The establishment of geodetic coordinate systems in any country (or region) evolves historically. During different periods, the reference ellipsoids and positioning methods adopted vary significantly, with continuous improvements and refinements. Coordinate systems established using different reference ellipsoids and positioning methods constitute distinct local space rectangular coordinate systems, which also differ from the unified geocentric space rectangular coordinate system with the Earth's center of mass as the origin. This necessitates the conversion between different geodetic coordinate systems.
 |
 |
| Figure 1: Three-parameter Method | Figure 2: Seven-parameter Method |
When performing data source projection or point coordinate transformation, the system provides eleven projection transformation methods in the dialog: Geocentric Translation(3-para), Molodensky(3-para), MolodenskyAbridged(3-para), Position Vector(7-para), Coordinate Frame(7-para), Bursa-wolf(7-para), MolodenskyBadekas(10-para), China_3D_7P(7-para), China_3D_7P(7-para), China_2D_4P(4-para), PROJ4 Transmethod.
| Projection Methods | |
| Name | Description |
| GeocentricTranslation | Three-parameter transformation method based on geocentric coordinates. |
| Molodensky | Molodensky transformation method. |
| MolodenskyAbridged | Simplified Molodensky transformation method. |
| PositionVector | Position vector method. |
| CoordinateFrame | Seven-parameter transformation method based on geocentric coordinates. |
| BursaWolf | Bursa-Wolf method. |
| MolodenskyBadekas | Molodensky-Badekas projection method, a ten-parameter spatial coordinate transformation model. |
| China_3D_7P | Three-dimensional seven-parameter transformation model, suitable for control point coordinate transformation between national/provincial geodetic coordinate systems with different Earth ellipsoid datums at 3-degree zones or larger. This model involves three translation parameters, three rotation parameters, and one scale factor, while considering differences in semi-major axis and flattening between the two Earth ellipsoids. |
| China_2D_7P | Two-dimensional seven-parameter transformation model for national/provincial control point coordinate transformation between geodetic coordinate systems with different Earth ellipsoid datums at 3-degree zones or larger. The model includes three translation parameters, three rotation parameters, and one scale factor. For transformations between Beijing 1954 and Xi'an 1980 coordinate systems to CGCS 2000, the two-dimensional seven-parameter method is recommended due to lower accuracy of geodetic heights in local coordinate systems. |
| China_2D_4P | Two-dimensional four-parameter transformation model suitable for provincial/local control point coordinate transformation within 2-degree zones. The model includes two translation parameters, one rotation parameter, and one scale factor. |
| PROJ4 Transmethod | PROJ4 transformation algorithm based on third-party PROJ4 projection tools, supporting more projection operations to meet overseas users' needs. This method only supports transformations between projections with corresponding EPSG codes. |
Common transformation methods are categorized into three-parameter and seven-parameter methods:
- Three-parameter Transformation
The simplest reference system transformation method uses three parameters. This mathematical model assumes only spatial translation between geodetic reference systems, ignoring other factors (see Figure 1). It requires three translation parameters (ΔX, ΔY, ΔZ). Though simple, it offers lower accuracy and is typically used for conversions between different geocentric space rectangular coordinate systems.
- Seven-parameter Transformation
The seven-parameter method considers coordinate system translation, rotation, and scale differences. It requires three translation parameters (ΔX, ΔY, ΔZ), three rotation parameters (Rx, Ry, Rz), and one scale factor (S). Translation parameters use meters, rotation parameters use arc-seconds, and the scale factor is measured in parts per million (see Figure 2).
-
Geocentric Translation, Molodensky, and MolodenskyAbridged methods are lower-precision projection approaches. Three-parameter methods require translation parameters (ΔX, ΔY, ΔZ). These methods are suitable when high data accuracy is not required.
- Position Vector, Coordinate Frame, and Bursa-Wolf methods provide higher precision. They require seven parameters: three translations (ΔX, ΔY, ΔZ), three rotations (Rx, Ry, Rz), and one scale factor (S). These methods are essentially equivalent but differ in regional naming conventions.
Tip:In practice, the choice of transformation method depends on specific requirements. Transformation accuracy depends on parameter settings. Parameters can be obtained from official surveying agencies, data providers, or calculated through field measurements. Parameter validity must be verified using control points existing in both reference systems.
Related Topics