title: Particle systems for efficient and accurate high-order finite element visualization.
abstract: Visualization has become an important component of the simulation pipeline, providing scientists and engineers a visual intuition of their models. Simulations that make use of the high-order finite element method for spatial subdivision, however, present a challenge to conventional isosurface visualization techniques. High-order finite element isosurfaces are often defined by basis functions in reference space, which give rise to a world-space solution through a coordinate transformation, which does not necessarily have a closed-form inverse. Therefore, world-space isosurface rendering methods such as marching cubes and ray tracing must perform a nested root finding, which is computationally expensive. We thus propose visualizing these isosurfaces with a particle system. We present a framework that allows particles to sample an isosurface in reference space, avoiding the costly inverse mapping of positions from world space when evaluating the basis functions. The distribution of particles across the reference space isosurface is controlled by geometric information from the world-space isosurface such as the surface gradient and curvature. The resulting particle distributions can be distributed evenly or adapted to accommodate world-space surface features. This provides compact, efficient, and accurate isosurface representations of these challenging data sets.
authors.affiliation: Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84103, USA. miriah@sci.utah.edu
authors.forename: Miriah
authors.initials: M
authors.lastname: Meyer
authors.forename: Blake
authors.initials: B
authors.lastname: Nelson
authors.forename: Robert
authors.initials: R
authors.lastname: Kirby
authors.forename: Ross
authors.initials: R
authors.lastname: Whitaker
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D020342:Finite Element Analysis; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D010316:Particle Size; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D014584:User-Computer Interface