Dense Vector Field Representations Electric field on epicardium

Dense Vector Field Representations Electric field on epicardium Viscous flow past a sphere • Texture-based • Interactive (GPU) • Steady / transient flows • Planar / curved geometries Return current in the brain Xavier Tricoche

Stream Surfaces • Spanned by advected curve • Visual exploration of 3 D/4 D flows • High geometric quality of tesselation Recirculation bubbles caused by vortex breakdown Electric current induced by dipolar cardiac source in the chest Vortical structures on lee side of high-speed train Xavier Tricoche

Topology • Asymptotic connectivity of the flow • Compact graph representation • Efficient computation • Vector / tensor fields in *D Poincaré map of magnetic field in a Tokamak Topological structure of recirculating flow in a rotating cylinder Hodge bifurcation in 2 D analytic vector field Shear stress over boundary of swirl motion engine Xavier Tricoche

Alternative Structure Definitions • Address practical limitations of flow-based definition of topology • transient flows (Lagrange view) • diffusion tensors (e. g. DT-MRI) White matter structure extracted through crease surfaces of anisotropy (here FA) in Brainstem Coherent Lagrangian structures captured by finite-time Lyapunov exponent in Boussinesq and von Karman flows Xavier Tricoche