Introduction to applied Matrix Transformations for Computer Graphics and Image Processing

The use of transformation matrices is common practice in both computer graphics and image processing, with applications also in similar fields like computer vision. The mathematics behind transformation matrices is simple and relies on basic linear algebra properties. Nevertheless, applying transformation matrices to real-life problems can sometimes be tricky, as there are numerous pitfalls one can step into. In this technical report I will try to present a thorough overview on rigid transformations and try to incorporate my own experience from working with transformations. I hope that this will give you the necessary insight to thoroughly understand transformations, avoid the common pitfalls and be able to apply them on real problems. Note that the current version of this report does not include applications in computer graphics and image processing, however, I think the issues addressed are very useful in both application domains. I would greatly appreciate your feedback (like/disliked report and why) in order to improve and extent it in the future.