Coordinate Transformations

Transforming Coordinates by Parameters
Transforming Coordinates by Control Points

A set of points from an open coordfile can be geometrically transformed either

directly by specifying the known parameters of a transformation, or
indirectly by specifying pairs of control points for a transformation from one coordinate system to another.

In each case, rotations are always about a vertical axis.

From the Calculation menu, choose Transform Coords, then either By Parameters or By Control Points.

1. Transforming Coordinates by Parameters

You can specify up to seven plus two parameters of an affine transformation. The seven affine transformation parameters are a rotation, three scales, and a 3D shift. The additional two parameters are the 2D coordinates of a point that is fixed with respect to rotation and scale.

To Transform by Parameters

Calculation | Transform Coords... | By Parameters...
Optionally Load... a transformation Parameters file.
Enter the fixed point number or the Northing and Easting of a point about which the rotation should pivot or from which the scaling should occur.
For a Rotation, enter the angle (+ve clockwise).
For a Scale change,
- choose Uniform or Differential scaling, and
- enter the Projection Scale Factor and choose the Units Factor as appropriate or enter the scale change value or values directly.
For a Shift, enter either a shift expression (see § Shift Expressions) or the Northing, Easting and Elevation values to be added.
Optionally Save the Transformation parameters file for later reuse.
Choose which Points to transform: All of them or Filter... a subset (See § Point Filters).
Transform or OK. The sequence will be rotation, scale, then shift.
Optionally Reverse transform the points. This performs the specified transformation in reverse (so effectively acts as an Undo button).

click for larger view

Notes

A transformation Parameters file is a binary file, and while it can have any name, it ought to have a .tfm name extension.

2. Transforming Coordinates by Control Points

Suppose you have a set of points to transform from one coordinate system, the source system, to another, the target system. You can estimate a best-fit transformation between specified lists of control points — points whose coordinates are available in both systems — then do the transformation.

The estimation is by least-squares and can be for

a rigid-body transformation having a rotation and a 2D shift or
a similarity transformation (or Helmert transformation) having a rotation, a scale, and a 2D shift.

The rotation and scale (if present) are with respect to an arbitrary 2D centroid.

To Transform by Control Points

Calculation | Transform Coords... | By Control Points...
Optionally Load... a Control Points file.
For each Source Control Point, enter the # and Add.
Do the same for each Target Control Point, ensuring that corresponding points are in the same order.
Select whatType of transformation: Rigid-body or Similarity.
Estimate the Parameters.
Optionally Save... the Control Points for later reuse.
Optionally Save... the Parameters for later use in Transform by Parameters.
Choose which Source points to transform: All of them or Filter... a subset (See § Point Filters). Target points are automatically protected so will not get transformed.
Transform or OK.
Optionally Reverse transform the points. This performs the specified transformation in reverse (so effectively acts as an Undo button).

click for larger view

The Transformation Control Point Pairs File Format

This plain text (or ascii) file has

Any name, though names with .tcp or .txt extensions are advisable.
One heading line containing Source and Target (exclude quotes and separate by whitespace).
Pairs of corresponding source and target point numbers (separated by whitespace), one per line.

Example: Transformation control point pairs file.

Source  Target
2       1002
3       1003
4       1004

Notes

The target control points must be in the same coordfile.
Any point that gets added to the target point list is automatically protected (prevented from being transformed) and remains so, even if subsequently removed from the list.
If only two control point pairs are used, an exact similarity transformation is determined.
You can Remove items from the control point lists and in future you will be able to also Move them Up or Down within the lists.
Transformed points are plotted in their new positions.

updated: 26-Nov-2009