The establishment of geodetic coordinate system in any country (or region) is a historical development process. In different periods, the Reference Spheroid and positioning methods used are different, and will be gradually improved and refined. Geodetic coordinate systems established by using different reference ellipsoids and positioning are different from each other in Space Rectangular Coordinate system, and are also different from the global unified geocentric Space Rectangular Coordinate system with the geocenter as the origin. Therefore, there is a problem of mutual conversion between different geodetic Coordinate Systems.
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| Figure 1: Three-parameter method | Figure 2: Seven-parameter method |
When Datasource Projection Transformation or point Coordinate Transformation is performed, you can see from the dialog box that the system provides eleven projection conversion methods. Geocentric Transalation (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 Transformation method | |
| Name | Description |
| GeocentricTranslation | Three-parameter conversion method based on geocenter. |
| Molodensky | Molodensky transformation. |
| MolodenskyAbridged | Simplified Molodensky transformation. |
| PositionVector | Position vector method. |
| CoordinateFrame | A seven parameter transformation method based on geocenter. |
| BursaWolf | The Bursa-Wolf method. |
| MolodenskyBadekas | Molodensky-Bardekas Projection Transformation method, a spatial Coordinate Transformation model with ten parameters. |
| China_3D_7P | The three-dimensional seven-parameter transformation model is applicable to the Coordinate Transformation of control points between geodetic Coordinate Systems under different earth ellipsoid datums of 3 degrees and above of the national and provincial ellipsoids. The model involves three translation parameters, three rotation parameters and one scale change parameter, and at the same time, it needs to take into account the semi-major axis and the flattening difference of the two earth ellipsoids corresponding to the two geodetic coordinate systems. |
| China_2D_7P | China _ 2D _ 7P two-dimensional seven-parameter transformation model is applicable to national and provincial Coordinate Transformation of control points between geodetic Coordinate Systems under different earth ellipsoid datums of 3 degrees and above. The model involves three translation parameters, three rotation parameters and one scale variation parameter. For the transformation from Beijing Coordinate System 1954 and Xi'an Coordinate System 1980 to China Geodetic Coordinate System 2000, it is suggested to adopt the two-dimensional seven-parameter transformation because of the low accuracy of the geodetic height under the two reference-centered systems. |
| China_2D_4P | The 2D Four-parameter Transformation model is applicable to Coordinate Transformation of local control points within 2 degrees at provincial level and below. The model involves three translation parameters and one scale variation parameter. |
| PROJ4 Transmethod | PROJ4 Transm ethodProjection Transformation algorithm, which is based on the third-party Projection Transformation tool of PROJ4. So as to support more Projection Transformation operations and meet the data Projection Transformation requirements of more overseas users. The Projection Transformation algorithm only supports the transformation between projections with corresponding EPSG Code. |
The above conversion methods are commonly divided into three-parameter conversion method and seven-parameter conversion method:
- Three-parameter conversion method When the
frame of reference is converted, a relatively simple conversion method is the so-called three-parameter conversion method. This transformation method is based on the mathematical model that only the coordinate origin of the space has been translated between the two Geodetic Reference System, without considering other factors (see Figure 1). This method inevitably produces three parameters, the translation of X, Y and Z directions. The three-parameter transformation method is simple in calculation, but low in accuracy, and is generally used for the transformation between different geocentric Space Rectangular Coordinates.
- Seven-parameter conversion method The mathematical model based on
the seven-parameter method considers not only the translation of the coordinate system, but also the rotation of the coordinate system and the different scales. Therefore, in addition to the three translation quantities, three rotation parameters (also known as three Euler angles) and Scale Factor (also known as Scale Factor) are required. The conversion principle is shown in Figure 2. The three translation quantities are represented by ΔX, ΔY and ΔZ, the three selection parameters are represented by Rx, Ry and Rz, and the Scale Factor is represented by S. Where Scale Factor represents the amount of scaling from the original coordinate system to the new coordinate system. In general, the translation factor is in meters (consistent with Unit), the rotation factor is in seconds, and the units are one in a million.
of the Scale Factor. Geocentric Transformation (the Geocentric Translation), Molodensky Transformation, Simplified MolodenskyAbridged transformation method belongs to Projection Transformation method with lower accuracy. The three-parameter transformation method requires three translation Transformation Parameters (ΔX, ΔY, ΔZ), and the Molodensky transformation method and the simplified Molodensky transformation method also require three translation Transformation Parameters (ΔX, ΔY, ΔZ). In the case of low data accuracy requirements, these methods can generally be used.
- Position Vector, Coordinate Frame and Bursa-Wolf are the conversion methods with high accuracy. Seven parameters are required for adjustment and transformation, including three translational Transformation Parameters (.DELTA.X.DELTA.Y.DELTA.Z), three rotational Transformation Parameters (Rx, Ry, Rz), and a scale parameter (S). These methods are exactly the same, but due to different countries, regions or schools of measurement, the customary appellation is different.
Hint: In practical work, which conversion method is used depends on the specific situation. The satisfactory result of the transformation depends on the setting of the Transformation Parameters. Transformation Parameters can be obtained from official measurement agencies and data providers, or can be measured and calculated. The suitability of the Transformation Parameters must be determined by the presence of control points in both frames of reference.
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