Time-Varying Vector Field Design on Surfaces

Vector field design has a wide variety of applications in computer graphics, including texture synthesis, non-photorealistic rendering, fluid and crowd simulation, and shape deformation. This paper addresses the problem of the design of time-varying vector fields on surfaces. The additional time dimension poses a number of unique challenges to the design tasks such as the introduction of more complex structural changes. To address these challenges, we present a number of novel techniques to enable efficient design over important characteristics in the vector field such as singularity paths, pathlines, and bifurcations. These vector field features are used to generate a vector field by either blending basis vector fields or performing a constrained optimization process. Unwanted singularities and bifurcations can lead to visual artifacts, and we address them through singularity and bifurcation editing. We demonstrate the capabilities of our system by applying it to the design of two types of vector fields: orientation field and advection field for the application of texture synthesis and animation. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism I.6.3 [Simulation and Modeling]: Applications J.6 [Computer-Aided Engineering]: ComputerAided Design (CAD)