Map Projection Animations

As per statement in chapter Cartography there are diverse *types of systematizations* of map projections.

Primarily we mention the differentiation according to the **type of the projection surface resp. auxiliary surface (plane, cone, cylinder)** (see True Projections), according to the **differential-geometrical characteristics (partial length-preserving, equal-area, conformal)**, according to the **position of the projection axis**, etc..

**Map projection animations** present a particular view of specific similarities among map projections or whose differences (see also [13] among Literature). The so called **Continuums** which are presented here are based primarily upon the variation of single projection parameters (as e.g. continously varied standard parallels)

Perspective Continuum

The ** perspective continuum** is based on

*vertical-perspective azimuthal map projections*. In this case the distance

**d**between the point of perspective and the centre of the Earth is varied continuously as a multiple of the Earth radius.

For **d = –1** the *stereographic projektion* is available, for **d = 0** the *gnomonic projection*, for **d = 1,4** the *CLARKE „twilight” projection*, for **d = 1,5** the *JAMES projection*, for **d = 1,71** the *DE LA HIRE projection* and for **d → ∞** the *orthographic projection*.

Here you see the construction principle:

Conic Continuum

The ** conic continuum** is based on the differentiation according to the

**type of the projection surface resp. auxiliary surface (plane, cone, cylinder)**. The basic idea of this continuum is a result of the imagination that plane and cylinder are „limit cases” of the cone (plane as infinite flat cone and cylinder as infinite high cone).

In case of the ** conic continuum** the standard parallel

**v**of a

_{0}*conic projection (with one single standard parallel)*is varied continuously between 90° and -90°. The limit cases result as follows: for

**v**we get the

_{0}= ± 90°*normal azimuthal projection*and for

**v**we get the

_{0}= 0°*cylindrcal projection*.

The ** intersection-cylinder continuum** is available for each of the three

*differential-geometrical variations:*

Pseudoconic Continuum

The ** pseudoconic continuum** is based on the

*parallel-reduction preserving, equal-area projection of BONNE with the standard parallel*

**v**.

_{0}In case of the ** pseudoconic continuum** the

*standard parallel*

**v**is varied continuously between 90° and -90° (as done for the conic continuum). As above-mentioned the limit cases also result as follows: for

_{0}**v**we get the

_{0}= ± 90°*projection of STAB-WERNER*and for

**v**the

_{0}= 0°*projection of SANSON*.

Here you see a preview:

Intersection-cylinder Continuum

The ** intersection-cylinder continuum** is based on

*cylinder projections with two standard parallels*±

**v**.

_{0}In case of the ** intersection-cylinder continuum** the two

*standard parallels*±

**v**, which are arranged symmetrically to the equator, are varied continuously between 0° und 90°.

_{0}The ** intersection-cylinder continuum** is available for each of the three

*differential-geometrical variations*: