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Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields
Computer Graphics Forum (Proc. Eurographics) 31(2), May 2012
We present the first general scheme to describe all four types of characteristic curves of flow fields - stream, path, streak, and time lines - as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter-free variant of the time line metaphor.
This novel mathematical description allows for a large number of feature extraction and analysis tools for all characteristic curves, which were previously only available for stream and path lines. Possible applications include the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.
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Since May 1, 2011:
Streak Lines as Tangent Curves of a Derived Vector Field
IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization 2010) 16(6), November - December 2010
Received the Vis 2010 Best Paper Award.
Stream and path lines can be described as tangent curves of a vector field. Such a description of streak lines is not yet available, which excludes them from most of the feature extraction and analysis tools that have been developed in our community.
We develop the first description of streak lines as tangent curves of a derived vector field. Furthermore, we apply a number of feature extraction and analysis tools to the new streak line vector field including the extraction of cores of swirling streak lines and the computation of streak line curvature fields.
Topology-based Smoothing of 2D Scalar Fields with C1-Continuity
Computer Graphics Forum (Proc. EuroVis) 29(3), June 2010
Data sets often contain noise that hinders their processing and analysis. When the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features.
We propose a smoothing method for 2D scalar fields that gives explicit control over the data features, i.e., critical points and the topological structure they induce. Feature significance is rated according to topological persistence.
This is the first topological smoothing method that guarantees a C1-continuous output scalar field with the exact specified features and topological structures.
Stable Feature Flow Fields
IEEE Transactions on Visualization and Computer Graphics 17(6), June 2011
Feature Flow Fields are a well-accepted approach for extracting and tracking features.
In the original approach, the stream lines around the feature line may diverge from it; creating a numerically unstable situation.
We introduce Stable Feature Flow Fields which guarantee that the neighborhood of a feature line has always converging behavior. This way, we have an automatic correction of numerical errors: if the integration moves slightly off the feature line, it automatically moves back to it during the ongoing integration.
