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## Particle systems for efficient and accurate high-order finite element visualization (2007)

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Venue: | IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS (UNDER REVIEW |

Citations: | 17 - 4 self |

### Citations

2696 | Marching Cubes: A high resolution 3D surface construction algorithm.
- Lorensen, Harvey
- 1987
(Show Context)
Citation Context ...h of the work in finite-element simulations has focused on linear elements. In the simplest case where the finite elements form a regular grid in world space, conventional methods like marching cubes =-=[19]-=- and direct volume rendering [20] are applicable. In general, however, the finite elements produce an irregular grid in world space that is incompatible with the assumptions these methods make about t... |

360 |
The Finite Element Method.
- Hughes
- 2000
(Show Context)
Citation Context ... accurate isosurface representations of these challenging data sets. Index Terms—Particle systems, high-order finite elements, isosurface visualization. Ç 1 INTRODUCTION THE method of finite elements =-=[14]-=- is a common spatialsubdivision scheme used by scientists and engineers to reduce large simulation domains to sets of small subdomains over which physical simulations can be computed robustly and effi... |

358 |
Finite Element Analysis
- Szabó, Babuˇska
- 1991
(Show Context)
Citation Context ...the element transformations. Today, high-order finite element techniques have reached a level of sophistication such that they are commonly applied to a broad range of engineering problems [9], [17], =-=[32]-=-. Although there exist some high-order finite element methods that do not rely on reference space transformations, the use of curvilinear coordinate transformations is of increasing interest [15]. Thi... |

291 | Optical models for direct volume rendering.
- Max
- 1995
(Show Context)
Citation Context ...imulations has focused on linear elements. In the simplest case where the finite elements form a regular grid in world space, conventional methods like marching cubes [19] and direct volume rendering =-=[20]-=- are applicable. In general, however, the finite elements produce an irregular grid in world space that is incompatible with the assumptions these methods make about the regularity of the grid. Early ... |

259 |
Spectral/hp Element Methods for CFD
- Karniadakis, Sherwin
- 1999
(Show Context)
Citation Context ...ll as the element transformations. Today, high-order finite element techniques have reached a level of sophistication such that they are commonly applied to a broad range of engineering problems [9], =-=[17]-=-, [32]. Although there exist some high-order finite element methods that do not rely on reference space transformations, the use of curvilinear coordinate transformations is of increasing interest [15... |

250 | A Polygonal Approximation to Direct Scalar Volume Rendering. Computer Graphics,
- Shirley, Tuchman
- 1990
(Show Context)
Citation Context ... however, the finite elements produce an irregular grid in world space that is incompatible with the assumptions these methods make about the regularity of the grid. Early work by Shirley and Tuchman =-=[30]-=- and Williams [39] propose a volume rendering approach for tetrahedral elements, and Bunyk et al. [3] propose a generalized raycasting algorithm for irregular grids. Doi and Koide [10] present the Mar... |

220 |
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- HUGHES, COTTRELL, et al.
- 2005
(Show Context)
Citation Context ...17], [32]. Although there exist some high-order finite element methods that do not rely on reference space transformations, the use of curvilinear coordinate transformations is of increasing interest =-=[15]-=-. This paper is addressing the problem of finite element methods that rely on higher order (higher than linear) basis functions for the solutions, as well as the coordinate transformations. Convention... |

216 | Surface modeling with oriented particle systems. Computer Graphics,
- Szeliski, Tonnesen
- 1992
(Show Context)
Citation Context ...lement data. The literature on using particle systems to represent and manipulate surfaces spans more than a decade—here, we give only a brief summary. The oriented particle system of Szeliski et al. =-=[34]-=-, [33] builds deformable surfaces with particle dynamics modeled from the molecular dynamics literature. De Figueiredo et al. [8] propose a polygonalization method that models particle interactions wi... |

208 |
Space Subdivision for Fast Ray Tracing
- Glassner
- 1984
(Show Context)
Citation Context ... element and, in practice, another layer of computation is required to determine which reference element contains the point u T1ðxÞ. Although efficient element lookups based on regular grids [27], =-=[11]-=- or low-order curves [38] can be applied to elements with planar or quadratic curved faces respectively, there is no closed form solution for the general problem. Spatial partitioning schemes can be u... |

157 | Curvature-based transfer functions for direct volume rendering: Methods and applications. In:
- Kindlmann, Whitaker, et al.
- 2003
(Show Context)
Citation Context ...spectively, and Dij is the average of the curvature magnitudes at xi and xj. The principle curvatures are computed analytically from the gradient and Hessian of the implicit function, as described in =-=[18]-=-. The parameter 0:5= cosð6Þ is derived from an ideal hexagonal packing of particles where the region of influence of the energy kernel at the center particle ends at the two ring of neighbors. Fo... |

102 | Hardware-accelerated volume and isosurface rendering based on cell-projection.
- Rottger, Kraus, et al.
- 2000
(Show Context)
Citation Context ...ide [10] present the Marching Tetrahedra method for triangulating isosurfaces defined over tetrahedral elements. More recently, work has moved the volume rendering [36], [4] and isosurface generation =-=[25]-=-, [23] algorithms onto the GPU to obtain faster rendering speeds. Applying these low-order linear methods to high-order finite elements, however, presents several challenges. First, high-order basis f... |

85 |
Tensor Analysis on Manifolds.
- Bishop, Goldberg
- 1980
(Show Context)
Citation Context ...e tensor, which is the result of computing the second derivative of the vector-valued coordinate transformation. To clarify these derivations, we use the Einstein notation convention, as described in =-=[1]-=-. Developed for dealing with curved spaces in physics, Einstein notation identifies relationships often hidden by conventional linear algebra notation such as transposition and order of operations. To... |

79 |
Modeling surfaces of arbitrary topology with dynamic particles.
- Szeliski, Tonnesen, et al.
- 1993
(Show Context)
Citation Context ... data. The literature on using particle systems to represent and manipulate surfaces spans more than a decade—here, we give only a brief summary. The oriented particle system of Szeliski et al. [34], =-=[33]-=- builds deformable surfaces with particle dynamics modeled from the molecular dynamics literature. De Figueiredo et al. [8] propose a polygonalization method that models particle interactions with a m... |

79 | Hardware-based ray casting for tetrahedral meshes
- Weiler
(Show Context)
Citation Context ...ithm for irregular grids. Doi and Koide [10] present the Marching Tetrahedra method for triangulating isosurfaces defined over tetrahedral elements. More recently, work has moved the volume rendering =-=[36]-=-, [4] and isosurface generation [25], [23] algorithms onto the GPU to obtain faster rendering speeds. Applying these low-order linear methods to high-order finite elements, however, presents several c... |

51 | Isosurface computation made simple: Hardware acceleration, adaptive refinement and tetrahedral stripping
- Pascucci
(Show Context)
Citation Context ...0] present the Marching Tetrahedra method for triangulating isosurfaces defined over tetrahedral elements. More recently, work has moved the volume rendering [36], [4] and isosurface generation [25], =-=[23]-=- algorithms onto the GPU to obtain faster rendering speeds. Applying these low-order linear methods to high-order finite elements, however, presents several challenges. First, high-order basis functio... |

48 | Isosurface extraction using particle systems
- CROSSNO, ANGEL
- 1997
(Show Context)
Citation Context ...mplicit surfaces for modeling and visualization. Several works [13], [12], [31] describe modifications and applications of this method. Research on geometric adaptivity in such particle systems [26], =-=[7]-=-, [16] has shown that the underlying formulation has limitations in this regard. Recent work by Meyer et al. [21] describes a new class of potential functions that provide more control over particle d... |

40 | Robust particle systems for curvature dependent sampling of implicit surfaces.
- Meyer, Georgel, et al.
- 2005
(Show Context)
Citation Context ...ined to an isosurface and exert repulsive forces on each other, resulting in even distributions across the surface. Previously, we showed how these types of system can be made robust and controllable =-=[21]-=-. Efficient visualization of high-order finite element data, however, requires some novel extensions of the particle system framework. First, to reduce the number of repulsive force computations betwe... |

35 |
Curvature-dependent triangulation of implicit surfaces
- KARKANIS, STEWART
(Show Context)
Citation Context ...it surfaces for modeling and visualization. Several works [13], [12], [31] describe modifications and applications of this method. Research on geometric adaptivity in such particle systems [26], [7], =-=[16]-=- has shown that the underlying formulation has limitations in this regard. Recent work by Meyer et al. [21] describes a new class of potential functions that provide more control over particle density... |

35 | Perspective accurate splatting.
- Zwicker, Rasanen, et al.
- 2004
(Show Context)
Citation Context ...sparse sampling of particles, which create artifacts when the particles are splat. One solution would be to implement a more sophisticated splatting algorithm that clips splats along these boundaries =-=[43]-=-. ACKNOWLEDGMENTS The authors wish to thank Joe Kniss for the helpful discussions on GPU rendering techniques and Nathan Galli for the creation of the diagrams in this paper. The authors also thank th... |

33 |
An Efficient Method of Triangulating Equivalued Surfaces by Using Tetrahedral Cells
- Doi, Koide
- 1991
(Show Context)
Citation Context ...ley and Tuchman [30] and Williams [39] propose a volume rendering approach for tetrahedral elements, and Bunyk et al. [3] propose a generalized raycasting algorithm for irregular grids. Doi and Koide =-=[10]-=- present the Marching Tetrahedra method for triangulating isosurfaces defined over tetrahedral elements. More recently, work has moved the volume rendering [36], [4] and isosurface generation [25], [2... |

31 |
Visibility-ordering meshed polyhedra
- WILLIAMS
- 1992
(Show Context)
Citation Context ...te elements produce an irregular grid in world space that is incompatible with the assumptions these methods make about the regularity of the grid. Early work by Shirley and Tuchman [30] and Williams =-=[39]-=- propose a volume rendering approach for tetrahedral elements, and Bunyk et al. [3] propose a generalized raycasting algorithm for irregular grids. Doi and Koide [10] present the Marching Tetrahedra m... |

28 |
High Order Methods for Incompressible Fluid Flow,”
- Deville, Fischer, et al.
- 2002
(Show Context)
Citation Context ...as well as the element transformations. Today, high-order finite element techniques have reached a level of sophistication such that they are commonly applied to a broad range of engineering problems =-=[9]-=-, [17], [32]. Although there exist some high-order finite element methods that do not rely on reference space transformations, the use of curvilinear coordinate transformations is of increasing intere... |

25 | Ray-tracing polymorphic multidomain spectral/hp elements for isosurface rendering.
- NELSON, KIRBY
- 2006
(Show Context)
Citation Context ...nar or quadratic curved faces respectively, there is no closed form solution for the general problem. Spatial partitioning schemes can be utilized to reduce the grid ambiguity to among a few elements =-=[22]-=-, but the inverse mapping u T1ðxÞwill (generally) require multiple iterations across multiple elements. The problem is becoming increasingly more difficult as results from the scientific computing ... |

21 |
Mesh generation in curvilinear domains using high-order elements
- Sherwin, Peiro
(Show Context)
Citation Context .... This formulation has a general applicability and could, for instance, be used to add curvature dependencies in other applications that make use of reference space regularity such as mesh generation =-=[29]-=-. 3.3 Reference Space Particles To avoid the computations associated with T1, we have developed a strategy that maintains particle positions in reference space while controlling the particle distribu... |

21 |
Using Particles to Sample and
- Witkin, Heckbert
- 1994
(Show Context)
Citation Context ...the molecular dynamics literature. De Figueiredo et al. [8] propose a polygonalization method that models particle interactions with a mass-spring system. Building on these ideas, Witkin and Heckbert =-=[40]-=- present a novel physicallybased system that uses repulsive particles to evenly sample implicit surfaces for modeling and visualization. Several works [13], [12], [31] describe modifications and appli... |

19 |
C.: A programmable particle system framework for shape modeling
- SU, HART
- 2005
(Show Context)
Citation Context ...these ideas, Witkin and Heckbert [40] present a novel physicallybased system that uses repulsive particles to evenly sample implicit surfaces for modeling and visualization. Several works [13], [12], =-=[31]-=- describe modifications and applications of this method. Research on geometric adaptivity in such particle systems [26], [7], [16] has shown that the underlying formulation has limitations in this reg... |

18 |
HardwareAssisted Visibility Ordering for Unstructured Volume Rendering
- Callahan, Ikits, et al.
- 2005
(Show Context)
Citation Context ...or irregular grids. Doi and Koide [10] present the Marching Tetrahedra method for triangulating isosurfaces defined over tetrahedral elements. More recently, work has moved the volume rendering [36], =-=[4]-=- and isosurface generation [25], [23] algorithms onto the GPU to obtain faster rendering speeds. Applying these low-order linear methods to high-order finite elements, however, presents several challe... |

17 | Interactive Visualization of Implicit Surfaces with Singularities," Implicit Surfaces '96
- R6sch, Ruhl, et al.
(Show Context)
Citation Context ...mple implicit surfaces for modeling and visualization. Several works [13], [12], [31] describe modifications and applications of this method. Research on geometric adaptivity in such particle systems =-=[26]-=-, [7], [16] has shown that the underlying formulation has limitations in this regard. Recent work by Meyer et al. [21] describes a new class of potential functions that provide more control over parti... |

16 |
Nonlinear particle tracking for high-order elements
- Coppola, Sherwin, et al.
- 2001
(Show Context)
Citation Context ...t planes of quadratic and cubic elements. A method to subdivide elements containing high-order basis functions so that low-order visualizing methods can be used is proposed [28], [35]. Coppola et al. =-=[6]-=- address the issue of vector visualization with high-order representations by formulating the particle advection problem on high-order basis functions. Similar to our framework, this work tracks parti... |

16 |
A 3-Dimensional Representation for Fast Rendering
- Whitted
- 1980
(Show Context)
Citation Context ...single element and, in practice, another layer of computation is required to determine which reference element contains the point u T1ðxÞ. Although efficient element lookups based on regular grids =-=[27]-=-, [11] or low-order curves [38] can be applied to elements with planar or quadratic curved faces respectively, there is no closed form solution for the general problem. Spatial partitioning schemes ca... |

15 | Fast Surface Particle Repulsion
- Heckbert
- 1997
(Show Context)
Citation Context ...Building on these ideas, Witkin and Heckbert [40] present a novel physicallybased system that uses repulsive particles to evenly sample implicit surfaces for modeling and visualization. Several works =-=[13]-=-, [12], [31] describe modifications and applications of this method. Research on geometric adaptivity in such particle systems [26], [7], [16] has shown that the underlying formulation has limitations... |

10 |
Robust Ray Casting of Irregular Grids
- Bunyk, Kaufman, et al.
- 2000
(Show Context)
Citation Context ...ssumptions these methods make about the regularity of the grid. Early work by Shirley and Tuchman [30] and Williams [39] propose a volume rendering approach for tetrahedral elements, and Bunyk et al. =-=[3]-=- propose a generalized raycasting algorithm for irregular grids. Doi and Koide [10] present the Marching Tetrahedra method for triangulating isosurfaces defined over tetrahedral elements. More recentl... |

10 | Ray casting curved-quadratic elements.
- WILEY, CHILDS, et al.
- 2004
(Show Context)
Citation Context ...tly adapting low-order visualization methods to high-order functions, and some work has been done to specifically address the problem of visualizing high-order finite element data. Wiley et al. [38], =-=[37]-=- formulate ray casting for curved-quadratic elements, and Brasher and Haimes [2] propose a GPU-based method for color mapping cut planes of quadratic and cubic elements. A method to subdivide elements... |

8 | Rendering planar cuts through quadratic and cubic finite elements
- Brasher, Haimes
- 2004
(Show Context)
Citation Context ...rk has been done to specifically address the problem of visualizing high-order finite element data. Wiley et al. [38], [37] formulate ray casting for curved-quadratic elements, and Brasher and Haimes =-=[2]-=- propose a GPU-based method for color mapping cut planes of quadratic and cubic elements. A method to subdivide elements containing high-order basis functions so that low-order visualizing methods can... |

8 |
Contouring curved quadratic elements.
- WILEY, CHILDS, et al.
- 2003
(Show Context)
Citation Context ..., another layer of computation is required to determine which reference element contains the point u T1ðxÞ. Although efficient element lookups based on regular grids [27], [11] or low-order curves =-=[38]-=- can be applied to elements with planar or quadratic curved faces respectively, there is no closed form solution for the general problem. Spatial partitioning schemes can be utilized to reduce the gri... |

6 |
Framework for visualizing higher-order basis functions
- Schroeder, Bertel, et al.
(Show Context)
Citation Context ...method for color mapping cut planes of quadratic and cubic elements. A method to subdivide elements containing high-order basis functions so that low-order visualizing methods can be used is proposed =-=[28]-=-, [35]. Coppola et al. [6] address the issue of vector visualization with high-order representations by formulating the particle advection problem on high-order basis functions. Similar to our framewo... |

2 |
Using Particles to Sample and
- Hart, Bachta, et al.
- 2002
(Show Context)
Citation Context ...ng on these ideas, Witkin and Heckbert [40] present a novel physicallybased system that uses repulsive particles to evenly sample implicit surfaces for modeling and visualization. Several works [13], =-=[12]-=-, [31] describe modifications and applications of this method. Research on geometric adaptivity in such particle systems [26], [7], [16] has shown that the underlying formulation has limitations in th... |

2 |
Visualizing Higher Order Finite Elements: Final Report
- Thompson, Pebay
(Show Context)
Citation Context ... for color mapping cut planes of quadratic and cubic elements. A method to subdivide elements containing high-order basis functions so that low-order visualizing methods can be used is proposed [28], =-=[35]-=-. Coppola et al. [6] address the issue of vector visualization with high-order representations by formulating the particle advection problem on high-order basis functions. Similar to our framework, th... |