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arXiv · 2107.02708

Exact Analytical Parallel Vectors

Hanqi Guo·Tom Peterka
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Abstract

This paper demonstrates that parallel vector curves are piecewise cubic rational curves in 3D piecewise linear vector fields. Parallel vector curves -- loci of points where two vector fields are parallel -- have been widely used to extract features including ridges, valleys, and vortex core lines in scientific data. We define the term \emph{generalized and underdetermined eigensystem} in the form of $\mathbf{A}\mathbf{x}+\mathbf{a}=\lambda(\mathbf{B}\mathbf{x}+\mathbf{b})$ in order to derive the piecewise rational representation of 3D parallel vector curves. We discuss how singularities of the rationals lead to different types of intersections with tetrahedral cells.

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Hanqi Guo, Tom Peterka. 2021-07-06. Exact Analytical Parallel Vectors. https://doi.org/10.1109/vis49827.2021.9623310

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