.gif)
Untrue Projections
The untrue projections develop from the true projections in consideration of one or more special additional conditions. Thus the 3 charcteristic properties of the true projections will disappear wholly or in part.
In this case the third property of the true projections, namely the rectangularity of the grid lines, is mainly affected. This is of particular mathematical importance concerning the local distortion values of a map, but will not be deepened here. To this the interested reader can find advanced informations in the (mathematical) Literature. Important keywords are: maximum distortion values, area distortion and angular deformation, ellipse of distortion, Tissot's Indicatrix.
Analog to the true projections the untrue projections are also called non-conical projections. We generally differentiate
- Pseudoconic Projections
- Pseudoazimuthal Projections
- Pseudocylindrical Projections
- Polyconic Projections
- Modified-azimuthal Projections and
- Miscellaneous Projections .
The additional term pseudo means that the accordant untrue projections often are based on true projections.
The differential-geometrical properties of the untrue projections are important too, but the equal-area projections dominate here.
The untrue projections are often used for an overall view of the Earth.
Advanced descriptions and explanations are offered in the program GridMaps .
Pseudoconic Projections
Parallel reduction preserving and equal-area projection by Bonne (1752) (Tissot's Indicatrices with 30° graticule)
Pseudoazimuthal Projections
Parallel reduction preserving and equal-area projection by Stab-Werner (1514) (Tissot's Indicatrices with 30° graticule)
Pseudocylindrical Projections
Parallel reduction preserving and equal-area projection by Sanson (1650) (Tissot's Indicatrices with 30° graticule)
Equal-area projection by Mollweide (1805) (Tissot's Indicatrices with 30° graticule)
Equal-area renumeralised projection by Sanson (Tissot's Indicatrices with 30° graticule)
Projection by Robinson (1963) (Tissot's Indicatrices with 30° graticule)
Equal-area projection IV by Wagner (1932) (Tissot's Indicatrices with 30° graticule)
Equal-area projection IV by Eckert (1906) (Tissot's Indicatrices with 30° graticule)
Projection V by Eckert (1921) (Tissot's Indicatrices with 30° graticule)
Equal-area projection VI by Eckert (1906) (Tissot's Indicatrices with 30° graticule)
Equal-area (triangular) projection by Collignon (1865) (Tissot's Indicatrices with 30° graticule)
Equal-area (diamond-shaped) projection by Collignon (1865) (Tissot's Indicatrices with 30° graticule)
Polyconic Projections
Polyconic projection by Hassler (1820) (Tissot's Indicatrices with 30° graticule)
Orthogonal polyconic projection (Tissot's Indicatrices with 30° graticule)
Conformal polyconic projection (Tissot's Indicatrices with 30° graticule)
Modified-azimuthal Projections
Projection by Aitoff (1889) (Tissot's Indicatrices with 30° graticule)
Equal-area projection by Hammer (1892) (Tissot's Indicatrices with 30° graticule)
Miscellaneous Projections
Projection by Van Der Grinten (1898) (Tissot's Indicatrices with 30° graticule)
Projection by Winkel (Tripel) (1913) (Tissot's Indicatrices with 30° graticule)
