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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.

Longitude / Latitude Projection uses the longitude and latitude coordinate system of the earth, usually in degrees. The basic principle is to imagine a cylinder that is consistent with the direction of the earth’s axis and cuts or severing the earth, project the longitude and latitude grid onto the cylindrical surface according to the equiangular condition, and then unfold the cylindrical surface into a plane to obtain a plane longitude and latitude grid. After projection, the meridians are a set of vertical equidistant parallel straight lines, and the latitudes are a set of parallel straight lines perpendicular to the meridians. The interval between adjacent latitudes increases from the equator to the poles.

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.

Transverse Mercator projection is a conformal cross-cylindrical projection that cuts the Earth ellipsoid along the meridian (central meridian) and unfolds it into a plane. It is widely used in large-scale topographic mapping and national coordinate systems (such as the UTM coordinate system) in mid-latitude regions.

UTM projection (Universal Transverse Mercator) is a coordinate system that divides the earth’s surface into zones and applies the Transverse Mercator projection to each zone. By dividing the earth into 60 zones, each zone is 6 degrees longitude apart, and projecting independently in each zone, high-precision plane rectangular coordinates can be obtained.

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.

Lambert Azimuthal Equal-Area Projection is an equal-area azimuthal projection proposed by German mathematician Johann Heinrich Lambert in 1772. This projection maps points on the earth’s surface onto a plane through spherical projection, keeping the projection area unchanged, that is, the area ratio of the area before and after the projection is strictly equal. There is no deformation at the center of the projection, and as the distance from the center increases, the angle and shape deformation gradually increase, but the area deformation is always zero.

Robinson projection is a compromise projection designed by Arthur H. Robinson in 1963 at the request of the Rand McNally Company. It was developed using graphic design rather than mathematical equations to provide a balanced visual effect for world maps. The projection is a pseudo-cylindrical projection. The meridians are regularly distributed curves that imitate elliptical arcs. They are concave to both sides with the central meridian as the center and do not intersect the parallels perpendicularly. The parallels are unequally distributed straight lines. The equator, the poles, and the central meridian are all projected as straight lines. The length of the central meridian is 0.5072 times the length of the projected equator, and the length of the polar line is 0.5322 times the length of the equator. The graticule is symmetrical along the equator and the central meridian. It is neither conformal nor equal-area, which will cause shape, area, distance, direction, and angle distortion. Area distortion increases with increasing latitude, but is not affected by changes in longitude. High latitudes will be exaggerated. Angular distortion is moderate near the center of the map and increases toward the edges. Distortion values are symmetrical along the equator and the central meridian.

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.

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.