The map projection used by Google Maps, Bing Maps, and most of ArcGIS Online, EPSG:3857. More...

#include <CesiumGeospatial/WebMercatorProjection.h>

Public Member Functions
	WebMercatorProjection (const Ellipsoid &ellipsoid CESIUM_DEFAULT_ELLIPSOID) noexcept
	Constructs a new instance. More...

const Ellipsoid &	getEllipsoid () const noexcept
	Gets the Ellipsoid.

glm::dvec3	project (const Cartographic &cartographic) const noexcept
	Converts geodedic ellipsoid coordinates to Web Mercator coordinates. More...

CesiumGeometry::Rectangle	project (const CesiumGeospatial::GlobeRectangle &rectangle) const noexcept
	Projects a globe rectangle to Web Mercator coordinates. More...

Cartographic	unproject (const glm::dvec2 &projectedCoordinates) const noexcept
	Converts Web Mercator coordinates to geodetic ellipsoid coordinates. More...

Cartographic	unproject (const glm::dvec3 &projectedCoordinates) const noexcept
	Converts Web Mercator coordinates to geodetic ellipsoid coordinates. More...

CesiumGeospatial::GlobeRectangle	unproject (const CesiumGeometry::Rectangle &rectangle) const noexcept
	Unprojects a Web Mercator rectangle to the globe. More...

bool	operator== (const WebMercatorProjection &rhs) const noexcept
	Returns `true` if two projections (i.e. their ellipsoids) are equal.

bool	operator!= (const WebMercatorProjection &rhs) const noexcept
	Returns `true` if two projections (i.e. their ellipsoids) are not equal.

Static Public Member Functions
static constexpr CesiumGeometry::Rectangle	computeMaximumProjectedRectangle (const Ellipsoid &ellipsoid CESIUM_DEFAULT_ELLIPSOID) noexcept
	Computes the maximum rectangle that can be covered with this projection. More...

static double	mercatorAngleToGeodeticLatitude (double mercatorAngle) noexcept
	Converts a Mercator angle, in the range -PI to PI, to a geodetic latitude in the range -PI/2 to PI/2. More...

static double	geodeticLatitudeToMercatorAngle (double latitude) noexcept
	Converts a geodetic latitude in radians, in the range -PI/2 to PI/2, to a Mercator angle in the range -PI to PI. More...

Static Public Attributes
static const double	MAXIMUM_LATITUDE
	The maximum latitude (both North and South) supported by a Web Mercator (EPSG:3857) projection. More...

static const GlobeRectangle	MAXIMUM_GLOBE_RECTANGLE
	The maximum bounding rectangle of the Web Mercator projection, ranging from -PI to PI radians longitude and from -MAXIMUM_LATITUDE to +MAXIMUM_LATITUDE.

Detailed Description

The map projection used by Google Maps, Bing Maps, and most of ArcGIS Online, EPSG:3857.

This projection uses geodetic longitude and latitude expressed with WGS84 and transforms them to Mercator using the spherical (rather than ellipsoidal) equations.

See also: GeographicProjection

Definition at line 24 of file WebMercatorProjection.h.

Constructor & Destructor Documentation

◆ WebMercatorProjection()

CesiumGeospatial::WebMercatorProjection::WebMercatorProjection ( const Ellipsoid &ellipsoid CESIUM_DEFAULT_ELLIPSOID )

noexcept

Constructs a new instance.

Parameters

ellipsoid The Ellipsoid.

Member Function Documentation

◆ computeMaximumProjectedRectangle()

static constexpr CesiumGeometry::Rectangle CesiumGeospatial::WebMercatorProjection::computeMaximumProjectedRectangle ( const Ellipsoid &ellipsoid CESIUM_DEFAULT_ELLIPSOID )

inlinestaticconstexprnoexcept

Computes the maximum rectangle that can be covered with this projection.

Parameters

ellipsoid The Ellipsoid. Default value: Ellipsoid::WGS84.

Returns: The rectangle

Definition at line 57 of file WebMercatorProjection.h.

◆ geodeticLatitudeToMercatorAngle()

static double CesiumGeospatial::WebMercatorProjection::geodeticLatitudeToMercatorAngle ( double latitude )

staticnoexcept

Converts a geodetic latitude in radians, in the range -PI/2 to PI/2, to a Mercator angle in the range -PI to PI.

Parameters

latitude The geodetic latitude in radians.

Returns: The Mercator angle.

◆ mercatorAngleToGeodeticLatitude()

static double CesiumGeospatial::WebMercatorProjection::mercatorAngleToGeodeticLatitude ( double mercatorAngle )

staticnoexcept

Converts a Mercator angle, in the range -PI to PI, to a geodetic latitude in the range -PI/2 to PI/2.

Parameters

mercatorAngle The angle to convert.

Returns: The geodetic latitude in radians.

◆ project() [1/2]

glm::dvec3 CesiumGeospatial::WebMercatorProjection::project ( const Cartographic & cartographic ) const

noexcept

Converts geodedic ellipsoid coordinates to Web Mercator coordinates.

Converts geodetic ellipsoid coordinates, in radians, to the equivalent Web Mercator X, Y, Z coordinates expressed in meters. The height is copied unmodified to the z coordinate.

Parameters

cartographic The geodetic coordinates in radians.

Returns: The equivalent web mercator X, Y, Z coordinates, in meters.

◆ project() [2/2]

CesiumGeometry::Rectangle CesiumGeospatial::WebMercatorProjection::project ( const CesiumGeospatial::GlobeRectangle & rectangle ) const

noexcept

Projects a globe rectangle to Web Mercator coordinates.

This is done by projecting the southwest and northeast corners.

Parameters

rectangle The globe rectangle to project.

Returns: The projected rectangle.

◆ unproject() [1/3]

CesiumGeospatial::GlobeRectangle CesiumGeospatial::WebMercatorProjection::unproject ( const CesiumGeometry::Rectangle & rectangle ) const

noexcept

Unprojects a Web Mercator rectangle to the globe.

This is done by unprojecting the southwest and northeast corners.

Parameters

rectangle The rectangle to unproject.

Returns: The unprojected rectangle.

◆ unproject() [2/3]

Cartographic CesiumGeospatial::WebMercatorProjection::unproject ( const glm::dvec2 & projectedCoordinates ) const

noexcept

Converts Web Mercator coordinates to geodetic ellipsoid coordinates.

Converts Web Mercator X and Y coordinates, expressed in meters, to a Cartographic containing geodetic ellipsoid coordinates. The height is set to 0.0.

Parameters

projectedCoordinates The web mercator projected coordinates to unproject.

Returns: The equivalent cartographic coordinates.

◆ unproject() [3/3]

Cartographic CesiumGeospatial::WebMercatorProjection::unproject ( const glm::dvec3 & projectedCoordinates ) const

noexcept

Converts Web Mercator coordinates to geodetic ellipsoid coordinates.

Converts Web Mercator X, Y coordinates, expressed in meters, to a Cartographic containing geodetic ellipsoid coordinates. The Z coordinate is copied unmodified to the height.

Parameters

projectedCoordinates The web mercator projected coordinates to unproject, with height (z) in meters.

Returns: The equivalent cartographic coordinates.

Member Data Documentation

◆ MAXIMUM_LATITUDE

const double CesiumGeospatial::WebMercatorProjection::MAXIMUM_LATITUDE

static

The maximum latitude (both North and South) supported by a Web Mercator (EPSG:3857) projection.

Technically, the Mercator projection is defined for any latitude up to (but not including) 90 degrees, but it makes sense to cut it off sooner because it grows exponentially with increasing latitude. The logic behind this particular cutoff value, which is the one used by Google Maps, Bing Maps, and Esri, is that it makes the projection square. That is, the rectangle is equal in the X and Y directions.

The constant value is computed by calling: CesiumGeospatial::WebMercatorProjection::mercatorAngleToGeodeticLatitude(CesiumUtility::Math::OnePi)

Definition at line 40 of file WebMercatorProjection.h.

The documentation for this class was generated from the following file:

/home/runner/work/cesium-native/cesium-native/CesiumGeospatial/include/CesiumGeospatial/WebMercatorProjection.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ WebMercatorProjection()

Member Function Documentation

◆ computeMaximumProjectedRectangle()

◆ geodeticLatitudeToMercatorAngle()

◆ mercatorAngleToGeodeticLatitude()

◆ project() [1/2]

◆ project() [2/2]

◆ unproject() [1/3]

◆ unproject() [2/3]

◆ unproject() [3/3]

Member Data Documentation

◆ MAXIMUM_LATITUDE