Modeling and editing flows using advected radial basis functions

Design of 2D time-varying vector fields

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.

Time-varying data visualization using functional representations

In many scientific simulations, the temporal variation and analysis of features are important. Visualization and visual analysis of time series data is still a significant challenge because of the large volume of data. Irregular and scattered time series data sets are even more problematic to visualize interactively. Previous work proposed functional representation using basis functions as one solution for interactively visualizing scattered data by harnessing the power of modern PC graphics boards. In this paper, we use the functional representation approach for time-varying data sets and develop an efficient encoding technique utilizing temporal similarity between time steps. Our system utilizes a graduated approach of three methods with increasing time complexity based on the lack of similarity of the evolving data sets. Using this system, we are able to enhance the encoding performance for the time-varying data sets, reduce the data storage by saving only changed or additional basis functions over time, and interactively visualize the time-varying encoding results. Moreover, we present efficient rendering of the functional representations using binary space partitioning tree textures to increase the rendering performance.

Two-way coupled SPH and particle level set fluid simulation

Grid-based methods have difficulty resolving features on or below the scale of the underlying grid. Although adaptive methods (e.g. RLE, octrees) can alleviate this to some degree, separate techniques are still required for simulating small-scale phenomena such as spray and foam, especially since these more diffuse materials typically behave quite differently than their denser counterparts. In this paper, we propose a two-way coupled simulation framework that uses the particle level set method to efficiently model dense liquid volumes and a smoothed particle hydrodynamics (SPH) method to simulate diffuse regions such as sprays. Our novel SPH method allows us to simulate both dense and diffuse water volumes, fully incorporates the particles that are automatically generated by the particle level set method in under-resolved regions, and allows for two way mixing between dense SPH volumes and grid-based liquid representations.