In cartography , geometry and geodesy, angle distortion is understood to mean , on the one hand, the property of many map projections that angles in nature (or measured angles ) are shown changed on a map , and on the other hand, the size of the angle distortion itself.
The angular distortion means a change in shape due to the map projection - as z. B. is recognizable in planiglobes by the distortion of the continents lying on the map edge. The distortion is i. a. Largest in the case of true-to-area (geographically used) projections, but zero for true-to-angle images (e.g. geodesy or measurement technology ).
On the other hand, there is no angular distortion, which is noticeable on some conformal maps such as the Mercator projection: z. B. the noticeable enlargement of Greenland or the apparent widening of Siberia . It is a consequence of the cartographic area distortion , as it occurs with maps that are not true to area and are mainly used in geography.
A geometric mapping is called conformal or conformal if it leaves the sizes of angles unchanged. Examples of conformal pictures are all Kongruenzabbildungen (about axis reflection , point reflection , parallel displacement and rotation ), generally, all similarity pictures , in particular the central dilation .
If the angle is correct (conformity) , the angle distortion is zero - then all angles in the figure correspond to those in the original . The image in the projection is similar to the original image in the smallest areas, the line distortion is therefore the same in all directions, the Tissot indicatrix remains circular. So you can enter directions correctly, and also distances after a small reduction .
Since there is no generally true-to-length mapping of a sphere or other two-dimensionally curved surfaces in the plane , either angular distortions or surface distortions or both have to be accepted. The distortions are only a few percent in common regional maps, but can grow to around 30–50% in global map displays.
- y³: 6r² (y = distance from the central meridian, r = earth radius)
While angular distortions play less of a role in geographical work (here the area fidelity is usually more important), they are particularly unpleasant when displaying measured variables . Therefore, one prefers projections with low angular distortions - or conformal maps - especially for:
- Astronomy and geometry
- Navigation and air traffic control
- Geodesy and surveying
- Geophysics and rock mechanics
Important conformal projections
- Mercator projection - cylinder projection for most nautical charts
- Lambert's conformal cone projection - cone projections for aeronautics (most aeronautical maps ) and special applications in geography
- Gauss-Krüger coordinate system and UTM coordinate system - transversal (equatorial) cylinder projection for measurement
- stereographic projection - azimuthal projection for astronomy and geometry.