<p>Large-scale 3D ocean simulations using supercomputers have enabled rapid and accurate visualization of the 3D distribution of ocean vortices. These simulations often rely on unstructured grid data (non-cubic grid data), whereas traditional vorticity definitions based on vector rotation require extensive computational resources. Moreover, conventional vorticity definitions fail to adequately account for the depth component of ocean velocity. This limitation arises because the vertical component of ocean current vectors is typically orders of magnitude smaller than the horizontal components, resulting in significant scale differences. To address these challenges, we transformed the unstructured grid data into point cloud data and introduced three novel vorticity definitions, collectively termed “eigenvorticity.” Eigenvorticity is derived from the eigenvalues of the local variance–covariance matrix of the velocity vector, enabling the inclusion of both horizontal and vertical flow effects. Using eigenvorticity, we perform the point-based transparent visualization of vortices to obtain a comprehensive understanding of their characteristics and behaviors in the 3D ocean environment.</p> Graphical abstract <p></p>