文摘
Integral surfaces are ideal to illustrate time-varying vector fields since they directly appeal to our basic understanding about coherently moving particles. Efficient generation of high-quality surfaces has been elusive due to the computational effort. We present a novel approach for the computation of high-quality integration-based geometric surfaces for complex, large, and time-dependent vector fields. Compared to previous work, our approach separates surface computation into two stages: surface approximation and graphical representation generation. We first describe an algorithm for surface integration that approximates a series of timelines using iterative refinement and computes a skeleton of the stream or path surface. To compute time and streak surfaces we extend our algorithm with a two-dimensional refinement scheme. Next, we generate a well-conditioned triangulation. We leverage inherent parallelization opportunities in the surface advection to fully exploit parallel computing architectures. This approach allows a highly accurate treatment of very large time-varying vector fields in an efficient, streaming fashion and allows us to overcome several limitations of existing techniques. We discuss a number of ways to improve surface depiction through advanced rendering and texturing while preserving interactivity. We obtain the entire evolution of an integral surface in a compact representation. This allows for high-quality rendering of the visualization while interactively exploring the evolving surface. Finally, we use these surface rendering techniques to visualize flow in the human anatomy. We analyze flow-sensitive MRI datasets which record anatomic movement and time-varying flow information. We create a novel approach and base it upon finite-time Lyapunov exponents that enable identification of vessel boundaries as high regions of separation. This strategy allows segmentation of the data, giving us the ability to restrict advection of flow within the vessel boundaries. We extract the integral lines and surfaces that are most appropriate for visualization of blood flow within the vessels. Our work advances the study of flow visualization by creating an efficient, robust, and scalable way to visualize measured and simulated datasets. Our techniques harness the strengths offered by surface-based renderings and apply them to solve real-world problems.