Coordinate Transformation Parameter Solving Online

Online coordinate transformation parameter solving tool, input a set of known point coordinates, and solve the parameters used for coordinate transformation. Coordinate conversion types support three parameter, four parameter, and seven parameter coordinate conversions.

1. Input Coordinates Type ： Supports the input of Cartesian spatial rectangular coordinate system coordinates (ECEF coordinates, XYZ) and geodetic coordinates (geodetic longitude, geodetic latitude, geodetic height, LBH). Use comma-separated values to enter one set of coordinates per line. Multiple lines are supported. The spatial Cartesian coordinate format is X , Y , Z, the unit is the meter (m). The geodetic coordinate format is L , B , H, longitude and latitude are in degrees and elevation is in meters.
2. Coordinate System 1 Coordinate : The coordinates of a known point in coordinate system 1. The format of XYZ and LBH coordinates is supported. If LBH coordinates are entered, the ellipsoid of coordinate system 1 must be selected. When the parameter is calculated, the LBH coordinates are automatically converted to XYZ coordinates for calculation.
3. Coordinate System 2 Coordinate : The coordinates of a known point in coordinate system 2. The format of XYZ and LBH coordinates is supported. If LBH coordinates are entered, the ellipsoid of coordinate system 2 must be selected. When the parameter is calculated, the LBH coordinates are automatically converted to XYZ coordinates for the calculation.
4. Convert Type : The tool supports three-parameter, four-parameter, and seven-parameter coordinate conversions. The calculation formula, known point coordinate requirements and output conversion parameter information corresponding to each conversion type are shown in the following.
5. Three-parameter coordinate conversion:
   1. Description of three-parameter coordinate conversion : Uses x-axis translation, y-axis translation, and z-axis translation for coordinate conversion, with no coordinate rotation or scaling involved.
   2. Input coordinate type : Requires the input of 3D coordinates and at least 1 set of known point coordinates.
   3. Output parameter results : x-axis translation (x), y-axis translation (y), z-axis translation (z) in meters m.
   4. Transformation Formula :
6. Four-parameter coordinate transformation:
   1. Description of the four-parameter coordinate transformation : Uses x-axis translation, y-axis translation, rotation angle, and scaling factor for planar coordinate conversions; no Z-axis coordinate conversions are involved.
   2. Input coordinate type : Requires input of 3D coordinates and at least 2 sets of known point coordinates. It is recommended to input at least 4 sets of known point coordinates, obtain conversion parameters, and based on the displayed residual data of known points, remove known points with residuals greater than 3 times the unit weight root mean square error.
   3. Output parameter results : x-axis translation (x), y-axis translation (y) in meters. theta Angle of rotation in arc seconds, s Scaling factor with no unit. The theta rotation angle is an angle in the clockwise direction.
   4. Transformation Formula :
7. Seven-parameter coordinate transformation:
   1. Description of seven-parameter coordinate conversion : Use x-axis translation, y-axis translation, z-axis translation, s scaling factor, x-axis rotation angle, y-axis rotation angle, and z-axis rotation angle for 3D coordinate conversion.
   2. Input coordinate type : Requires the input of 3D coordinates, with at least three sets of known point coordinates. It is recommended to input at least 6 sets of known point coordinates, obtain conversion parameters, and based on the displayed residual data of known points, remove known points with residuals greater than 3 times the unit weight root mean square error.
   3. Output parameter results : x-axis translation (x), y-axis translation (y), z-axis translation (z) in meters m . s Scaling factor in ppm . x-axis rotation (rx), y-axis rotation (ry), and z-axis rotation (rz) in arc-seconds.
   4. Convention : Indicates the convention to express the rotational terms when a 3D transform is involved. As soon as a rotational parameter is specified (one of rx, ry, rz, drx, dry, drz), convention is required. The two conventions are equally popular and a frequent source of confusion. The coordinate frame convention is also described as an clockwise rotation of the coordinate frame. It corresponds to EPSG method code 1032 (in the geocentric domain) or 9607 (in the geographic domain) The position vector convention is also described as an anticlockwise (counter-clockwise) rotation of the coordinate frame. It corresponds to as EPSG method code 1033 (in the geocentric domain) or 9606 (in the geographic domain). The result obtained with parameters specified in a given convention can be obtained in the other convention by negating the rotational parameters (rx, ry, rz, drx, dry, drz)
   5. Precise Calculate : Choose whether to compute the rotation matrix precisely or approximately. This is a parameter used for 3D coordinate transformation. When high-precision coordinate transformation is required, or when any rotation angle exceeds 0.1 arc seconds, the rotation matrix should be precisely calculated.
   6. The conversion convention for the Bursa-Wolf seven-parameter calculation model needs to be set as position_vector. Then, decide whether to precisely calculate the rotation matrix based on your needs.
   7. Transform Formula: (When the rotation angle is small, the rotation matrix is approximately calculated)
      
      
      For the calculation formula of the precise rotation matrix, please refer to the instruction document of the Coordinate Frame Convert Online tool on this website.
8. Four Parameters Simple coordinate transformation:
   1. Four parameter simple calculation instructions: Use x-axis translation, y-axis translation, theta rotation angle, and s scaling factor for plane coordinate conversion, without involving Z-axis coordinate conversion.
   2. Input coordinate type: requires input of 3D coordinates, input of 2 sets of coordinate system 1 coordinates, no need for coordinate system 2 coordinates (no need to know the coordinates of the point in the target coordinate system). Only supports inputting XYZ type coordinates. The line formed by these two sets of coordinates needs to be parallel to the X-axis or Y-axis of the target coordinate system.
   3. Applicable scenarios: No known points are required, only two sets of coordinates in coordinate system 1 are needed to calculate the four parameters of coordinate system 2 conversion. Especially suitable for scenarios where the origin of coordinate system 2 is insensitive and only the rotation angle from coordinate system 1 to coordinate system 2 needs to be calculated. The coordinate system formed is defined as: the origin is the first coordinate point of the input, and the line connecting the first and second coordinates is the direction of the selected target coordinate axis. Coordinate system 2 conforms to the right-hand coordinate system.
   4. Output parameter results : x-axis translation (x), y-axis translation (y) in meters. theta Angle of rotation in arc seconds, s Scaling factor with no unit. The theta rotation angle is an angle in the clockwise direction.
9. Detailed explanation of the definition of rotation angle direction:
   1. Coordinate conversion runs by default in the right-handed spatial Cartesian coordinate system.
   2. If the coordinate transformation has a rotation angle (such as theta or rx, ry, rz), the rotation angle has two directions defined, The rotation angle direction applied to the coordinate axis and the rotation angle direction applied to the coordinate point.
   3. Table of rotation angle directions for four and seven parameters:

      Transform Type	Convention	Parameters	Apply to Coordinate Frame	Apply to Position Vector	Note
      Four parameters	Default	theta	Anticlockwise is positive	Clockwise is positive	The four parameter related tools on this site are defined in this direction
      Seven parameters	coordinate_frame	rx, ry, rz	Clockwise is positive	Anticlockwise is positive	reference document EPSG 1032
      Seven parameters	position_vector	rx, ry, rz	Anticlockwise is positive	Clockwise is positive	reference document EPSG 1033

10. Precision Evaluation :
    1. The tool lists X residual, Y residual, Z residual, X residual root mean square error, Y residual root mean square error, Z residual root mean square error, point root mean square error and unit weight root mean square error in the calculation results for evaluating the accuracy of the coordinate conversion parameters.
    2. Residual Formula : V = Known point transformation coordinate values - Known point coordinate system 2 coordinate values .
    3. X residual root mean square error formula :
    4. Y residual root mean square error formula :
    5. Z residual root mean square error formula :
    6. Point residual root mean square error formula : 2D plane coordinates -
       , 3D spatial coordinates -
    7. Unit weight root mean square error formula :
       , Among them, V is the residual vector, P is the weight matrix, n is the total number of observations (including components), and t is the number of unknown parameters.
11. The coordinate transformation parameters solved by this tool can be verified using the Coordinate Frame Convert Online tool on this site with the following parameter filling rules:
    1. Three Parameter Transform : Select the Three Parameter transform type, and then directly fill in the corresponding x, y, z conversion parameters.
    2. Four Parameter Transform : Select the Four Parameter 2 transform type, and then directly fill in the corresponding x, y, theta, s conversion parameters.
    3. Seven Parameter Transform : Select the Seven Parameter transform type, and then directly fill in the corresponding x, y, z, s, rx, ry, rz conversion parameters. The convention and the requirement for precise calculation of the rotation matrix must be consistent.
12. Open File : Support for opening UTF-8 encoded text files.
13. This tool has a certain frequency limit, please use this tool reasonably. Anonymous : 3/IP*Hour, Normal user : 3/Hour, VIP : 360/Hour, Senior VIP : 360/Hour.