An Approximate Parallel Vectors Operator for Multiple Vector Fields

The Parallel Vectors (PV) Operator extracts the locations of points where two vector fields are parallel. In general, these features are line structures. The PV operator has been used successfully for a variety of problems, which include finding vortex-core lines or extremum lines. We present a new generic feature extraction method for multiple 3D vector fields: The Approximate Parallel Vectors (APV) Operator extracts lines where all fields are approximately parallel. The definition of the APV operator is based on the application of PV for two vector fields that are derived from the given set of fields. The APV operator enables the direct visualization of features of vector field ensembles without processing fields individually and without causing visual clutter. We give a theoretical analysis of the APV operator and demonstrate its utility for a number of ensemble data.