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Streak Lines as Tangent Curves of a Derived Vector Field Corresponding Publication
Logo Characteristic curves of vector fields include stream, path, and streak lines. Stream and path lines can be obtained by a simple vector field integration of an autonomous ODE system, i.e., they can be described as tangent curves of a vector field. This facilitates their mathematical analysis including the extraction of core lines around which stream or path lines exhibit swirling motion, or the computation of their curvature for every point in the domain without actually integrating them. 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. In this paper, we develop the first description of streak lines as tangent curves of a derived vector field - the streak line vector field - and show how it can be computed from the spatial and temporal gradients of the flow map, i.e., a dense path line integration is required. We demonstrate the high accuracy of our approach by comparing it to solutions where the ground truth is analytically known and to solutions where the ground truth has been obtained using the classic streak line computation. 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. These first applications foreshadow the large variety of possible future research directions based on our new mathematical description of streak lines. T. Weinkauf, H. Theisel
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
[slideshow]
5000 forward integrated streak lines in the flow around a cylinder. They have been computed using the streak line vector field. Cover image of Vis10 Proceedings.
5000 forward integrated streak lines in the flow around a cylinder. They have been computed using the streak line vector field. Cover image of Vis10 Proceedings.
5000 backward integrated streak lines. The streak line vector field allows to compute a large number of streak lines orders of magnitude faster than the classic approach. Cover image of Vis10 Proceedings.
5000 backward integrated streak lines. The streak line vector field allows to compute a large number of streak lines orders of magnitude faster than the classic approach. Cover image of Vis10 Proceedings.
Volume rendering of the streak line curvature in the flow around a cylinder. Cover image of Vis10 Proceedings.
Volume rendering of the streak line curvature in the flow around a cylinder. Cover image of Vis10 Proceedings.
BeadsProblemAttractorPathLines
BeadsProblemAttractorPathLines
BeadsProblemAttractorStreakCoreSurf
BeadsProblemAttractorStreakCoreSurf
BeadsProblemAttractorStreamPathCore
BeadsProblemAttractorStreamPathCore
BeadsTop.0000
BeadsTop.0000
BeadsTop.0023
BeadsTop.0023
BeadsTop.0037
BeadsTop.0037
BeadsTop.0046
BeadsTop.0046
BeadsTop.0072
BeadsTop.0072
BeadsTop.0142
BeadsTop.0142
ClassicViewOnStreakLinesAnno
ClassicViewOnStreakLinesAnno
ComputingWAnno
ComputingWAnno
CylinderFTLE
CylinderFTLE
CylinderStreakCurvatureVolRenDetail
CylinderStreakCurvatureVolRenDetail
CylinderStreakISLStreamLIC
CylinderStreakISLStreamLIC
CylinderStreakLIC_tau00
CylinderStreakLIC_tau00
CylinderStreakLIC_tau07
CylinderStreakLIC_tau07
CylinderStreakLIC_tau25
CylinderStreakLIC_tau25
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CylinderStreakMagnitudeVolRen
CylinderStreakMagnitudeVolRenDetail
CylinderStreakMagnitudeVolRenDetail
CylinderStreamLIC
CylinderStreamLIC
CylinderStreamLICMinusAmbient
CylinderStreamLICMinusAmbient
DefiningWAnno
DefiningWAnno
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EvaluationCylinderStreakLines
EvaluationCylinderStreakLines
MovingSinkFocusStreakCore
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ObviousComputingWAnno
SquareCylinderStreakSurfaces
SquareCylinderStreakSurfaces
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StreakLineParametrizationAnno
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