GV:Small: Lagrangian Visualization Methods for Very Large Time-Dependent Vector Fields

拉格朗日方法在许多应用领域的模拟和测量所产生的矢量场的分析和可视化中起着核心作用。这些方法提供了对矢量场结构和动力学的关键见解，但基于昂贵的积分曲线计算。应用于大规模问题和数据集时，它们的计算成本非常高。为了改善这种情况，矢量场可视化技术中使用的积分曲线的特定问题计算被两阶段过程所取代，包括积分曲线集的自适应预计算和这些集合内的插值方法，有效地将向量场表示转移到拉格朗日域。因此，计算负担被隔离到预计算阶段。得到的拉格朗日表示被存储到有效的核外数据结构中。基于积分的可视化算法可以利用由此产生的积分曲线的快速插值，其近似特性将详细检查，从这个预先计算的数据。该通用框架允许增强现有的基于集成的可视化方法，使其具有交互性，并为研究大型向量场的新型高效交互式向量场可视化提供了基础。利用这些特性，利用拉格朗日分析开发了新的可视化工具来研究矢量场中的输运过程。为了增加这项研究的影响并将其分发给科学家和工程师的大型社区，开发的算法与开源可视化包集成在一起。这些新技术被整合到课程作业和学生项目中，使学生能够学习流计算分析的新方法。有关这些新方法的信息可以在项目网站（http://idav.ucdavis.edu/~joy/NSF-IIS-0916289）上找到。

Lagrangian methods assume a central role in the analysis and visualization of vector fields resulting from simulation and measurement across many application domains. These methods provide key insight into vector field structures and dynamics, but are based on the expensive computation of integral curves. Applied to large-scale problems and data sets, they are burdened heavily by enormous computational cost.To improve this situation, the problem-specific computation of integral curves employed in vector field visualization techniques is replaced by a two-stage process consisting of an adaptive pre-computation of integral curve sets and methods for interpolation within these sets, effectively transferring the vector field representation to the Lagrangian domain. Hence, the computational burden is isolated into a pre-computation stage. The obtained Lagrangian representation is stored into efficient out-of-core data structures. Integration-based visualization algorithms can leverage the resulting fast interpolation of integral curves, whose approximative characteristics are examined in detail, from this pre-computed data. This generic framework permits enhancement of existing integration-based visualization methods to become interactive and provides a basis for research into novel efficient and interactive vector field visualization for very large vector fields. Taking advantage of these properties, new visualization tools are developed to study transport processes in vector fields using Lagrangian analysis. To increase the impact of this research and distribute it to a large community of scientists and engineers, the developed algorithms are integrated with an open-source visualization package. These new techniques are integrated into coursework and student projects that enable students to study new methods of analysis of flow computations. Information concerning these new methods are found on the project website (http://idav.ucdavis.edu/~joy/NSF-IIS-0916289).