This article describes the LuciadLightspeed support for map projections. It does not describe the theory of map projections. For a theoretical background refer to the literature as given in Literature on map projections.

Using an ILcdProjection describes the interface ILcdProjection, which forms the basis. Extensions of ILcdProjection describes the main extensions of this interface, and Main implementations of ILcdProjection describes the main implementations of these extensions.

Using an ILcdProjection

An ILcdProjection is a transformation of geographically referenced data into a planar (flat) representation of the earth’s surface and conversely. In LuciadLightspeed a planar coordinate representation is denoted as world coordinates. The geographically referenced data are expressed as geodetic lon-lat-height coordinates with respect to an ILcdGeodeticDatum. The planar representation is expressed in a Cartesian two-dimensional coordinate system using X and Y coordinates. The planar representation is usually used for visualization or for the definition of a grid reference system.

The main methods of the interface ILcdProjection concern the transformation of geographically referenced data to the planar representation and the other way around. The approximation of the earth can either be with a sphere or an ellipsoid.

Program: Transformations between geodetic and world coordinates shows how to transform geodetic lon-lat-height coordinates based on an ILcdEllipsoid (called ellipsoid) to planar XY coordinates which are represented by ILcd2DEditablePoint objects. For the inverse transformation of projections that take the ellipsoidal height into account, the assumption is that this height is already available within the side effect parameter LLHP2 (of type ILcd3DEditablePoint), such that only the longitude and latitude have to be determined.

Program: Transformations between geodetic and world coordinates
projection.lonlatheight2worldOnEllipsoidSFCT(LLHP, ellipsoid, XY);
projection.world2lonlatOnEllipsoidSFCT(XY, ellipsoid, LLHP2);

projection.lonlatheight2worldOnSphereSFCT(LLHP, radius, XY);
projection.world2lonlatOnSphereSFCT(XY, radius, LLHP2);

In general, an ILcdProjection projects only a part of the world to a plane. If a coordinate is passed to the methods shown in Program: Transformations between geodetic and world coordinates, and that coordinate cannot be projected to a plane by the given ILcdProjection, a TLcdOutOfBoundsException is thrown.

The interface ILcdProjection has several methods that define the valid area of a map projection. The method inLonLatBounds checks whether a given lon-lat-height coordinate is inside the valid area of the ILcdProjection. The methods boundaryLons(aLatitude) and boundaryLats(aLongitude) determine the valid longitude and latitude intervals, respectively, for a given latitude or a given longitude. The inverse transformation of an ILcdProjection also has a valid domain. The methods inWorldBoundsOnSphere and inWorldBoundsOnEllipsoid check whether a given Cartesian coordinate is inside the domain of the inverse transformation for a sphere and an ellipsoid, respectively.

Classes implementing the interface ILcdProjection provide transformations for both spherical and ellipsoidal models of the earth. If the ellipsoidal formulas are not useful or not available, you can approximate the ellipsoidal methods by the spherical methods using the semi-major axis as the earth radius.

Each ILcdProjection has a point of origin. The point of origin is the geodetic coordinate that corresponds to the origin of the planar Cartesian coordinate system. How this point of origin is specified or how it can be set, depends on the characteristics of the ILcdProjection and is specified by the classes implementing the interface ILcdProjection. In addition to the projection origin, an ILcdProjection has other properties depending on the type of ILcdProjection as described in Extensions of ILcdProjection.

The interface ILcdProjection applies the Listener pattern in collaboration with java.beans.PropertyChangeListener. A PropertyChangeListener accepts java.beans.PropertyChangedEvent objects from the ILcdProjection objects to which it is registered. A PropertyChangeEvent is sent from an ILcdProjection to its listeners whenever one of its properties has changed.

For more information on listening to changes, refer to Notifying objects of changes with listeners.

Extensions of ILcdProjection

The interface ILcdProjection is further extended in several interfaces. This is done through a classification of the projections according to their properties.

  • ILcdCylindrical specifies a cylindrical ILcdProjection. It is defined by wrapping a cylinder around the earth globe such that it touches the equator. The point of origin of the ILcdProjection is always located on the equator and is only determined by the longitude.

ILcdProjection cylindrical
Figure 1. Cylindrical
ILcdProjection transverse cylindrical
Figure 2. Transverse Cylindrical
ILcdProjection oblique cylindrical
Figure 3. Oblique Cylindrical

  • ILcdAzimuthal specifies an azimuthal ILcdProjection. It is defined by a tangent plane at the point of origin defined by a geodetic latitude and longitude.

azimuthal
Figure 4. Azimuthal

  • ILcdConic specifies a conical ILcdProjection that cuts the earth globe at two standard parallels and for which the point of origin of the ILcdProjection is defined by a geodetic latitude and longitude.

ILcdProjection conic
Figure 5. Conic

For a complete list of available sub-interfaces, refer to the package projection in the API reference.

Main implementations of ILcdProjection

LuciadLightspeed provides implementations for commonly used projections. All implementations extend abstract adapter classes for the interfaces defined in Extensions of ILcdProjection. These abstract classes implement the properties specific for each type of ILcdProjection. They also have a method loadProperties to initialize instances of each class. TLcdProjectionFactory creates ILcdProjection objects using this properties mechanism.

For a detailed description of the available implementations of the interface ILcdProjection, refer to the package projection in the API reference.

Literature on map projections

  • Snyder, Map Projections: A Working Manual, 1987.

  • Bugayevskiy, Snyder, Map Projections : A Reference Manual, 1995.

  • Snyder, Flattening the Earth : Two Thousand Years of Map Projections, 1997.

  • Pearson, Map Projections : Theory and Applications, 1990.

  • Maling, Coordinate systems and map projections, 1992.