A set of conceptually simple and robust algorithms for fast pattern recognition and track reconstruction using 3D space points developed for the ATLAS Level 2 (LVL2) Trigger at the LHC is presented. Results on execution time and physics performance demonstrating the effectiveness of this approach in a demanding, online trigger environment are presented. Both this strategy and a complimentary lookup table based strategy provided results appearing in the recent ATLAS High-Level Trigger, Data Acquisition and Controls Technical Design Report and were successfully implemented online during data taking for the recent ATLAS combined test beam
