Translation
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Translation is the easiest kind of transformation. Translating a point means that it is shifted by a translation vector. So the translation vector is added to the position vector of . The position vector of the resulting transformed point is calculated as follows:
The figure on the right shows an example in two-dimensional space. In robotics usually three dimensions are regarded. Considering the particular components of the vectors, a translation looks as follows:
For further information about vector addition and examples, please have a look at the article about simple arithmetic vector operations.
Multimedial educational material
http://olli.informatik.uni-oldenburg.de/Grafiti3/grafiti/flow5/page5.html Applet: two-dimensional translation (in german) |