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The polar stereographic projection is a method of projecting the earth’s surface onto a plane. With the pole as the center, the points on the earth’s surface are projected onto a plane tangent to the pole through rays. The core principle is to regard the earth as a sphere, with the pole as the viewpoint, the projection surface as a plane tangent to the pole, the meridians projected as radial straight lines, the latitudes projected as concentric circles, and the meridians and latitudes intersecting at right angles, presenting a spider web shape. This projection method can keep the local angles and shapes unchanged, with less deformation in polar regions, and can accurately maintain the relative distance relationship between points on the earth’s surface, ensuring that the direction on the map is consistent with the actual geographical direction.

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.

Miller Cylindrical Projection is a map projection method that projects the earth’s surface onto a two-dimensional plane. Its characteristic is that it emphasizes the left-right symmetry (mirror effect) of geographic information. This method is mainly used in scenes that value visual balance and overall grasp. It does not focus on the distance or shape from a specific center point, but focuses more on overall visibility and comparability.

Mercator Projection is one of the most famous map projections. It was first proposed by Franz Walter Mercator (Gerardus Mercator) in 1569 and is mainly used for drawing nautical charts. Mercator projection is a kind of orthogonal cylindrical projection, also known as “standard cylindrical projection”. Its characteristic is that it can project the longitude and latitude coordinates of the earth onto a plane, keeping the angle unchanged, so it is very useful in navigation and aviation.

Van der Grinten projection is a world map projection developed by American geographer Alphons J. van der Grinten in 1898. The notable features of this projection are that it can represent the entire earth in a circle and present a visually balanced and elegant world map by depicting the meridians and parallels as curves.

Sinusoidal projection is a pseudo-cylindrical equal-area projection created by French cartographer Samson in 1650. It is also called the Samson projection or the Samson-Flamsteed projection. Its core features are that the latitudes are equidistant parallel straight lines, the meridians are sinusoidal curves symmetrical to the central meridian, the central meridian is a straight line with a length ratio of 1, and the equator is a non-deformed line, which can effectively maintain the accurate area ratio. After projection, the length of the equator is twice that of the central meridian, the poles are projected as points and form protruding edges, and the graticule is symmetrically distributed along the equator and the central meridian.

Gauss–Krüger projection is a map projection based on the Transverse Mercator projection, developed by the German geographers Carl Friedrich Gauss and Johann Heinrich Krüger. It is widely used for large-scale topographic maps and precision surveying, and is adopted as part of the national coordinate system by many countries, notably Germany, Russia, and China.

The Albers Equal-Area Conic Projection is an area-preserving conic projection widely used in geographic information systems (GIS) and cartography.

Pseudo Mercator projection is a sphere-based conformal cylindrical projection. It converts longitude and latitude coordinates into plane rectangular coordinates by approximating the earth as a sphere and using a tangent cylindrical projection. It is widely used in global Web map services (such as Google Maps and OpenStreetMap) and supports seamless splicing and layered tile loading.

Lambert Conformal Conic Projection is a conic projection method that projects the earth’s surface onto a cone and then unfolds the cone into a flat map. This projection method was developed by French mathematician Johann Heinrich Lambert and is widely used because it is particularly suitable for map making in mid-latitude areas.