Enhanced vector field visualization via Lagrangian accumulation

In this paper, we revisit the Lagrangian accumulation process that aggregates the local attribute information along integral curves for vector field visualization. Similar to the previous work, we adopt the notation of the Lagrangian accumulation field or A field for the representation of the accumulation results. In contrast to the previous work, we provide a more in-depth discussion on the properties of A fields and the meaning of the patterns exhibiting in A fields. In particular, we revisit the discontinuity in the A fields and provide a thorough explanation of its relation to the flow structure and the additional information about the flow that it may reveal. In addition, other remaining questions about the A field, such as its sensitivity to the selection of integration time, are also addressed. Based on these new insights, we demonstrate a number of enhanced flow visualizations aided by the accumulation framework and the A fields, including a new A field guided ribbon placement, an A field guided stream surface seeding and the visualization of particle-based flow data. To further demonstrate the generality of the accumulation framework, we extend it to the non-integral geometric curves (i.e., streak lines), which enables us to reveal information about the flow behavior other than those revealed by the integral curves. Finally, we introduce the Eulerian accumulation, which can reveal different flow behaviors from those revealed by Lagrangian accumulation. In summary, we believe that Lagrangian accumulation and the resulting A fields offer valuable techniques to investigate flow behavior complementary to the current state-ofthe-art techniques. c © 2017 Elsevier B. V. All rights reserved.