Coordinate transformation calculation formula-EEWORLD

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Conversion between geocentric coordinates and rectangular coordinates in centric space

1 Glossary:
A: Geocentric space rectangular coordinate system:
a) The origin of the coordinate is the geocentric 0;
b) The Z axis coincides with the minor axis (rotation axis) of the reference ellipsoid;
c) The X axis coincides with the intersection of the starting meridian plane and the equator;
d) The Y axis is perpendicular to the X axis on the equatorial plane, forming a right-handed rectangular coordinate system 0-XYZ;
e) The position of the ground point P is represented by (X, Y, Z);
B: Geocentric geodetic coordinate system:
a) The origin of the coordinate is the center of the reference ellipsoid, and the minor axis of the ellipsoid coincides with the rotation axis of the reference ellipsoid;
b) Geodetic latitude B: The angle between the ellipsoid normal passing through the ground point and the equatorial plane
of the ellipsoid is the geodetic latitude B; c) Geodetic longitude L: The angle between the ellipsoid meridian plane passing through the ground point and the starting meridian plane is the geodetic longitude L;
d) Geodetic height H: The distance from the ground point to the ellipsoid surface along the ellipsoid normal is the geodetic height H;
e) The position of a ground point is represented by (B, L, H).
2 Convert the geocentric coordinates to the geocentric space rectangular coordinates:

In the formula, N is the radius of curvature of the ellipsoidal surface, e is the first eccentricity of the ellipsoid, a and b are the major and minor radii of the ellipsoid, f is the flattening of the ellipsoid, and W is the first auxiliary coefficient.

3. Conversion of centric spatial rectangular coordinates to centric geodetic coordinates

2. Gauss projection and Gauss rectangular coordinate system

1. Overview of Gaussian Projection Conditions of Gaussian-Krüger projection: 1. It is a conformal projection; 2. The central meridian is not deformed

Gauss projection properties: 1. The angle remains unchanged after projection; 2. The length ratio is related to the point position, not the direction; 3. The farther away from the central meridian, the greater the deformation
In order to control the length deformation after projection, the zoning projection method is used. The 3-degree or 6-degree zoning is commonly used. The coordinates of the city or engineering control network can use any zone that is not based on the 3-degree central meridian.

2. Gaussian projection forward calculation formula: