Fast Clifford Fourier Transformation for Unstructured Vector Field Data

Vector fields play an important role in many areas of computational physics and engineering. For effective visualization of vector fields it is necessary to identify and extract important features inherent in the data, defined by filters that characterize certain “patterns”. Our prior approach for vector field analysis used the Clifford Fourier transform for efficient pattern recognition for vector field data defined on regular grids [1,2]. Using the frequency domain, correlation and convolution of vectors can be computed as a Clifford multiplication, enabling us to determine similarity between a vector field and a pre-defined pattern mask (e.g., for critical points). Moreover, compression and spectral analysis of vector fields is possible using this method. Our current approach only applies to rectilinear grids. We combine this approach with a fast Fourier transform to handle unstructured scalar data [6]. Our extension enables us to provide a feature-based visualization of vector field data defined on unstructured grids, or completely scattered data. Besides providing the theory of Clifford Fourier transform for unstructured vector data, we explain how efficient pattern matching and visualization of various selectable features can be performed efficiently. We have tested our method for various vector data sets.