Eurographics Symposium on Parallel Graphics and Visualization (2015) C. Dachsbacher, P. Navrátil (Editors) Visualization of 2D Wave Propagation by Huygens’ Principle Stefan Heßel 1 , Oliver Fernandes 1 , Sebastian Boblest 1 , Philipp Offenhäuser 2 , Malte Hoffmann 1 , Andrea Beck 1 , Thomas Ertl 1 , Colin Glass 2 , Claus-Dieter Munz 1 , and Filip Sadlo 3 1 University of Stuttgart, Germany 2 High Performance Computing Center Stuttgart, Germany 3 Heidelberg University, Germany Abstract We present a novel technique to visualize wave propagation in 2D scalar fields. Direct visualization of wave fronts is susceptible to visual clutter and interpretation difficulties due to space-time interference and global influence. To avoid this, we employ Huygens’ principle to obtain virtual sources that provide a concise space- time representation of the overall dynamics by means of elementary waves. We first demonstrate the utility of our overall approach by computing a dense field of virtual sources. This variant offers full insight into space-time wave dynamics in terms of elementary waves, but it reflects the full problem of inverse wave propagation and hence suffers from high costs regarding memory consumption and computation. As an alternative, we therefore provide a less accurate and less generic but more efficient approach. This alternative performs wave front extraction with subsequent Hough transform to identify potential virtual sources. We evaluate both approaches and demonstrate their strengths and weaknesses by means of a GPU-based prototype and an implementation on a Cray XC40 supercomputer, using data from different domains. Categories and Subject Descriptors (according to ACM CCS): I.6.6 [Simulation and Modeling]: Simulation Output Analysis—; J.2 [Physical Sciences and Engineering]: Physics— 1. Introduction Scientific visualization has a long and successful history of revealing essential structures in complex data. While already 3D scalar fields demand advanced visualization techniques for proper analysis, visualization of vector and tensor fields poses even more difficult problems due to the high complex- ity of the involved phenomena and the structures they cause. Propagation of waves is an omnipresent phenomenon occur- ring in most of these data, which has been, however, widely neglected in their visualization so far. While vector fields represent a single direction at each point, and the visualization of n-dimensional tensor fields is typically based on their n-dimensional eigensystem, there are possibly infinitely many waves propagating simultane- ously through each point of a domain, each of them poten- tially having global impact. This complexity is present not only on the structural side—wave propagation phenomena are also computationally expensive to simulate and repre- sent, because very small time steps and high spatial resolu- tions are required. Together with the high computational cost of inverse wave projection discussed below, this makes vi- sualization of wave propagation exceptionally difficult and costly—and is the reason why this paper addresses wave propagation in 2D domains only. Nevertheless, extension to higher dimensions would be straightforward. Wave propagation phenomena are traditionally examined by observing displacement (amplitude) in space and time. In 2D fields, mapping amplitude to color and observing the resulting video is commonly used. A drawback with this ap- proach is, however, that already single frames of such video exhibit complexity that is beyond visual interpretation—the massive superposition of wave fronts rapidly exceeds the limits of human perception and reasoning. Following the basic visualization aim of reducing data to their essential structure, we seek for a more effective rep- resentation of wave fronts. A straightforward approach to reduce the time-dependent 2D field to a set of 1D curves, would be to obtain the wave fronts by extracting crease lines, i.e., ridge and valley lines, and observing the resulting an- imations. To avoid the difficulty of perceiving video, one could additionally employ a space-time representation, i.e., treat time as an additional ‘spatial’ dimension. In this repre- c  The Eurographics Association 2015.