How to use the „Geodetic Transformations
Toolbox“?
For a start, this toolbox does nothing which is “new” – all the functionality is well known and
used in hundreds of commercial and non-commercial products all over the world. There
even are similar tools on Matlab File Exchange with different key aspects and usability, of
course. Now, why another geodetic transformation and projection toolbox then?
Basically, these functions are meant for usage in the exercises of “Geodesy and
Geoinformatics” studies at Technische Universität München. So it was the goal to combine
a set of functions which fits exactly our educational needs with full control on source code,
updates etc.
Additionally, I was not very satisfied with some code I found on the net; e.g. I did not find
any Matlab-coded transformation to UTM projection which could handle non-standard zone
width or includes polar stereographic projection.
And last reason, programming is fun and instructional: if you can code it, you have
understood it
Now have a few examples and explanations on the usage of the implemented functions.
Whenever a function is mentioned the first time, it is highlighted in yellow. For further
function details in the examples, please refer to the function help text.
A great acknowledgement goes to Andrea Pinna from the University of Cagliari. He
improved my coding in the Helmert parameter estimation functions for speed and memory
efficiency, so that it can work on millions of points now (which I never tried). Thanks a lot!
1. A first look on different transformation types
Before starting with applications, let’s have a short look on different standard transformation
types included in the toolbox and what has to be obeyed. The commonly used
transformation types in geodesy are similarity transformation, affine transformation and
projective transformation.
Many tasks in geodesy are done using similarity transformations, i.e. coordinate relations in
both systems may differ in position, orientation and scale, but segment ratio and angles are
preserved. One may use similarity transformations in 1D (using 1 translation in z and 1 scale
factor), in 2D (using 2 translations in x,y, 1 orientation rotation around z-axis and 1 scale
factor identical for both axes) and in 3D (using 3 translations, 3 rotations and 1 scale factor):
This toolbox offers the function-files d1trafo.m, d2trafo.m and d3trafo.m.
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