Ellipsoids

Overview of ellipsoids

Ellipsoids are used to represent the shape of the Earth. For many applications, and especially in small-scale mapping (typically world maps), the Earth can be represented as a sphere.

Most of the projections supplied in the ilog.views.maps.projection package assume by default that the Earth is a sphere with a radius of approximately 6371 kilometers. However, because the Earth rotates on its axis, it is slightly flattened at the poles, and is therefore better approximated by an ellipsoid rotating on the polar axis. Ellipsoidal projections are used for accurate, large-scale maps and flat coordinate systems. However, in very large scale maps, representing a continent or the whole planet, it is recommended that you use spherical projections. Indeed, the elliptical form of most of the projections in the projection package is accurate only for a few degrees of latitude or longitude around the projection center.

Defining new ellipsoids

Ellipsoids can be described by many parameters. The ellipsoids provided in the JViews Maps package are defined by two parameters:

The equatorial radius or semi-major axis (a) of the ellipsoid.
The eccentricity squared of the ellipsoid.

If the eccentricity squared is null , the ellipsoid is a sphere.

Defining a spherical ellipsoid

If only one parameter is provided, the ellipsoid is assumed to be a sphere. The following example defines a sphere with a radius of 6 000 kilometers (6000000 meters).

IlvEllipsoid ellipsoid = new IlvEllipsoid(6000000D);

Most of the mapping applications use the ellipsoid IlvEllipsoid.SPHERE that defines a sphere having dimensions very close to those of the Earth. Generally, the selected ellipsoid should be as close as possible to the actual shape of the Earth as far as the region to be represented is concerned. The radius of the sphere is expressed in meters.

The following example defines an ellipsoid with an equatorial radius of 6000 kilometers and an eccentricity squared of 0.0067:

IlvEllipsoid ellipsoid = new IlvEllipsoid(6000000D,0.0067D);

If you prefer to provide some other parameter than the eccentricity squared, you can use the conversion methods provided by the IlvEllipsoid class.

The following example defines an ellipsoid with an equatorial radius of 6000 kilometers and a polar radius of 5900 kilometers:

IlvEllipsoid ellipsoid = new IlvEllipsoid(6000000D,
                      IlvEllipsoid.ESFromPolarRadius(6000000D, 5900000D));

The polar radius is converted to an eccentricity squared value with the ESFromPolarRadius() method.

The class IlvEllipsoid provides the following conversion methods for polar radius and flattening:

Predefined ellipsoids

The IlvEllipsoidCollection class manages lists of predefined ellipsoids. A list of predefined ellipsoids, or kernel collection, can be retrieved using the method GetKernelCollection.

Ellipsoid collections are read from XML files containing the ellipsoid definitions. The Document Type Definition (DTD) for these definition files is as follows:

<!DOCTYPE ellipsoid-list [
   <!ELEMENT ellipsoid EMPTY>
  <!ATTLIST ellipsoid
     a       CDATA   #IMPLIED
     b       CDATA   #IMPLIED
     invf    CDATA   #IMPLIED
     name    CDATA   #REQUIRED
     comment CDATA   #IMPLIED
  >

  <!ELEMENT ellipsoid-ref EMPTY>
  <!ATTLIST ellipsoid-ref
     ref     CDATA   #REQUIRED
     id      CDATA   #REQUIRED
  >

  <!ELEMENT ellipsoid-list (ellipsoid|ellipsoid-ref)* >
]>

In an ellipsoid definition file, you can find:

An ellipsoid

Defined either by its name, or by its semi-major axis a and inverse flattening invf , or its semi-major axis a and semi-minor axis b .
An alias for an ellipsoid

Defined in the kernel collection of Maps. For an alias, the required information is the id of the ellipsoid (the name used to retrieve the ellipsoid) and the name of the ellipsoid in the kernel. When retrieving an ellipsoid alias from a collection, the ellipsoid is searched for using its id as a key, while the name of the returned ellipsoid is the one defined in the kernel collection.

The following XML file defines the Clarke 1880 ellipsoid, modified for IGN. This ellipsoid will be available as “Clarke 1880 (IGN)”. Then you must set “WGS 1984” as an alias for the kernel “WGS 84” ellipsoid:

<ellipsoid-list>
  <ellipsoid name="Clarke 1880 (IGN)"
     comment="Clarke 1880 (Modified for IGN)"
     a="6378249.2"
     invf="293.4660213"
  />

  <ellipsoid-ref id="WGS 1984"
                 ref="WGS84"
  />

</ellipsoid-list>