Lagrangian representations of flow fields with parameter curves

There are two main principles in which a flow field can be described. In its Eulerian representation, the immediate direction of the flow is used. In its Lagrangian representation, the paths of fluid parcels are stored. The latter way has proven less prone to error in cases when only a sparse subset of the original flow field can be used due to restrictions in computational capacity, which are inevitable in practice. But so far, a main drawback of the Lagrangian representation is that it leads to unsightly lines with sharp edges, because the spanning trajectories are stored as polygonal chains to minimize storage space. In this paper, we tackle this issue by proposing to represent the trajectories by means of parameter curves, like composite Bézier curves and cubic Hermite splines, instead of polygonal chains. We demonstrate that a parameter representation results in smoother lines with comparable approximation error under equal conditions of limited storage capacity.