Abstract In this paper, we propose a novel local feature extraction algorithm for the parallel vectors (PV) operator. Our method is based on Bézier clipping, which is a bracketing‐based root finding method that is commonly‐used in computer‐aided geometric design. Compared to Bézier bisection, our clipping method exhibits significantly faster convergence and reduces duplicate solutions. Compared to the general Newton‐Raphson algorithm, the success of our approach does not depend on the quality of an initial guess. The Bézier‐based formulation readily generalizes to polynomial higher‐order interpolants, such as for tricubic interpolation. With this, we derive the acceleration in the Sujudi‐Haimes vortex coreline criterion directly from the vector field interpolant. In addition, we describe the cross product of two polynomial vector fields in arbitrary polynomial degree, which can be used to approximate non‐polynomial interpolants. Further, we examine the effect of Newton refinement on the proposed Bézier clipping method. We evaluate our Bézier clipping method thoroughly on a range of different data sets.

Across many scientific disciplines, the pursuit of even higher grid resolutions leads to a severe scalability problem in scientific computing. Feature extraction is a commonly chosen approach to reduce the amount of information from dense fields down to geometric primitives that further enable a quantitative analysis. Examples of common features are isolines, extremal lines, or vortex corelines. Due to the rising complexity of the observed phenomena, or in the event of discretization issues with the data, a straightforward application of textbook feature definitions is unfortunately insufficient. Thus, feature extraction from spatial data often requires substantial pre- or post-processing to either clean up the results or to include additional domain knowledge about the feature in question. Such a separate pre- or post-processing of features not only leads to suboptimal and incomparable solutions, it also results in many specialized feature extraction algorithms arising in the different application domains. In this paper, we establish a mathematical language that not only encompasses commonly used feature definitions, it also provides a set of regularizers that can be applied across the bounds of individual application domains. By using the language of variational calculus, we treat features as variational minimizers, which can be combined and regularized as needed. Our formulation not only encompasses existing feature definitions as special case, it also opens the path to novel feature definitions. This work lays the foundations for many new research directions regarding formal definitions, data representations, and numerical extraction algorithms.