Almagest, a new trackless ring finding algorithm

A fast ring finding algorithm is a crucial point to allow the use of RICH in on-line trigger selection. The present algorithms are either too slow (with respect to the incoming data rate) or need the information coming from a tracking system. Digital image techniques, assuming limited computing power (as for example Hough transform), are not perfectly robust for what concerns the noise immunity. We present a novel technique based on Ptolemy's theorem for multi-ring pattern recognition. Starting from purely geometrical considerations, this algorithm (also known as "Almagest") allows fast and trackless rings reconstruction, with spatial resolution comparable with other offline techniques. Almagest is particularly suitable for parallel implementation on multi-cores machines. Preliminary tests on GPUs (multi-cores video card processors) show that, thanks to an execution time smaller than 10 μs per event, this algorithm could be employed for on-line selection in trigger systems. The user case of the NA62 RICH trigger, based on GPU, will be discussed.