The Hermite radial basis functions (HRBF) implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e. unstructured points and their corresponding normals). Experiments suggest that HRBF implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and/or non-uniform samplings, even in the presence of close sheets. HRBF implicits theory unifies a recently introduced class of surface reconstruction methods based on radial basis functions (RBF), which incorporate normals directly in their problem formulation. Such class has the advantage of not depending on manufactured offset-points to ensure existence of a non-trivial implicit surface RBF interpolant.In fact, we show that HRBF implicits constitute a particular case of Hermite-Birkhoff interpolation with radial basis functions, whose main results we present here. This framework not only allows us to show connections between the present method and others but also enable us to enhance the flexibility of our method by ensuring well-posedness of an interesting combined interpolation/regularization approach.

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We propose a novel vortex core line extraction method based on the λ 2 vortex region criterion in order to improve the detection of vortex features for 3D flow visualization. The core line is defined as a curve that connects λ 2 minima restricted to planes that are perpendicular to the core line. The basic algorithm consists of the following stages: (1) λ 2 field construction and isosurface extraction; (2) computation of the curve skeleton of the λ 2 isosurface to build an initial prediction for the core line; (3) correction of the locations of the prediction by searching for λ 2 minima on planes perpendicular to the core line. In particular, we consider the topology of the vortex core lines, guaranteeing the same topology as the initial curve skeleton. Furthermore, we propose a geometry-guided definition of vortex bifurcation, which represents the split of one core line into two parts. Finally, we introduce a user-guided approach in order to narrow down vortical regions taking into account the graph of λ 2 along the computed vortex core line. We demonstrate the effectiveness of our method by comparing our results to previous core line detection methods with both simulated and experimental data; in particular, we show robustness of our method for noise-affected data.

Implicit surface reconstruction from unorganized point sets has been recently approached with methods based on multi-level partition of unity. We improve this approach by addressing local approximation robustness and iso-surface extraction issues. Our method relies on the J A 1 triangulation to perform both the spatial subdivision and the isosurface extraction. We also make use of orthogonal polynomials to provide adaptive local approximations in which the degree of the polynomial can be adjusted to accurately reconstruct the surface locally. Finally, we compare our results with previous work to demonstrate the robustness of our method.