Large-Scale Integration-Based Vector Field Visualization - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 311

Fig. 26.1 Left Direct visualization of integral curves in a spinning turbine. Right Visualization of
Lagrangian coherent structures in a jet flow
while linear interpolation is commonly found in visualization applications, other
interpolation schemes can be used if specific problems mandate it.
26.2.2 Integration-Based Visualization
The visualization and analysis of vector fields is an active research area, and
so-called integration-based techniques that derive vector field visualization from
integral curves have progressed well beyond the direct depiction of individual
integral curves (see Fig. 26.1 left) or a small subset of them [ 12 ]. Integral sur-
face techniques [ 7 , 9 ] compute and visualize a surface consisting of all streamlines
emanating from a common curve, while flow volumes examine the behavior of entire
volumes of particles [ 1 , 22 ]. Topological methods, on the other hand, aim at extract-
ing the structural skeleton of a vector field by considering the dynamical system
induced by it and computing critical points and stable and unstable manifolds. More
recently, the notions of Finite-Time Lyapunov Exponents and Lagrangian Coher-
ent Structures [ 11 , 18 ] were introduced to allow for an accurate structural analysis
of time-varying vector fields. These Lagrangian methods, which can require many
thousands to millions of integral curves, are built on observing the separation be-
tween closely neighboring particles as they are advected, and coherent structures are
then identified by lines and surfaces along which this separation is maximal (see
Fig. 26.1 right).
The computational overhead induced by integration-based vector field analysis
tools significantly extends beyond the approximation of few curves. In the case of
integral surfaces, hundreds to thousands of integral curves must be computed,
whereas for Lagrangian methods, the required curves can number in the millions.
The improving computational capability of modern supercomputers allows the simu-