Edge Maps: Representation of Consistent Flow, Error and Uncertainty

Publications:H. Bhatia, S. Jadhav, P.-T. Bremer, G. Chen, J.A. Levine, L.G. Nonato, V. Pascucci. “Edge Maps: Representing Flow with Bounded Error,” In Proceedings of IEEE Pacific Visualization Symposium 2011, Hong Kong, China. March, 2011 (accepted).

S. Jadhav, H. Bhatia, P.-T. Bremer, J.A. Levine, L.G. Nonato, V. Pascucci. “Consistent Approximation of Local Flow Behavior for 2D Vector Fields using Edge Maps,” TopoInVis 2011, Zurich, Switzerland. Apr 2011 (accepted).

Edge Maps: explicit representation of flow

Origin-destination pair (p, q)Pair of points on the boundary such that there exists a streamline between them which is contained entirely in the interior

Origin-destination pair (p, q)Pair of points on the boundary such that there exists a streamline between them which is contained entirely in the interior

Edge MapCollection of all o-d pairs can be represented as a map between the boundary.

Edge MapCollection of all o-d pairs can be represented as a map between the boundary.

Interval MappingMerge adjacent origin points if their destinations are adjacent

Interval MappingMerge adjacent origin points if their destinations are adjacent

p

q

: P Q , such that p = q

Edge Maps: Representation of Consistent Flow, Error and Uncertainty

Edge Maps: Equivalence Classes

23 equivalence classes for linearly varying flow – each class represents a structurally different flow

Edge Maps: Representation of Consistent Flow, Error and Uncertainty

Streamwaves: Error Propagation

p

QExpansion of entry point p as a set of possible exit points Q for a given error .

StreamwaveExpansion of a streamline into a region of possible destinations at every step of propagation.

Edge maps know where flow bifurcates. Only end points of the propagating front need to be advanced.

StreamwaveExpansion of a streamline into a region of possible destinations at every step of propagation.

Edge maps know where flow bifurcates. Only end points of the propagating front need to be advanced.

p , =Q

Edge Maps: Representation of Consistent Flow, Error and Uncertainty

Streamwaves - Results

Propagation of streamwaves for increasing amounts of error

Edge Maps: Representation of Consistent Flow, Error and Uncertainty

Visualization of fuzzy topologyStreamwaves can help visualize the stable and unstable regions under given local

error in flow with overlapping areas as regions of uncertainty

Edge Maps: Representation of Consistent Flow, Error and Uncertainty

Discussion

ContributionsThe edge maps are an explicit representation of flow which provides control for consistent streamline computation

They help store local error information and generation of streamwaves which is an effective way of visualizing error / uncertainty in flow.

LimitationsExplicit flow information has storage overhead as compared to conventional methods.

Moderate pre-computation is required.

Future WorkExtend representation to higher dimensional simplices and other types of meshes; and to other interpolation schemes.

Edge Maps: Representation of Consistent Flow, Error and Uncertainty