Werner Benger 1 and Georg Ritter 3 and Simon Su 4 and Dimitris E. Nikitopoulos 2 and Eamonn Walker 2 and Sumanta Acharya 2 and Somnath Roy 2 and Farid Harhad 1 and Wolfgang Kapferer 3 1 Center for Computation and Technology, Louisiana State University, USA 2 Department for Mechanical Engineering, Louisiana State University, USA 3 Institute for Astro- and Particle Physics, University of Innsbruck 4 Princeton Institute for Computational Science and Engineering

 The Problem  The Approach  Application Examples

Visualizing Vectors in 3D & 4D

 Splatting Technique: Drawing of Gaussian spots as billboard per vertex  Used for Volume Rendering of Unstructured Meshes  Gaussian splats in view plane – Efficiently done via OpenGL Point Sprites

 Elongate along direction of vector in a field 1.Stretch 2.Orient 3.Offset

 Stretch according to Vector Magnitude  Freedom in various scaling factors and mappings (like vector arrows)

 Compute Projection of Vector in View Plane  View-dependent shape – requires GL fragment shader View Plane

Free parameter to allow animation of display element T=0.0 T=0.2 T=0.5

 Physical Effect: movement of wave-emitting objects influences observed frequency  Known as sound of passing street cars:  Movement to observer increases frequency  Movement from observer decreases frequency  Light: Color change of moving objects  Approaching - higher frequency – blueshift  Escaping - lower frequency - redshift

1. Couette Flow (Analytic Vector field) 2. Microchannel Droplet (Uniform Grid) 3. Stirtank Fluid (Curvilinear Multiblock) 4. Galaxy Evolution (Particle System)

VECTOR ARROWSDOPPLER SPECKLES

STREAMLINESDOPPLER SPECKLES

DOWN VIEWUP VIEW

FRONT VIEWBACK VIEW

STREAMLINES SPECKLES ON STREAMLINES

STREAMLINES SPECKLES ON STREAMLINES

 2088 Curvilinear Blocks

SIDE VIEWUP VIEW

 16 Million particles, each representing one galaxy  Cosmological evolution over several billion years  300GB of raw data  Velocity given for each galaxy

 Algorithms implemented and available in  Vish – Visualization Shell  Freely available for academic usage  Code development management:   Available via SVN in source code for registered users at