Coordinate conversion for the Hough transform

Sammanfattning: This thesis attempts to develop a conversion algorithm between local coordinates in constituent detector modules and global coordinates encompassing the whole detector structure in a generic detector. The thesis is a part of preparatory work for studying the Hough Transform as a means of track reconstruction in the level-1 hardware trigger in the upgraded trigger and data acquisition (TDAQ) system in the phase 2 upgrade of the ATLAS detector at CERN. The upgrades being made are to withstand much more extreme conditions that come with the high-Luminosity Large Hadron Collider (HL-LHC). Two algorithms have been made and then implemented in Python scripts to test their feasibility and to compare them against each-other. The Rotation algorithm uses several rotations to correctly place the local coordinates in the global system. The second, the Shear algorithm, simplifies the process into two shears and one rotation, using the small angle approximation. Both algorithms need to be extended to work with more parts of the detector to be considered complete. Despite having lower maximum precision the second algorithm is considered the most promising attempt, since it is much less sensitive to the truncation error that results from working in an integer environment, which is a requirement for use in FPGAs.