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Extracting Higher Order Critical Points and Topological Simplification of 3D Vector Fields Corresponding Publication
Logo This paper presents an approach to extracting and classifying higher order critical points of 3D vector fields. To do so, we place a closed convex surface s around the area of interest. Then we show that the complete 3D classification of a critical point into areas of similar flow behavior is equivalent to extracting the topological skeleton of an appropriate 2D vector field on s, if each critical point is equipped with an additional Bit of information. Out of this skeleton, we create an icon which replaces the complete topological structure inside s for the visualization. We apply our method to find a simplified visual representation of clusters of critical points, leading to expressive visualizations of topologically complex 3D vector fields. T. Weinkauf, H. Theisel, K. Shi, H.-C. Hege, H.-P. Seidel
Extracting Higher Order Critical Points and Topological Simplification of 3D Vector Fields
Proc. IEEE Visualization 2005, Minneapolis, U.S.A., October 23 - 28, 2005
[slideshow]
Topologically simplified representation of the electrostatic field around the benzene molecule with one higher order critical point elucidating the far field behavior of the benzene. The field consists of 184 first order critical points. Cover image of Vis05 Proceedings.
Topologically simplified representation of the electrostatic field around the benzene molecule with one higher order critical point elucidating the far field behavior of the benzene. The field consists of 184 first order critical points. Cover image of Vis05 Proceedings.
3DConstruction
3DConstruction
3DSectors
3DSectors
AuxVFieldwSmall
AuxVFieldwSmall
BenzeneHighLevelExplain
BenzeneHighLevelExplain
BenzeneHighLevelExtractedSkeleton
BenzeneHighLevelExtractedSkeleton
BenzeneHighLevelMinimizedSkeleton
BenzeneHighLevelMinimizedSkeleton
BenzeneLowFrontOtherLight
BenzeneLowFrontOtherLight
BenzeneLowNoBoxesSideTransBlue
BenzeneLowNoBoxesSideTransBlue
BenzeneMediumIcon
BenzeneMediumIcon
BenzeneOriginalTopoCompare
BenzeneOriginalTopoCompare
BenzeneOriginalTopoCP
BenzeneOriginalTopoCP
BenzeneOriginalTopoISL
BenzeneOriginalTopoISL
Cases3erAreasSinkInside
Cases3erAreasSinkInside
Cases3erAreasSourceInside
Cases3erAreasSourceInside
Cases4erAreas
Cases4erAreas
CentralProjection1
CentralProjection1
CentralProjection2
CentralProjection2
Extract3DSectorsExplainFClassAreas
Extract3DSectorsExplainFClassAreas
Extract3DSectorsExplainIcon
Extract3DSectorsExplainIcon
Extract3DSectorsExplainSkeleton
Extract3DSectorsExplainSkeleton
Extract3DSectorsExplainSkeletonFClass
Extract3DSectorsExplainSkeletonFClass
Extract3DSectorsExplainSkeletonFClassLIC
Extract3DSectorsExplainSkeletonFClassLIC
Extract3DSectorsExplainSkeletonMinimal
Extract3DSectorsExplainSkeletonMinimal
FClassificationElliptic
FClassificationElliptic
FClassificationHyperbolic
FClassificationHyperbolic
FClassificationInflow
FClassificationInflow
FClassificationOutflow
FClassificationOutflow
FirstOrderSaddle
FirstOrderSaddle
MinimalSkeletonAfter
MinimalSkeletonAfter
MinimalSkeletonBefore
MinimalSkeletonBefore
OriginalVFWithBox
OriginalVFWithBox
Projection
Projection
Restriction
Restriction
Substructures
Substructures
WInflowOutflowAndStreamline
WInflowOutflowAndStreamline
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