Wagner Projection

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Introduction

The Wagner Projection is a modified azimuthal projection developed by Winkel in 1921. It is essentially a projection of a sphere on a plane, designed to minimize three types of distortion: area, direction, and distance. The projection is neither equal-area nor conformal, and its main feature is that all latitudes are curved except for the poles and the equator, which are straight lines. Its design is achieved through graphic design rather than mathematical equations, and it has certain characteristics in terms of visual balance and global deformation, but it has disadvantages such as non-equal areas and non-conformal angles. In local areas or specific applications, characteristics such as area, shape, and angle may be significantly distorted.

Projection Composition

The projection basis of the Wegener triple projection is the projection of a sphere on a plane. The core of its design is to achieve a compromise expression of global geographic information through graphic design rather than relying on strict mathematical equations. Specifically:

Projection method: The Wegener triple projection uses an azimuthal projection method to project the surface of a sphere onto a plane. During the projection process, all latitudes appear as curves, except for the poles and the equator, which are straight lines.
Deformation characteristics:
- Non-equal area and non-equal angle: The Wegener triple projection can neither strictly maintain the area nor the angle. During the projection process, characteristics such as area, shape, and angle may be distorted to a certain extent.
- Deformation distribution: The deformation of this projection is relatively small globally, but in some areas, the shape and area may still be distorted to a certain extent. This distortion increases with the distance from the projection center.

Pros

**Good visual balance: **The Wegener triple projection compromises the three distortions of shape, area, and distance, making the world map visually balanced. This projection is suitable for displaying global maps and can provide readers with an intuitive and comprehensive geographical overview.
**Suitable for displaying global scope: **Compared with some projections that perform well in specific areas but have large distortions on a global scale, the Wegener triple projection has relatively small distortions on a global scale, so it is more suitable for drawing world maps.

Cons

**Does not strictly preserve any one property: **Because the Wegener Triple projection is a compromise projection, it does not strictly preserve areas, shapes, or distances. In local areas or for specific applications, this projection may cause some distortion of geographic features.
**Shapes and areas are distorted: **Although the Wegener Triple projection has relatively little distortion on a global scale, some distortion of shapes and areas may still be present in certain areas. This distortion may affect the accurate interpretation of the map information.

Application Scenario

The Wagner projection is suitable for map application scenarios that need to take into account multiple deformation characteristics and balance the three main distortions (area, direction, and distance), such as teaching wall maps, geography popular science books, or decorative maps that need to intuitively display the global geographical distribution and can accept moderate deformation.

Example

Wagner VI projection of the world.

The Wagner VII map projection is shown centered on Greenwich.

Mercator Projection

Transverse Mercator Projection

Lambert Conformal Conic Projection

Longitude / Latitude Projection