1, Gauss Kruger projection is an isometric projection of an elliptic cylinder, which was proposed by German mathematician Gauss at the beginning of19th century and named after being improved by German geographer Kruger. This kind of projection divides the earth's surface into several zones according to meridian, and then projects by zones, which has the inherent characteristics of maintaining area, angle and shape. This projection is used for topographic maps of China1:over 500,000.
2. The mathematical basis of Gaussian Krueger projection is the perspective orthogonal projection relationship between the transverse ellipsoid and the plane, that is, cutting the transverse ellipsoid with a group of straight lines parallel to the equatorial plane of the transverse ellipsoid, projecting the tangent to the cross section (that is, the plane) to form a plane figure, and then reducing the figure to a certain proportion to turn the long axis of the transverse ellipsoid into a straight line, that is, forming Gaussian Krueger projection.
3. In the concrete realization, China adopts Gaussian Kruger projection with double standard latitudes, that is, based on the central meridian, the earth is divided into two hemispheres, east and west, and each hemisphere is divided into three equal zones, and the width of each equal zone is longitude 15 degrees. This projection method can keep the orientation, direction, shape and relative position of the map unchanged, and can meet the needs of making various conventional maps and thematic maps.
Characteristics of Gaussian-Kruger Projection
1, isometric projection: the biggest feature of Gaussian-Kruger projection is isometric projection, that is, the angle remains unchanged after projection. This projection method can keep the orientation, direction, shape and relative position of the map unchanged, making the map more accurate and reliable. Transverse elliptic cylinder projection: Gaussian Kruger projection is to divide the earth's surface into several zones according to the meridian, and then project according to the zones.
2. Area deformation: An important feature of Gauss-Kruger projection is its small area deformation. In the process of projection, the area deformation of the projection area is very small and can be basically ignored. Therefore, it can be considered that Gaussian Kruger projection is a projection method without area deformation.
3. Directional deformation: The directional deformation of Gaussian Kruger projection is also relatively small. In the process of projection, the directional deformation is relatively small because of the way of crossing the elliptical column. But with the increase of the distance from the central meridian, the directional deformation will gradually increase. Length distortion: the length distortion of Gaussian Kruger projection is also relatively small.