Interpreting and understanding complex, organ-level mass cytometry datasets represents a formidable interdisciplinary challenge. This study aims to identify, describe, and interpret potential developmental trajectories of thymocytes and mature T cells. We developed tviblindi, a trajectory inference algorithm that integrates several autonomous modules - pseudotime inference, random walk simulations, real-time topological classification using persistence homology, and autoencoder-based 2D visualization using the vaevictis algorithm. This integration facilitates an interactive exploration of developmental trajectories. The utility and proficiency of tviblindi are demonstrated through comprehensive analysis of the thymic and peripheral T-cell compartment. Our approach not only uncovers and elucidates the canonical CD4 and CD8 development but also offers insights into various checkpoints such as TCRβ selection and positive/negative selection, elucidating the crossroads between further development and apoptosis. Finally, we identify and thoroughly characterize thymic regulatory T cells, tracing their development from the negative selection stage to mature thymic regulatory T cells with an extensive proliferation history and an immunophenotype of activated and recirculating cells. tviblindi is a versatile and generic approach suitable for any single-cell dataset, equipping biologists with an effective tool for interpreting complex data.