TrafoStar

Overdetermined 3D transformations

Also known as 3D BestFit transformation or 3D Helmert transformation.

In many areas and situations coordinates have to be transformed into different coordinate systems. This task can be performed by using simple mathematical methods. The conversion of the task is the determination of transformation parameters from coordinates of points that exist in two different coordinate systems, also called identical points. If more points exist than are necessary for the uniqueness of the calculation, this overdetermination creates an equalisation problem.

TrafoStar is an extremely flexible tool for determining transformation parameters and the residuals resulting from the equalisation.

Applications TrafoStar

• Flexible 3D transformation of two 3D datasets with identical points
• Determination of the relation of robot coordinate system to vehicle coordinate system, for example for generating a RobCad file
• Analysis of 3D coordinate measurements, accuracy, error parameters and gross error detection
• Identification of error parameters of fixed coordinate measuring machines, CMM
• Overdetermined determination of transformation parameters
• Aftertransformation of new points with these transformation parameters

Capture of TrafoStar Calculation

TrafoStar receives two datasets as data input with the information: point number, x, y and z coordinate in form of ASCII-files. Alternatively an entry directly from the clipboard is possible. The calculation of the 3D transformation can be performed with outstanding flexibility:

• 1 to 12 parameter transformation
• 3 translations, 3 rotations, 3 scales, 3 affine parameters: angle x to y axis, angle z axis to xy plane and its azimuth
• Each parameter can be set independently to either fix or float. When set to float, a fix value for the parameter can be set.
• Translation y can be set to a fixed value, for example -1100.000
• The loading of each coordinate can be set using a table function. At the same time selected areas of the table can be edited at once.
• Alternative selection of robust L1 norm, [|v|] → min gross error detection, and L2 norm, [vv] → min
• Graphic illustration of the points in the graphic window, display of error vectors, change of magnitude and analysis mode for dynamic and magnified display of deviations
• Calculation of all possible combinations of rotation angles, Euler Angle, different rotation sequences, display of rotation matrix, as well as indication of both possible solutions for rotation angle