Analysis of sparse vector data using tessellation based on root volume–optimal cycles

This study proposes a novel approach to investigate sparse vector datasets. The key feature of our method is the tessellation of space using volume–optimal cycles, a useful tool in persistent homology. Using this tessellation, we divide the space into polygons with short edges, which enables the evaluation of the vorticity or circulation of the vector field. The proposed method is applied to both artificial and real datasets, and the results show that our approach effectively visualizes and quantifies the rotational component of a vector field.