Abstract We propose a novel vortex core line extraction method based on the λ2vortex 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 λ2minima restricted to planes that are perpendicular to the core line. The basic algorithm consists of the following stages: (1) λ2field construction and isosurface extraction; (2) computation of the curve skeleton of the λ2isosurface to build an initial prediction for the core line; (3) correction of the locations of the prediction by searching for λ2minima 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 λ2along 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.

Point-based models are gaining lately considerable attention as an alternative to traditional surface meshes. In this context, Point Set Surfaces (PSS) were proposed as a modeling and rendering method with important topological and approximation properties. However, ray-tracing PSS is computationally expensive. Therefore, we propose an interactive ray-tracing algorithm for PSS implemented completely on commodity graphics hardware. We also exploit the advantages of PSS to propose a novel technique for extracting surfaces directly from volumetric data. This technique is based on the well known predictor-corrector principle from the numerical methods for solving ordinary differential equations. Our technique provides good approximations to surfaces defined by a certain property in the volume, such as iso-surfaces or surfaces located at regions of high gradient magnitude. Also, local details of the surfaces could be manipulated by changing the local polynomial approximation and the smoothing parameters used. Furthermore, the surfaces generated are smooth and low frequency noise is naturally handled.

This paper introduces the concept of digital planar surfaces and corresponding Morse operators. These operators offer a novel and powerful method for construction and de-construction of such surfaces in a way that global topological control of the resulting object is always maintained. In that respect, this paper offers a complete pixel characterization tool. Image handling is a natural application for such approach. We present a novel fast algorithm for image segmentation using Morse operators for digital planar surfaces. It classifies as a region growing technique with added topological control and is extremely useful for applications that need proper object description. Results from real data are stimulating, and show that the segmentation algorithm compares very well with other methods. The topological approach also forms a base for future expansion to applications such as volume segmentation.