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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2012003943
pages 225-240


Marcel Hlawatsch
VISUS, University of Stuttgart, Stuttgart, Germany
Filip Sadlo
VISUS, University of Stuttgart, Stuttgart, Germany
Daniel Weiskopf
VISUS, University of Stuttgart, Stuttgart, Germany


Flow fields are often investigated by adopting a Lagrangian view, for example, by particle tracing of integral curves such as streamlines and path lines or by computing delocalized quantities. For visual exploration, mouse interaction is predominantly used to define starting points for time-dependent Lagrangian methods. This paper focuses on the uncertainty of mouse input and its impact on the visualization process. In typical cases, the interaction is achieved by mouse motion, exhibiting uncertainty in the range of a screen pixel. From the perspective of dynamical systems theory, an integral curve represents an initial value problem, the uncertainty a perturbation of its initial condition, and the uncertainty of the visualization procedure a predictability problem. Predictability analysis is concerned with the growth of perturbations under the action of flow. In our case, it is not unusual that the perturbations grow from single pixels to substantial deviations. We therefore present an interaction scheme based on the largest finite-time Lyapunov exponent and the flow map gradient, providing accurate, smooth, and easy-to-use flow exploration. This scheme employs data-driven adaptation of mouse speed and direction as well as optional augmentation by an adaptive zoom lens with consistent magnification. We compare our approach to nonadaptive mouse interaction and demonstrate it for several examples of data sets. Furthermore, we present results from a user study with nine domain experts.