What is a Projection?

Coordinate system

In Isatis.neo, two kinds of coordinate systems are distinguished:

  • Geographic coordinate system

    A geographic coordinate system is a coordinate system that enables each location on the Earth to be specified by a latitude φ and a longitude λ. These coordinate systems can be expressed using several ways and the main geographic coordinate systems are NTF, RGF93, ED50 and WGS84. Note that the GPS signal usually uses the geographic coordinate system: WGS84.

  • Cartesian coordinate system

    A cartesian coordinate system is a coordinate system that enables a restricted area on the earth to be specified by a coordinate x and a coordinate y with more or less precision. These coordinates are expressed using a Cartesian coordinate system (that is to say two perpendicular axis and a common origin). Isatis.neo use two kinds of Cartesian coordinate systems:

    • Local coordinate system

      The local coordinate systems are Cartesian coordinate systems created by the user and do not correspond to any international convention which implies their coordinates can’t be projected to another coordinate system.

    • Projected coordinate system

      These Cartesian coordinate systems are internationally known and there is a mathematical function that enables to transform the coordinates from (x, y) to geographic coordinates φ, λ or to another projected coordinate system.

Projection

Maps are visualized in two dimensions while they represent three-dimensional sections of the Earth. Isatis.neo uses projections, to reduce the map’s distortion due to the curvature of the Earth, that is to say to reduce the shortcomings of describing maps in two dimensions when the real coordinates are in three dimensions. A projection is an equation or a set of equations. When particular values are assigned to the parameters of the projection, one called it Coordinate system.

Projections are the transition of a spherical form to a plane surface. From a mathematical point of view, the link can be written as:

With x and y corresponding to plane coordinates, φ to the latitude, λ to the longitude and f1 and f2 functions which are continuous throughout the whole departure except for a small number of lines and points (such as poles).

The principle of cartographic projection is to project the positions of the earth's surface on a given geometrical surface (cylinder, cone and plane surface). The three types of projections associated with these geometric forms are:

  • The cylindrical projection used for low latitude regions (close to the equator). Example: UTM, Mercator.
  • The conical projection used for mid latitude areas. Example: Lambert projections.
  • The azimuthal projections used for polar areas. Example: Stereographic projection, Equidistant zenith projection.

These three types of projections have also different properties:

  • The cylindrical projection: Equivalent projections preserve locally surfaces (the area ratios are maintained while the angles and the distances change.),
  • The conical projection: conformal projections preserve angles locally and then forms,
  • The azimuthal projections: conservation of the distances on meridian lines.

It is essential to adapt the type of projection according to different uses of the map, the country's situation, the position on the Earth's surface (near a pole, equator) and extent of the country (island of small surface or country continent).