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## Coordinate transformations / Transformations |

Coordinate transformations / Transformations

Transformations category in Coordinate transformations folder contains a list of coordinate transformations which can be used to transform the position of laser data, trajectories, and other data.

You can Add, Edit, and Delete transformation by using the corresponding buttons in the Settings dialog. The Copy button copies the selected transformation to the clipboard. With the Paste button you can paste a transformation from the clipboard. The Derive button can be used for Deriving a transformation from a set of control point pairs.

Several types of coordinate transformations are supported:

•Equation transformation - discarded feature in x64 software

•3D translate & rotate transformation

•Projection change transformation

To define a new transformation:

1. Open the Transformations category in the Coordinate transformations folder.

2. Click Add in the Settings dialog.

This opens the Transformation dialog.

3. Type a Name for the transformation and select a transformation Type. Define the other settings depending on the transformation type.

4. Close the Settings dialog in order to save the modified settings for TerraScan.

Linear transformation scales and/or translates coordinate values. You can assign a coefficient and a constant offset for each coordinate axis. The target coordinates are computed by multiplying the original coordinates with the given coefficient and by adding a given constant value.

SETTING |
EFFECT |

Multiply by - X |
Coefficient for multiplying the easting coordinate. |

Multiply by - Y |
Coefficient for multiplying the northing coordinate. |

Multiply by - Z |
Coefficient for multiplying the elevation coordinate. |

Add constant - X |
Value to add to the easting coordinate. |

Add constant - Y |
Value to add to the northing coordinate. |

Add constant - Z |
Value to add to the elevation coordinate. |

Known points transformation lets you specify the coordinates of two known points in the original coordinate system (survey coordinates) and their respective coordinates in the target system (design file coordinates).

SETTING |
EFFECT |

Survey X, Y, Z |
First known point in the original coordinate system. |

X, Y, Z |
Second known point in the original coordinate system. |

Design X, Y, Z |
First known point in the target coordinate system. |

X, Y, Z |
Second known point in the target coordinate system. |

Xy multiply applies a transformation using equations:

NewX = dx + a * Sx + b * Sy

NewY = dy + c * Sx + d * Sy

NewZ = dz + e * Sz

where dx, dy, dz, a, b, c, d, and e are constant parameters of the transformation and Sx, Sy, Sz are the original (survey) coordinates. This is often used as 2D Helmert type of transformation.

3D translate & rotate transformation

3D translate & rotate applies a three dimensional translation and rotation to coordinates.

SETTING |
EFFECT |

Dx, Dy, Dz |
Values to add to X, Y, Z coordinates. |

Ox, Oy, Oz |
X, Y, Z coordinates of the rotation center point. |

Rx, Ry, Rz |
Rotation angle in radians around X, Y, Z axes. |

3D Affine applies separate translation, rotation and scaling for each coordinate axis. The transformation is defined by equations:

NewX = dx + (1.0 + mx) * X + rz * Y - ry * Z

NewY = dy + (1.0 + my) * Y - rz * X + rx * Z

NewZ = dz + (1.0 + mz) * Z + ry * X - rx * Y

where dx, dy, dz, mx, my, mz, rz, ry, and rz are constant parameters of the transformation and X, Y, Z are the original coordinates.

SETTING |
EFFECT |

Dx, Dy, Dz |
Values to add to X, Y, Z coordinates (translation). |

Mx, My, Mz |
Factors to scale the data along the X, Y, Z axes. |

Rx, Ry, Rz |
Rotation angle in radians around X, Y, Z axes. |

Projection change transformation

Projection change transforms coordinates from one projection system to another. The software transforms the X, Y, Z coordinates from the source projection system back into WGS84 geocentric X, Y, Z and then computes the transformation into the target projection system.

All projections systems that are active in Coordinate transformations / Built-in projection systems, Coordinate transformations / US State Planes, or defined in Coordinate transformations / User projection systems are available for a projection change transformation.

If you already applied a geoid correction, you should run a reverse geoid correction to the data set before using a projection change transformation. This is essential in cases where the source and the target systems use different ellipsoids or datums. A geoid correction or a reverse geoid correction is only applied automatically if the UK National Grid system is used in the transformation.

SETTING |
EFFECT |

From |
Source projection system. |

To |
Target projection system. |

Modify |
Coordinate values to modify: •Xyz - modifies all coordinates. •Xy only - no changes to elevation values. |

You can copy transformations from one Terra application to another. Select the transformation in the Settings dialog and click on the Copy button to copy the definition to the clipboard. Click on the Paste button in the other Terra application to paste the definition.

You can also derive transformation parameter values from point pairs. This requires that identical control points (point pairs) are available in source and target coordinate values. The points must be stored in text files. The number of required control point pairs depends on the transformation type.

To derive a transformation, click on the Derive button in the Settings dialog. This opens the Derive transformation from points dialog:

SETTING |
EFFECT |

Type |
Type of the derived transformation: •2D transformation - parameter values for a 2D Helmert transformation are derived. •3D translate & rotate - parameter values for a 3D translation and rotation transformation are derived. •7 parameter affine - parameter values for a 3D affine transformation (7 parameters) are derived. •9 parameter affine - parameter values for a 3D affine transformation (9 parameters) are derived. |

Use |
Points used for deriving the transformation: •All point pairs - uses all control point pairs. •Inside source fence only - points inside a fence in the source coordinate system are used. •Inside target fence only - points inside a fence in the target coordinate system are used. |

Source |
Text file that contains the point pair coordinates in the source system. |

Target |
Text file that contains the point pair coordinates in the target system. |

The transformation derivation can be tested by using the Test button. This computes the parameter values and displays the result in a report window. To create the transformation, click on the Create button. This opens the Transformation dialog that displays the derived parameter values. Type a Name for the transformation and click OK in order to add the transformation to the list in the Settings dialog.