DCL:GRPH1:Summary:2-D Normalization Transformation
In the DCL, map projection coordinates are treated as normal U-coordinates.
There are many different types of map projections,
and a whole book would be needed to explain all of them.
Here, we will introduce the fundamentals that you should know for using the DCL library.
For details on the map projections, the user is referred to "Map Projections" by Masahichi Nomura.
(This book is out of press.)
A map projection is basically a method to "project a spherical surface onto a 2-D plane."
Since the Earth is actually nearer to a spheroid and not a perfect sphere,
a spheroid must be projected onto a plane in the strict sense of map projection.
However, this library supports
projection from a spherical surface,
and not from a spheroid.
The projected object may have 3-D characteristics depending on the projection method used,
but keep in mind that the map projection coordinates are only 2-D.
In many map projection methods, geometric techniques are used to project the spherical surface onto a plane, and the methods can be classified into several groups according to the morphology of the plane.
| Cylindrical projection | the globe is positioned inside a cylinder with the same radius, and the latitudes and longitudes are projected onto the surrounding cylinder, which is then spread out. |
| Conic projection | the globe is positioned in a right circular cone, and the latitudes and longitudes are projected onto the cone, which is then spread out. |
| Azimuthal projection | the globe is placed on a plane touching the globe at one point, and the latitudes and longitudes are projected onto this plane. |
| Conventional projection | Methods other than the above |
Since spherical surfaces are projected onto a plane in a map projection, distortions always exist to some extent. Therefore, many projections are designed to preserve either the area or angle. In principle, it is impossible to preserve both area and angle in map projections. The projections are classified into the following groups according to the properties they preserve
| equal-area projection | the relative area is displayed properly in all parts of the map |
| conformal projection | the local angle is displayed properly in all parts of the map |
| equidistant projection | the distance is displayed properly along the latitudes, longitudes, and azimuth lines. |
The following map projections are supported in this library.
| Number | Projection | Equal-area | Conformal | Equidistant |
| 10 | equidistant cylindrical projection | n | n | meridian |
| 11 | Mercator's projection | n | y | n |
| 12 | Mollweide's projection | y | n | n |
| 13 | Hammer's projection | y | n | n |
| 14 | Eckert VI projection | y | n | n |
| 15 | Kitada's elliptic projection | y | n | n |
| Number | Projection | Equal-area | Conformal | Equidistant |
| 20 | equidistant conical projection | n | n | meridian |
| 21 | Lambert's equal-area conical projection | y | n | n |
| 22 | Lambert's conformal conical projection | n | y | n |
| 23 | Bonne's projection | y | n | n |
| Number | Projection | Equal-area | Conformal | Equidistant |
| 30 | orthographic projection | n | n | n |
| 31 | polar stereo projection | n | y | n |
| 32 | azimuthal equidistant projection | n | n | azimuthal line |
| 33 | Lambert's azimuthal equal - area projection | y | n | n |
In cartography, Hammer's projection is classified as a variant of the Lambert's azimuthal equal - area projection,
but its form and use are more similar to cylindrical projections,
so it will be classified under cylindrical projections here, for convenience.
All of these projections can be shown on normal, transverse, and oblique aspects.
The satellite view, which is a variant of an orthogonal projection and resembles the Earth as seen from a satellite, is also supported in the library, although it is usually not considered as a normal map projection. A normal orthogonal projection views the Earth from a line at infinity, but the satellite view views the Earth from a finite point.