The 3D marching lines algorithm
Graphical Models and Image Processing
A higher-order method for finding vortex core lines
Proceedings of the conference on Visualization '98
The “parallel vectors” operator: a vector field visualization primitive
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Vortex tracking in scale-space
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Vortex tubes in turbulent flows: identification, representation, reconstruction
VIS '94 Proceedings of the conference on Visualization '94
Ray-Tracing Polymorphic Multidomain Spectral/hp Elements for Isosurface Rendering
IEEE Transactions on Visualization and Computer Graphics
Methods and Framework for Visualizing Higher-Order Finite Elements
IEEE Transactions on Visualization and Computer Graphics
Ray casting implicit fractal surfaces with reduced affine arithmetic
The Visual Computer: International Journal of Computer Graphics
Journal of Scientific Computing
Using PVsolve to Analyze and Locate Positions of Parallel Vectors
IEEE Transactions on Visualization and Computer Graphics
Predictor-Corrector Schemes for Visualization ofSmoothed Particle Hydrodynamics Data
IEEE Transactions on Visualization and Computer Graphics
Particle Systems for Efficient and Accurate High-Order Finite Element Visualization
IEEE Transactions on Visualization and Computer Graphics
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The parallel vectors (PV) operator is a feature extraction approach for defining line-type features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higher-order data represented by piecewise analytical functions defined over grid cells. The extraction uses PV in two distinct stages. First, seed points on the feature lines are placed by evaluating the inclusion form of the PV criterion with reduced affine arithmetic. Second, a feature flow field is derived from the higher-order PV expression where the features can be extracted as streamlines starting at the seeds. Our approach allows for guaranteed bounds regarding accuracy with respect to existence, position, and topology of the features obtained. The method is suitable for parallel implementation and we present results obtained with our GPU-based prototype. We apply our method to higher-order data obtained from discontinuous Galerkin fluid simulations.