Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields

• M , the equivalent of a single time step, if we explore the curves for a given (t, τ). Examples of this are shown using LIC images throughout the paper, for example Figures 7d and 7e. Furthermore, this case applies to advected stream surfaces for a given (t, τ) such as the one shown in Figure 9. It shall be noted that the pre-computed ̄̄ q can be used to compute all advected stream surfaces for the given (t, τ). In other words, the user can interactively change the seeding line (the gray line in Figure 9) and a new surface is computed almost instantly, since these surfaces are stream surfaces of ̄̄ q. Such an instant response is not possible with a classic approach to computing such surfaces. To compute time surfaces for a given (t, τ), on the other hand, we require two time line vector fields. This is explained in Section 4 and examples of time surfaces are shown in Figure 8. Nevertheless, an interactive exploration is just as possible as for advected stream surfaces, since the only added overhead is the computation of a time line before the actual computation of the time surface. Again, such an instant response is not possible with the classic, geometric approach for computing time surfaces.