|Using IDL: Map Projections|
Standard graphics techniques are insufficient when projecting areas on a sphere to a two-dimensional surface for two reasons. First, two points on a sphere are connected by two different lines. Second, areas may wrap around the edges of cylindrical and pseudo-cylindrical projections.
Graphical entities on the surface of a sphere can be properly represented on any map by using a combination of the following four stages: splitting, 3D clipping, projection, and rectangular clipping. The IMAP and MAP_SET procedures automatically sets up the proper mapping technique to best fit the projection selected by the user.
For proper rendering, splitting, and clipping, polygons must be traversed in counter-clockwise order when observed from outside the sphere. If this requirement is not met, the exterior, instead of the interior, of the polygons may be filled. Also, vectors connecting the points spanning the singular line for cylindrical projections will be drawn in the wrong direction if polygons are not traversed in the correct order.
The splitting stage is used for cylindrical and pseudo-cylindrical projections. The singular line, one half of a great circle line, is located opposite the center of the projection; points on this line appear on both edges of the map. The singular line is the intersection of the surface of the sphere with a plane passing through the center of projection, one of the poles of projections, and the center of the sphere.
Map graphics are clipped to one side of an arbitrary clipping plane in one or more clipping stages. For example, to draw a hemisphere centered on a given point, the clipping plane passes through the center of the sphere and has a normal vector that coincides with the given point.
In the projection stage, a point expressed in latitude and longitude is transformed to a point on the mapping plane.
After the map graphics have been projected onto the mapping plane, a conventional rectangular clipping stage ensures that the graphics are properly bounded and closed in the rectangular display area.
IDL Online Help (June 16, 2005)