## Transformation

### Summary

LiDAR360 software supports multiple coordinate transformation methods. Users can select a transformation method to perform coordinate conversion according to their needs.

The four supported coordinate transformation methods are:

### Steps

1. Input Data: The input file can be a single point cloud data file or multiple data files. File Format: *.LiData.
2. Select the Transformation Method. Users can select the desired transformation method from the drop-down box and set the relevant parameters.
3. Output Path: Path of the output folder. After the algorithm being executed, new files after coordinate conversion will be generated.

### Usage

Click Data Management > Projections and Transformations > Transformation

### Settings

Linear The linear transformation is used to pan and zoom a point cloud. A panning parameter and a scaling parameter need to be set to the X, Y, Z coordinates, respectively. The targeted coordinates are calculated using the following formula: Among them: Sx, Sy, Sz are the scaling factors for the x, y, and z coordinates. Px, Py, and Pz are the panning parameters for the x, y, and z coordinates. x, y, and z are the original coordinates, and X, Y, and Z are coordinates obtained after the linear transformation.

XYMultiply The targeted coordinates are calculated using the following formula: Among them, Px, Py, Pz, a, b, c, d, e are the transformation parameters, Sx, Sy, Sz are the original coordinates, and X, Y, Z are the transformed coordinates. This is often used as a 2D Helmert transformation.

Translate and Rotate The targeted coordinates are calculated using the following formula: R11、R12、R13、R21、R22、R23、R31、R32、R33 are calculated as follows:

R11 = cos( Ry ) * cos( Rz )

R21 = cos( Ry ) * sin( Rz )

R31 = -sin( Ry )

R12 = sin( Rx ) sin( Ry ) cos( Rz ) - cos( Rx ) * sin( Rz )

R22 = sin( Rx ） sin( Ry ) sin( Rz ) + cos( Rx ) * cos( Rz )

R32 = sin( Rx ) * cos( Ry )

R13 = cos( Rx ) sin( Ry ) cos( R_z ) + sin( Rx ) * sin( Rz )

R23 = cos( Rx ) sin( Ry ) sin( Rz ) - sin( Rx ) * cos( Rz )

R33 = cos( Rx )* cos( Ry )

• λ (default value is "0"): Scale factor applied to X, Y, Z.
• Dx, Dy, Dz (default value is "0"): Panning values added to X, Y, Z.
• Rx, Ry, Rz (default value is "0"): The angle of rotation about the X, Y, and Z axes in degrees.

Note: To achieve millimeter-level accuracy, there should be at least eight decimal places after the decimal point.

3D Affine The targeted coordinates are calculated using the following formula: • Dx, Dy, Dz (default value is "0"): Panning values added to X, Y, Z.
• Mx, My, Mz (default value is "0"): Scale factor applied to X, Y, and Z.
• Rx, Ry, Rz (default value is "0"): The angle of rotation about the X, Y, and Z axes in degrees.

Note: To achieve millimeter-level accuracy, there should be at least eight decimal places in the user inputs.