.2612, 192.868}, "ITRF00"] ``` ### Scope (19) #### Position Specification (9) A geo position identified by values of latitude and longitude, respectively, both in degrees: ```wl In[1]:= GeoPosition[{40.11, -88.24}] Out[1]= GeoPosition[{40.11, -88.24}] ``` Specify height, in meters: ```wl In[2]:= GeoPosition[{40.11, -88.24, 244.32}] Out[2]= GeoPosition[{40.11, -88.24, 244.32}] ``` Specify time as well, in seconds since 1900: ```wl In[3]:= GeoPosition[{40.11, -88.24, 244.32, 3.6*^9}] Out[3]= GeoPosition[{40.11, -88.24, 244.32, 3.6*^9}] ``` --- Give an average location for a geographical entity: ```wl In[1]:= city = Entity["City", {"London", "GreaterLondon", "UnitedKingdom"}] Out[1]= Entity["City", {"London", "GreaterLondon", "UnitedKingdom"}] In[2]:= GeoPosition[city] Out[2]= GeoPosition[{51.5, -0.116667}] ``` --- Angles given as ``Quantity`` objects are converted into numeric angles, in degrees: ```wl In[1]:= GeoPosition[{Quantity[40.11, "AngularDegrees"], Quantity[-2., "Radians"]}] Out[1]= GeoPosition[{40.11, -114.592}] ``` Heights and dates are also canonicalized to meters and seconds, respectively: ```wl In[2]:= GeoPosition[{Quantity[20, "AngularDegrees"], Quantity[-10, "AngularDegrees"], Quantity[1, "Kilometers"], DateObject[]}] Out[2]= GeoPosition[{20, -10, 1000, 3.814198481337339*^9}] ``` --- Input angles as DMS strings: ```wl In[1]:= GeoPosition[{"40°6'36.''", "28°14'24.''W"}] Out[1]= GeoPosition[{40.11, -28.24}] ``` --- Write ``GeoPosition`` objects in DMS string form: ```wl In[1]:= DMSString[GeoPosition[{40.11, -28.24}]] Out[1]= "40°6'36.000\"N 28°14'24.000\"W" ``` --- A ``GeoPosition`` object with no height information is assumed to have zero geodetic height: ```wl In[1]:= GeoPositionXYZ[GeoPosition[{40, 30}]] === GeoPositionXYZ[GeoPosition[{40, 30, 0}]] Out[1]= True ``` A ``GeoPosition`` object with no time information is assumed to have the current date: ```wl In[2]:= {DateValue[GeoPosition[{40, 30}]], DateObject[]} Out[2]= {DateObject[{2020, 11, 12, 13, 34, 51.074481}, "Instant", "Gregorian", -6.], DateObject[{2020, 11, 12, 13, 34, 51.074496}, "Instant", "Gregorian", -6.]} ``` --- Extract Exif location information from an image: ```wl In[1]:= GeoPosition[[image]] Out[1]= GeoPosition[{40.1259, -88.21, 225.}] ``` --- A geo position that specifies its datum: ```wl In[1]:= GeoPosition[{40.11, -88.24}, "WGS72"] Out[1]= GeoPosition[{40.11, -88.24}, "WGS72"] ``` Transform to a different datum: ```wl In[2]:= GeoPosition[%, "ITRF90"] Out[2]= GeoPosition[{40.11, -88.2398}, "ITRF90"] ``` Transform to the original datum: ```wl In[3]:= GeoPosition[%, "WGS72"] Out[3]= GeoPosition[{40.11, -88.24}, "WGS72"] ``` Height is modified in a change of datum, but not time: ```wl In[4]:= GeoPosition[{40.11, -88.24, 244.32, 3.6*^9}, "WGS72"] Out[4]= GeoPosition[{40.11, -88.24, 244.32, 3.6*^9}, "WGS72"] In[5]:= GeoPosition[%, "ITRF90"] Out[5]= GeoPosition[{40.11, -88.2398, 246.525, 3.6*^9}, "ITRF90"] ``` --- Named locations: ```wl In[1]:= GeoPosition["NorthPole"] Out[1]= GeoPosition[{90, 0}] In[2]:= GeoPosition["NullIsland"] Out[2]= GeoPosition[{0, 0}] ``` These are the current locations of the magnetic poles, as determined by ``GeomagneticModelData`` : ```wl In[3]:= GeoPosition["NorthGeomagneticPole"] Out[3]= GeoPosition[{80.63, -72.6821}] In[4]:= GeoPosition["NorthModelDipPole"] Out[4]= GeoPosition[{86.4187, 158.312}] ``` #### Geo Position Arrays (4) To speed up computations, use an array of points as the first argument: ```wl In[1]:= pairs = RandomReal[{-90, 90}, {10000, 2}]; ``` All points are transformed at once: ```wl In[2]:= AbsoluteTiming[r1 = GeoGridPosition[GeoPosition[pairs], "Albers"];] Out[2]= {0.00622, Null} ``` Here each point is transformed individually: ```wl In[3]:= AbsoluteTiming[r2 = GeoGridPosition[GeoPosition[#], "Albers"]& /@ pairs;] Out[3]= {2.18029, Null} ``` Results coincide up to numerical error: ```wl In[4]:= First[r1] - (First /@ r2)//Abs//Max Out[4]= 8.881784197001252`*^-16 ``` --- Changes of datum are also faster using an array of points as the first argument: ```wl In[1]:= pairs = RandomReal[{-90, 90}, {10000, 2}]; In[2]:= AbsoluteTiming[r1 = GeoPosition[GeoPosition[pairs, "WGS72"], "ITRF90"];] Out[2]= {0.022857, Null} In[3]:= AbsoluteTiming[r2 = GeoPosition[GeoPosition[#, "WGS72"], "ITRF90"]& /@ pairs;] Out[3]= {15.7248, Null} In[4]:= First[r1] - (First /@ r2)//Abs//Max Out[4]= 2.842170943040401`*^-14 ``` --- ``GeoPosition`` can contain nested lists of points, as long as all points have the same length and depth: ```wl In[1]:= GeoPosition[{{{1., 2., 3.}, {4., 5., 6.}}, {{7., 8., 9.}}}] Out[1]= GeoPosition[{{{1., 2., 3.}, {4., 5., 6.}}, {{7., 8., 9.}}}] ``` Manipulations will preserve the nesting structure: ```wl In[2]:= GeoGridPosition[%, "Mercator"] Out[2]= GeoGridPosition[{{{2., 1.0000507734366284, 3.}, {5., 4.0032532172070825, 6.}}, {{8., 7.017479226876329, 9.}}}, "Mercator"] In[3]:= GeoPosition[%] Out[3]= GeoPosition[{{{1.0000000000000013, 2., 3.}, {4.000000000000005, 5., 6.}}, {{6.999999999999997, 8., 9.}}}] ``` However, this is not allowed, because the first point has a height specification, but not the second: ```wl In[4]:= GeoPosition[{{1, 2, 3}, {4, 5}}] ``` GeoPosition::gdim: Geo location GeoPosition[{{1,2,3},{4,5}}] contains coordinate lists of different dimensions. ```wl Out[4]= GeoPosition[{{1, 2, 3}, {4, 5}}] ``` This is not allowed because the second point is deeper than the first: ```wl In[5]:= GeoPosition[{{1, 2}, {{3, 4}}}] ``` GeoPosition::gdepth: Geo location GeoPosition[{{1,2},{{3,4}}}] contains coordinate lists of different array depths. ```wl Out[5]= GeoPosition[{{1, 2}, {{3, 4}}}] ``` --- Convert a list of geo positions into a single geo position array: ```wl In[1]:= {GeoPosition[{0, 0}], GeoPosition[{40.3, -20.}], GeoPosition[{90, 90}]} Out[1]= {GeoPosition[{0, 0}], GeoPosition[{40.3, -20.}], GeoPosition[{90, 90}]} In[2]:= GeoPosition[%] Out[2]= GeoPosition[{{0, 0}, {40.3, -20.}, {90, 90}}] ``` Convert back to a list of geo positions: ```wl In[3]:= Thread[%] Out[3]= {GeoPosition[{0, 0}], GeoPosition[{40.3, -20.}], GeoPosition[{90, 90}]} ``` #### Coordinate Extraction (4) Extract date information using ``DateValue`` : ```wl In[1]:= DateString[] Out[1]= "Thu 12 Nov 2020 13:37:02" In[2]:= p = GeoPosition[{-40.3, 178.1, 0., %}] Out[2]= GeoPosition[{-40.3, 178.1, 0., 3.814198622*^9}] In[3]:= DateValue[p] Out[3]= DateObject[{2020, 11, 12, 19, 37, 2.}, "Instant", "Gregorian", 0.] ``` Numeric time in ``GeoPosition`` is interpreted as GMT time. Convert to local time: ```wl In[4]:= TimeZoneConvert[%, $TimeZone] Out[4]= DateObject[{2020, 11, 12, 13, 37, 2.}, "Instant", "Gregorian", -6.] ``` Extract the year as an integer number: ```wl In[5]:= DateValue[p, "Year", Integer] Out[5]= 2020 ``` --- Extract the coordinates from a ``GeoPosition`` object: ```wl In[1]:= p = GeoPosition[{40.21, -85.53, 125.2}] Out[1]= GeoPosition[{40.21, -85.53, 125.2}] In[2]:= First[p] Out[2]= {40.21, -85.53, 125.2} ``` Extract latitude, longitude or both, as ``Quantity`` angles: ```wl In[3]:= Latitude[p] Out[3]= Quantity[40.21, "AngularDegrees"] In[4]:= Longitude[p] Out[4]= Quantity[-85.53, "AngularDegrees"] In[5]:= LatitudeLongitude[p] Out[5]= {Quantity[40.21, "AngularDegrees"], Quantity[-85.53, "AngularDegrees"]} ``` --- Use properties to extract information from a ``GeoPosition`` object: ```wl In[1]:= p = Here Out[1]= GeoPosition[{40.11, -88.24}] In[2]:= p["Properties"] Out[2]= {"AbsoluteTime", "Count", "Data", "DateList", "DateObject", "Datum", "Depth", "Dimension", "Elevation", "Latitude", "LatitudeLongitude", "Longitude", "LongitudeLatitude", "PackingType"} In[3]:= AssociationMap[p, %]//Normal//Column Out[3]= "AbsoluteTime" -> 3.814198653609565`16.3339782976706*^9 "Count" -> 1 "Data" -> {40.11, -88.24} "DateList" -> {2020, 11, 12, 19, 37, 33.609676} "DateObject" -> DateObject[{2020, 11, 12, 19, 37, 33.609746}, "Instant", "Gregorian", 0.] "Datum" -> "ITRF00" "Depth" -> 0 "Dimension" -> 2 "Elevation" -> 0 "Latitude" -> 40.11 "LatitudeLongitude" -> {40.11, -88.24} "Longitude" -> -88.24 "LongitudeLatitude" -> {-88.24, 40.11} "PackingType" -> None ``` --- Use properties to extract information from a ``GeoPosition`` array: ```wl In[1]:= p = RandomGeoPosition["World", {10, 20}] Out[1]= GeoPosition[CompressedData["«4389»"]] ``` There are 200 points: ```wl In[2]:= p["Count"] Out[2]= 200 ``` It is a matrix of points, so it has point depth 2: ```wl In[3]:= p["Depth"] Out[3]= 2 ``` Each point has dimension 2, namely latitude and longitude: ```wl In[4]:= p["Dimension"] Out[4]= 2 ``` ``RandomGeoPosition`` returns a ``GeoPosition`` object containing a packed array with type ``Real`` : ```wl In[5]:= p["PackingType"] Out[5]= Real ``` Any other property will return an array of values corresponding to the points of the array: ```wl In[6]:= p["AbsoluteTime"]//Dimensions Out[6]= {10, 20} In[7]:= p["DateList"]//Dimensions Out[7]= {10, 20, 6} ``` #### Datum Transformations (2) Perform a datum transformation from the default ``"ITRF00"`` to the British datum ``"OGB7"`` of 1936: ```wl In[1]:= p = GeoPosition[{27.7, -170.4}] Out[1]= GeoPosition[{27.7, -170.4}] In[2]:= q = GeoPosition[p, "OGB7"] Out[2]= GeoPosition[{27.6933, -170.402}, "OGB7"] ``` To estimate the implied spatial change, compute geo distance ignoring the datum information: ```wl In[3]:= GeoDistance[LatitudeLongitude[p], LatitudeLongitude[q]] Out[3]= Quantity[0.4838893707366225, "Miles"] In[4]:= UnitConvert[%] Out[4]= Quantity[778.744455458759, "Meters"] ``` The change is smaller for locations in the UK: ```wl In[5]:= p = RandomGeoPosition[Entity["Country", "UnitedKingdom"]] Out[5]= GeoPosition[{57.9093, -4.34461}] In[6]:= q = GeoPosition[p, "OGB7"] Out[6]= GeoPosition[{57.9096, -4.34327}, "OGB7"] In[7]:= GeoDistance[LatitudeLongitude[p], LatitudeLongitude[q]] Out[7]= Quantity[283.325659643541, "Feet"] In[8]:= UnitConvert[%] Out[8]= Quantity[86.35766105935129, "Meters"] ``` --- Convert a geo position array of locations from the American ``"NAD27"`` datum to the European ``"EURM"`` : ```wl In[1]:= GeoPosition[{{43.4, -104.27}, {38.51, -100.24}, {42.47, -100.9}}, "NAD27"] Out[1]= GeoPosition[{{43.4, -104.27}, {38.51, -100.24}, {42.47, -100.9}}, "NAD27"] In[2]:= GeoPosition[%, "EURM"] Out[2]= GeoPosition[{{43.4022941849546, -104.26980305962404}, {38.512319256913194, -100.23959796924173}, {42.472293324798905, -100.89961552302022}}, "EURM"] ``` Extract the new coordinate values: ```wl In[3]:= %["LatitudeLongitude"] Out[3]= {{43.4023, -104.27}, {38.5123, -100.24}, {42.4723, -100.9}} ``` ### Generalizations & Extensions (3) Use positions on a sphere of 100 kilometers of radius: ```wl In[1]:= GeoPosition[{32., -73.4}, Quantity[100, "Kilometers"]] Out[1]= GeoPosition[{32., -73.4}, Quantity[100, "Kilometers"]] ``` Convert to a 3D vector: ```wl In[2]:= GeoPositionXYZ[%] Out[2]= GeoPositionXYZ[{24227.7, -81270.4, 52991.9}, Quantity[100, "Kilometers"]] ``` The vector components are given in meters: ```wl In[3]:= Norm[%["XYZ"]] Out[3]= 100000. ``` Transform back to a ``GeoPosition`` object on the sphere: ```wl In[4]:= GeoPosition[%%] Out[4]= GeoPosition[{32., -73.4, -1.4551915228366852`*^-11}, Quantity[100, "Kilometers"]] ``` --- Use positions on an ellipsoid of given semiaxes: ```wl In[1]:= GeoPosition[{-29.4, 32.7}, {Quantity[1, "Kilometers"], Quantity[900, "Meters"]}] Out[1]= GeoPosition[{-29.4, 32.7}, {Quantity[1, "Kilometers"], Quantity[900, "Meters"]}] ``` Convert to a 3D vector: ```wl In[2]:= GeoPositionXYZ[%] Out[2]= GeoPositionXYZ[{750.519, 481.825, -407.06}, {Quantity[1, "Kilometers"], Quantity[900, "Meters"]}] ``` Transform back to a ``GeoPosition`` object on the ellipsoid: ```wl In[3]:= GeoPosition[%] Out[3]= GeoPosition[{-29.4, 32.7, 0.}, {Quantity[1, "Kilometers"], Quantity[900, "Meters"]}] ``` --- A position on a geo reference model other than the Earth: ```wl In[1]:= SolarSystemFeatureData[Entity["SolarSystemFeature", "TychoBraheMars"], "Position"] Out[1]= GeoPosition[{-49.41, 146.12}, Entity["Planet", "Mars"]] ``` Distance from the Tycho Brahe crater to the South Pole of Mars: ```wl In[2]:= GeoDistance[%, GeoPosition[{-90, 0}, Entity["Planet", "Mars"]]] Out[2]= Quantity[1499.8085984389527, "Miles"] ``` Computations are performed with an ellipsoid of these semiaxis lengths: ```wl In[3]:= PlanetData[Entity["Planet", "Mars"], {"EquatorialRadius", "PolarRadius"}] Out[3]= {Quantity[2110.294629364511254275`4.229961983205559, "Miles"], Quantity[2097.8734192316869482224`4.5284281655255025, "Miles"]} ``` ### Applications (3) ``GeoPosition`` is the main object in the Wolfram Language denoting point-like locations on the Earth: ```wl In[1]:= p = $GeoLocation Out[1]= GeoPosition[{40.11, -88.24}] In[2]:= q = GeoPosition[{51.5, -0.12}] Out[2]= GeoPosition[{51.5, -0.12}] ``` Compute distance between two points: ```wl In[3]:= d = GeoDistance[p, q] Out[3]= Quantity[4065.30268136569, "Miles"] ``` Compute the initial bearing of a geodesic from ``p`` to ``q`` : ```wl In[4]:= α = GeoDirection[p, q] Out[4]= Quantity[46.76553570829383, "AngularDegrees"] ``` Draw the geodesic between them and respective geo circles: ```wl In[5]:= GeoGraphics[{GeoPath[{p, q}], GeoCircle[p, d / 4], GeoCircle[q, d / 4]}] Out[5]= [image] ``` Check that the end of the geodesic starting at ``p`` is actually the point ``q`` : ```wl In[6]:= GeoDestination[p, GeoDisplacement[{d, α}]] Out[6]= GeoPosition[{51.5, -0.12}] ``` --- Geographical locations returned by ``EntityValue`` are given as ``GeoPosition`` objects: ```wl In[1]:= EntityValue[Entity["Building", "TourEiffel"], "Position"] Out[1]= GeoPosition[{48.8583, 2.29444}] ``` They can also include height and time information: ```wl In[2]:= SatelliteData[Entity["Satellite", "25544"], "Position"] Out[2]= GeoPosition[{-51.4707, -103.378, 426845., 3.814198690167561`16.333978299105656*^9}] ``` --- Geographical polygons have their coordinates inside a ``GeoPosition`` head: ```wl In[1]:= polygon = EntityValue[Entity["Country", "Peru"], "Polygon"] Out[1]= Polygon[GeoPosition[CompressedData["«28152»"]]] ``` Draw the polygon or its boundary: ```wl In[2]:= {GeoGraphics[polygon], GeoGraphics[GeoBoundary[polygon]]} Out[2]= {[image], [image]} ``` ### Properties & Relations (7) Convert a geodetic location to a three-dimensional Cartesian vector with respect to the reference frame of the datum, assuming geodetic height 0: ```wl In[1]:= p = $GeoLocation Out[1]= GeoPosition[{40.11, -88.24}] In[2]:= GeoPositionXYZ[p] Out[2]= GeoPositionXYZ[{150028., -4.882543214978031*^6, 4.0873344399887016*^6}] ``` Convert back to a ``GeoPosition`` specification, now with some small residual value of height: ```wl In[3]:= GeoPosition[%] Out[3]= GeoPosition[{40.11, -88.24, 0.}] ``` --- Convert geodetic coordinates to Cartesian coordinates for an ellipsoid of these semiaxis lengths: ```wl In[1]:= a = 1.; b = 0.5; ``` Take a point ``p`` of geodetic latitude 60°, zero longitude, and geodetic height 0.15: ```wl In[2]:= p = GeoPosition[{60., 0., 0.15}, {a, b}] Out[2]= GeoPosition[{60., 0., 0.15}, {1., 0.5}] ``` Convert it to Cartesian coordinates: ```wl In[3]:= pxyz = GeoPositionXYZ[p] Out[3]= GeoPositionXYZ[{0.830929, 0., 0.457231}, {1., 0.5}] ``` Convert back to geodetic coordinates: ```wl In[4]:= GeoPosition[pxyz] Out[4]= GeoPosition[{60., 0., 0.15}, {1., 0.5}] ``` Take a point ``q`` of the same latitude and longitude, but zero height: ```wl In[5]:= q = GeoPosition[{60., 0., 0.}, {a, b}] Out[5]= GeoPosition[{60., 0., 0.}, {1., 0.5}] In[6]:= qxyz = GeoPositionXYZ[q] Out[6]= GeoPositionXYZ[{0.755929, 0., 0.327327}, {1., 0.5}] ``` Represent the relation between the coordinates on a vertical cut of the ellipsoid: ```wl In[7]:= pxz = {pxyz["X"], pxyz["Z"]} qxz = {qxyz["X"], qxyz["Z"]} Out[7]= {0.830929, 0.457231} Out[7]= {0.755929, 0.327327} ``` The blue line is perpendicular to the tangent at ``q`` and forms an angle of 60° with the $x$ axis: ```wl In[8]:= Graphics[{Circle[{0, 0}, {a, b}], PointSize[Medium], Red, Point[pxz], Line[{{0, 0}, pxz}], Blue, Point[qxz], Line[{pxz, pxz - 0.75{Cos[60Degree], Sin[60Degree]}}]}, Axes -> True] Out[8]= [image] ``` The geodetic height of ``p`` along the geodetic vertical is the distance between ``p`` and ``q`` : ```wl In[9]:= Norm[pxz - qxz] Out[9]= 0.15 ``` --- Project a geodetic location using various geo projections, using their default parameters: ```wl In[1]:= p = $GeoLocation Out[1]= GeoPosition[{40.11, -88.24}] In[2]:= GeoGridPosition[p, "Mercator"] Out[2]= GeoGridPosition[{-88.24, 43.8552}, "Mercator"] In[3]:= GeoGridPosition[p, "Albers"] Out[3]= GeoGridPosition[{-0.949732, 1.1029}, "Albers"] In[4]:= GeoGridPosition[p, "WinkelTripel"] Out[4]= GeoGridPosition[{-1.12062, 0.731425}, "WinkelTripel"] ``` Convert back to a ``GeoPosition`` specification: ```wl In[5]:= GeoPosition /@ {%, %%, %%%} Out[5]= {GeoPosition[{40.11, -88.24}], GeoPosition[{40.11, -88.24}], GeoPosition[{40.11, -88.24}]} ``` --- The antipode of a ``GeoPosition`` object is another ``GeoPosition`` object: ```wl In[1]:= Here Out[1]= GeoPosition[{40.11, -88.24}] In[2]:= GeoAntipode[%] Out[2]= GeoPosition[{-40.11, 91.76}] ``` --- ``GeoPosition[{}]`` represents an empty array of geo positions: ```wl In[1]:= GeoPosition[{}] Out[1]= GeoPosition[{}] ``` It contains zero positions: ```wl In[2]:= %["Count"] Out[2]= 0 ``` ``GeoPosition[]`` is invalid syntax: ```wl In[3]:= GeoPosition[] ``` GeoPosition::argt: GeoPosition called with 0 arguments; 1 or 2 arguments are expected. ```wl Out[3]= GeoPosition[] ``` --- ``GeoPosition`` inside ``Graphics`` primitives marks coordinates as being in ``{lat, lon}`` notation: ```wl In[1]:= coords = {{0, 0}, {0, 60}, {10, 60}, {10, 0}, {0, 0}}; In[2]:= GeoGraphics[{Red, Polygon[GeoPosition[coords]], Green, Polygon[coords]}, GeoRange -> {{-10, 70}, {-10, 70}}, Frame -> True, GeoProjection -> "Equirectangular"] Out[2]= [image] ``` --- ``Graphics`` primitives containing ``GeoPosition`` coordinates are formed by straight segments in the projected map: ```wl In[1]:= coords = {{0, 0}, {0, 60}, {10, 60}, {10, 0}, {0, 0}}; In[2]:= GeoGraphics[{Opacity[0.5], Red, Line[GeoPosition[coords]], Blue, GeoPath[coords]}, Frame -> True, GeoProjection -> "Bonne"] Out[2]= [image] ``` ### Possible Issues (2) ``Degree`` is considered as any other numeric expression: ```wl In[1]:= GeoPosition[{30.Degree, 3.Pi}] Out[1]= GeoPosition[{0.523599, 9.42478}] ``` Use ``Quantity`` to denote that angles are given in radians: ```wl In[2]:= GeoPosition[{Quantity[30.Degree, "Radians"], Quantity[3.Pi, "Radians"]}] Out[2]= GeoPosition[{30., 540.}] ``` --- From Version 10 of the Wolfram Language, numeric time is interpreted as seconds since 1900, not as years: ```wl In[1]:= GeoPosition[{40.11, 30.23, 0., 2014.3}] ``` GeoPosition::secs: Warning: Numeric date 2014.3\` is interpreted as seconds since the beginning of 1900, not as a year specification. ```wl Out[1]= GeoPosition[{40.11, 30.23, 0., 2014.3}] ``` ### Neat Examples (1) Take a list of images with Exif location information: ```wl In[1]:= images = {[image], [image], [image], [image], [image], [image], [image]}; ``` Extract their respective positions: ```wl In[2]:= positions = GeoPosition /@ images; ``` Draw the points on a map, using tooltips to show the respective images: ```wl In[3]:= GeoGraphics[{Darker[Green], GeoPath[positions], Darker[Brown], PointSize[Medium], Tooltip[Point[#1], #2]&@@@Transpose[{positions, images}]}] Out[3]= [image] ``` ## See Also * [`GeoPositionENU`](https://reference.wolfram.com/language/ref/GeoPositionENU.en.md) * [`GeoPositionXYZ`](https://reference.wolfram.com/language/ref/GeoPositionXYZ.en.md) * [`GeoGridPosition`](https://reference.wolfram.com/language/ref/GeoGridPosition.en.md) * [`GeoDistance`](https://reference.wolfram.com/language/ref/GeoDistance.en.md) * [`GeoDestination`](https://reference.wolfram.com/language/ref/GeoDestination.en.md) * [`Latitude`](https://reference.wolfram.com/language/ref/Latitude.en.md) * [`Longitude`](https://reference.wolfram.com/language/ref/Longitude.en.md) * [`GeoAntipode`](https://reference.wolfram.com/language/ref/GeoAntipode.en.md) * [`FindGeoLocation`](https://reference.wolfram.com/language/ref/FindGeoLocation.en.md) * [`\$GeoLocation`](https://reference.wolfram.com/language/ref/$GeoLocation.en.md) * [`GeodesyData`](https://reference.wolfram.com/language/ref/GeodesyData.en.md) * [`GeoVector`](https://reference.wolfram.com/language/ref/GeoVector.en.md) * [`GeoGraphics`](https://reference.wolfram.com/language/ref/GeoGraphics.en.md) * [`GeoPath`](https://reference.wolfram.com/language/ref/GeoPath.en.md) * [`GeoCircle`](https://reference.wolfram.com/language/ref/GeoCircle.en.md) * [`GeoDisk`](https://reference.wolfram.com/language/ref/GeoDisk.en.md) * [`LocalTime`](https://reference.wolfram.com/language/ref/LocalTime.en.md) * [`GeographicRegion`](https://reference.wolfram.com/language/ref/entity/GeographicRegion.en.md) * [`GeoCoordinates`](https://reference.wolfram.com/language/ref/interpreter/GeoCoordinates.en.md) * [`USGSDEM`](https://reference.wolfram.com/language/ref/format/USGSDEM.en.md) * [`SDTSDEM`](https://reference.wolfram.com/language/ref/format/SDTSDEM.en.md) * [`GeoTIFF`](https://reference.wolfram.com/language/ref/format/GeoTIFF.en.md) ## Tech Notes * [GeoGraphics](https://reference.wolfram.com/language/tutorial/GeoGraphics.en.md) ## Related Guides * [`Geodesy`](https://reference.wolfram.com/language/guide/Geodesy.en.md) * [Geographic Data & Entities](https://reference.wolfram.com/language/guide/GeographicData.en.md) * [Maps & Cartography](https://reference.wolfram.com/language/guide/MapsAndCartography.en.md) * [Weather Data](https://reference.wolfram.com/language/guide/WeatherData.en.md) * [Free-Form & External Input](https://reference.wolfram.com/language/guide/FreeFormAndExternalInput.en.md) * [Locations, Paths, and Routing](https://reference.wolfram.com/language/guide/LocationsPathsAndRouting.en.md) * [Scientific Data Analysis](https://reference.wolfram.com/language/guide/ScientificDataAnalysis.en.md) * [Angles and Polar Coordinates](https://reference.wolfram.com/language/guide/AnglesAndPolarCoordinates.en.md) * [Knowledge Representation & Access](https://reference.wolfram.com/language/guide/KnowledgeRepresentationAndAccess.en.md) * [Database Connectivity](https://reference.wolfram.com/language/guide/DatabaseConnectivity.en.md) * [WDF (Wolfram Data Framework)](https://reference.wolfram.com/language/guide/WDFWolframDataFramework.en.md) ## Related Links * [An Elementary Introduction to the Wolfram Language: Geocomputation](https://www.wolfram.com/language/elementary-introduction/18-geocomputation.html) ## History * [Introduced in 2008 (7.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn70.en.md) \| [Updated in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) ▪ [2019 (12.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn120.en.md)