Before writing the forward functions for the Mercator projection, you must be familiar with the IlvProjection::forward function.

The IlvProjection::forward public function is called by the user to project data. The function prepares data for projection computation and scales it appropriately. It then redirects the calls to either one of the eForward or sForward protected functions which are defined in the projection subclass (the Mercator class in our example).

The IlvProjection::forward function:

The sForward protected function implements the projection for a sphere.

Since the appropriate scaling is actually carried out by the function IlvProjection::forward, the sForward function always assumes that the radius of the sphere is 1.

In our example, the Mercator function is the projection of a sphere on a cylinder that is tangent to the equator. The x coordinate is equal to the longitude (expressed in radians) because we assume that the radius of the sphere is 1. In this case, we do not have to change the x value of ll.

Because the Mercator projection cannot show regions near the poles, an error code is returned if the latitude is too close to PI/2.

We apply the following equation to compute the y coordinate of the projected data.

The eForward protected function is called by the IlvProjection::forward function if data is projected from a nonspherical ellipsoid.

It is not necessary for you to implement the eForward function for your projection. If you are projecting data from a nonspherical ellipsoid and if the projection you are using does not support this kind of ellipsoid, the forward function will return the error code given by IlvProjection::UnsupportedFeatureError(). In this case, you can use any spherical ellipsoid or create an equivalent sphere using the appropriate conversion functions of the class IlvEllipsoid.

The eForward function is slightly more complex than the sForward function although the formulas obtain equivalent results if getEllipsoid()->getE() returns 0.