Design of 2D Time-Varying Vector Fields


Chen, Guoning
Kwatra, Vivek
Wei, Li-Yi
Hansen, Charles D.
Zhang, Eugene

KAUST Grant Number


Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects. © 1995-2012 IEEE.

Chen G, Kwatra V, Wei L-Y, Hansen CD, Zhang E (2012) Design of 2D Time-Varying Vector Fields. IEEE Transactions on Visualization and Computer Graphics 18: 1717–1730. Available:

We would like to thank Dr. Konstantin Mischaikow for the valuable discussion on the topology and dynamics of vector fields, which initiated this work. We also thank Dr. Mark van Langeveld for the valuable discussion on potential applications. We appreciate the help by Timothy O'Keefe on proofreading the paper. This work was supported by NSF IIS-0546881, IIS-0917308, OCI-0906379, and CCF-0830808 award. Guoning Chen was partially supported by King Abdullah University of Science and Technology (KAUST) Award No. KUS-C1-016-04 and DOE VACET.

Institute of Electrical and Electronics Engineers (IEEE)

IEEE Transactions on Visualization and Computer Graphics


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