The Web Mercator projection is almost indistinguishable at global scale from a Mercator projection cropped to around 85°N to 85°SHomepage of OpenStreetMap in 2018. The standard style for OpenStreetMap, like most Web maps, uses the Web Mercator projection
Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator[1] or WGS 84/Pseudo-Mercator is a variant of the Mercatormap projection and is the de facto standard for Web mapping applications. It rose to prominence when Google Maps adopted it in 2005.[2] It is used by virtually all major online map providers, including Google Maps, CARTO, Mapbox,[3]Bing Maps, OpenStreetMap, Mapquest, Esri, and many others.[4] Its official EPSG identifier is EPSG:3857, although others have been used historically.
Web Mercator is a slight variant of the Mercator projection, one used primarily in Web-based mapping programs. It uses the same formulas as the standard Mercator as used for small-scale maps. However, the Web Mercator uses the spherical formulas at all scales whereas large-scale Mercator maps normally use the ellipsoidal form of the projection.[citation needed] The discrepancy is imperceptible at the global scale but causes maps of local areas to deviate slightly from true ellipsoidal Mercator maps at the same scale.
While the Web Mercator's formulas are for the spherical form of the Mercator, geographical coordinates are required to be in the WGS 84 ellipsoidal datum. This discrepancy causes the projection to be slightly non-conformal. General lack of understanding that the Web Mercator differs from standard Mercator usage has caused considerable confusion and misuse.[4]:87 Mistaking Web Mercator for the standard Mercator during coordinate conversion can lead to deviations as much as 40km on the ground.[5][6] For all these reasons, the United States Department of Defense through the National Geospatial-Intelligence Agency has declared this map projection to be unacceptable for any official use.[5]
Formulas for the Web Mercator are fundamentally the same as for the standard spherical Mercator, but before applying zoom, the "world coordinates" are adjusted such that the upper left corner is (0, 0) and the lower right corner is ( , ):[7] where is the longitude in radians and is geodetic latitude in radians.[8]
Because the Mercator projects the poles at infinity, a map using the Web Mercator projection cannot show the poles. Services such as Google Maps cut off coverage at 85.051129° north and south. This is not a limitation for street maps, which is the primary purpose for such services. The value 85.051129° is the latitude at which the full projected map becomes a square, and is computed as given y = 0:
Spherical and ellipsoidal mix
The projection is neither strictly ellipsoidal nor strictly spherical. EPSG's definition says the projection "uses spherical development of ellipsoidal coordinates".[9] The underlying geographic coordinates are defined using the WGS84 ellipsoidal model of the Earth's surface, but are projected as if defined on a sphere.[6] This practice is uncontroversial for small-scale maps (such as of the entire world), but has little precedent in large-scale maps (such as of a city or province).[10]
Advantages and disadvantages
Web Mercator is a spherical Mercator projection, and so it has the same properties as a spherical Mercator: north is up everywhere, meridians are equally spaced vertical lines, angles are locally correct (assuming spherical coordinates), and areas inflate with distance from the equator such that the polar regions are grossly exaggerated. The ellipsoidal Mercator has these same properties, but models the earth as an ellipsoid.
Unlike the ellipsoidal Mercator, however, the Web Mercator is not quite conformal. This means that angles between lines on the surface will not be drawn to the same angles in the map, although they will not deviate enough to be noticeable by eye. Lines deviate because Web Mercator specifies that coordinates be given as surveyed on the WGS 84 ellipsoidal model. By projecting coordinates surveyed against the ellipsoid as if they were surveyed on a sphere, angular relationships change slightly. This is standard practice on the standard spherical Mercator projection, but unlike Web Mercator, the spherical Mercator is not normally used for maps of local areas, such as street maps, and so the accuracy of positions needed for plotting is typically less than the angular deviation caused by using spherical formulas. The benefit the Web Mercator gains is that the spherical form is much simpler to calculate than the ellipsoidal form, and so requires only a fraction of the computing resources.[11]
Identifiers
Due to slow adoption by the EPSG registry, the Web Mercator is represented by several different names and spatial reference system identifiers (SRIDs), including EPSG:900913, EPSG:3785 and EPSG:3857, the latter being the official EPSG identifier since 2009.[12]
EPSG:900913
The projected coordinate reference system originally lacked an official spatial reference identifier (SRID), and the Geodesy subcommittee of the OGP's Geomatics committee (also known as EPSG) refused to provide it with one, declaring "We have reviewed the coordinate reference system used by Microsoft, Google, etc. and believe that it is technically flawed. We will not devalue the EPSG dataset by including such inappropriate geodesy and cartography."[13] The unofficial code "EPSG:900913" (GOOGLE transliterated to numbers) came to be used. It was originally defined by Christopher Schmidt in his Technical Ramblings blog[14] and became codified in OpenLayers 2,[15] which, technically, would make OpenLayers the SRID authority.
EPSG:3785
In 2008, EPSG provided the official identifier EPSG:3785 with the official name "Popular Visualisation CRS / Mercator", but noted "It is not an official geodetic system".[6] This definition used a spherical (rather than ellipsoidal) model of the Earth.
EPSG:3857
Later that year, EPSG provided an updated identifier, EPSG:3857 with the official name "WGS 84 / Pseudo-Mercator".[6] The definition switched to using the WGS84 ellipsoid (EPSG:4326), rather than the sphere.
Although the projection is closely associated with Google, Microsoft is listed as the "information source" in EPSG's standards.[12]
Other identifiers
Other identifiers that have been used include ESRI:102113, ESRI:102100, and OSGEO:41001.[16][14]
ESRI:102113 corresponds to EPSG:3785 while ESRI:102100 corresponds to EPSG:3857.[17]
In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.
The Mercator projection is a conformal cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation due to its ability to represent north as "up" and south as "down" everywhere while preserving local directions and shapes. However, as a result, the Mercator projection inflates the size of objects the further they are from the equator. In a Mercator projection, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator. Despite these drawbacks, the Mercator projection is well-suited to marine navigation and internet web maps and continues to be widely used today.
A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.
Earth radius is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) to a minimum of nearly 6,357 km (3,950 mi).
A projected coordinate system – also called a projected coordinate reference system, planar coordinate system, or grid reference system – is a type of spatial reference system that represents locations on Earth using Cartesian coordinates (x, y) on a planar surface created by a particular map projection. Each projected coordinate system, such as "Universal Transverse Mercator WGS 84 Zone 26N," is defined by a choice of map projection (with specific parameters), a choice of geodetic datum to bind the coordinate system to real locations on the earth, an origin point, and a choice of unit of measure. Hundreds of projected coordinate systems have been specified for various purposes in various regions.
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM). The standard is published and maintained by the United States National Geospatial-Intelligence Agency.
In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion is composed of a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different geodetic datums. Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems.
The transverse Mercator map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the Universal Transverse Mercator. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent.
A geodetic datum or geodetic system is a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates or geocentric coordinates. Datums are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography. A horizontal datum is used to measure a horizontal position, across the Earth's surface, in latitude and longitude or another related coordinate system. A vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). A three-dimensional datum enables the expression of both horizontal and vertical position components in a unified form. The concept can be generalized for other celestial bodies as in planetary datums.
ED50 is a geodetic datum which was defined after World War II for the international connection of geodetic networks.
The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, which means it ignores altitude and treats the earth surface as a perfect ellipsoid. However, it differs from global latitude/longitude in that it divides earth into 60 zones and projects each to the plane as a basis for its coordinates. Specifying a location means specifying the zone and the x, y coordinate in that plane. The projection from spheroid to a UTM zone is some parameterization of the transverse Mercator projection. The parameters vary by nation or region or mapping system.
A Lambert conformal conic projection (LCC) is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in his 1772 publication Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten.
A spatial reference system (SRS) or coordinate reference system (CRS) is a framework used to precisely measure locations on the surface of Earth as coordinates. It is thus the application of the abstract mathematics of coordinate systems and analytic geometry to geographic space. A particular SRS specification comprises a choice of Earth ellipsoid, horizontal datum, map projection, origin point, and unit of measure. Thousands of coordinate systems have been specified for use around the world or in specific regions and for various purposes, necessitating transformations between different SRS.
Space-oblique Mercator projection is a map projection devised in the 1970s for preparing maps from Earth-survey satellite data. It is a generalization of the oblique Mercator projection that incorporates the time evolution of a given satellite ground track to optimize its representation on the map. The oblique Mercator projection, on the other hand, optimizes for a given geodesic.
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.
Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a reference ellipsoid. They include geodetic latitude (north/south) ϕ, longitude (east/west) λ, and ellipsoidal heighth. The triad is also known as Earth ellipsoidal coordinates.
The geo URI scheme is a Uniform Resource Identifier (URI) scheme defined by the Internet Engineering Task Force's RFC 5870 as:
a Uniform Resource Identifier (URI) for geographic locations using the 'geo' scheme name. A 'geo' URI identifies a physical location in a two- or three-dimensional coordinate reference system in a compact, simple, human-readable, and protocol-independent way.
Transverse Mercator projection has many implementations. Louis Krüger in 1912 developed one of his two implementations that expressed as a power series in the longitude difference from the central meridian. These series were recalculated by Lee in 1946, by Redfearn in 1948, and by Thomas in 1952. They are often referred to as the Redfearn series, or the Thomas series. This implementation is of great importance since it is widely used in the U.S. State Plane Coordinate System, in national and also international mapping systems, including the Universal Transverse Mercator coordinate system (UTM). They are also incorporated into the Geotrans coordinate converter made available by the United States National Geospatial-Intelligence Agency. When paired with a suitable geodetic datum, the series deliver high accuracy in zones less than a few degrees in east-west extent.
EPSG Geodetic Parameter Dataset is a public registry of geodetic datums, spatial reference systems, Earth ellipsoids, coordinate transformations and related units of measurement, originated by a member of the European Petroleum Survey Group (EPSG) in 1985. Each entity is assigned an EPSG code between 1024 and 32767, along with a standard machine-readable well-known text (WKT) representation. The dataset is maintained by the IOGP Geomatics Committee.
The stereographic projection, also known as the planisphere projection or the azimuthal conformal projection, is a conformal map projection whose use dates back to antiquity. Like the orthographic projection and gnomonic projection, the stereographic projection is an azimuthal projection, and when on a sphere, also a perspective projection.
↑ "Our Map Data". MapBox. Retrieved June 20, 2018. Mapbox supports the popular Web Mercator projection, and currently does not support any other projections for display.
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
