The paper introduces a new air flow analysis approach based on particle tracking velocimetry (PTV). One of the special features of the proposed method is that after the tracer particles are detected, matching and tracking are jointly conducted. To this end, we introduce an interpretation module based on a directed hypergraph for 3D curve reconstruction. At first, the 2D inter-frame locations are localised and used for the extraction and calculation of 3D keypoints. Through 3D keypoints, which are evaluated by the hypergraph together with the time information in several steps, reverse curve matching for path selection can be reconstructed and the resulting trajectories visualised. In contrast to the preceding works, our approach tries to describe the measuring data by 3D trajectories directly instead of estimating 2D trajectories first and then matching afterwards. A higher precision can be achieved also with complicated trajectories. A certain independence of the reflections and lighting conditions is reached by the interpretation. Moreover, the path of particles can also be reconstructed with the minimum number of 3D keypoints under consideration of the path energy minimisation.