Simple quad domains for field aligned mesh parametrization
Proceedings of the 2011 SIGGRAPH Asia Conference
A Quantized Boundary Representation of 2D Flows
Computer Graphics Forum
Nearly Recurrent Components in 3D Piecewise Constant Vector Fields
Computer Graphics Forum
Lagrangian coherent structures with guaranteed material separation
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Stable morse decompositions for piecewise constant vector fields on surfaces
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
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Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories which are sensitive to noise and errors introduced by simulation and interpolation. This makes such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG's, while fast, are overly conservative and usually results in MCG's that are too coarse to be useful. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCG's than existing techniques. Furthermore, the choice of tau provides a natural tradeoff between the fineness of the MCG's and the computational costs. We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps.