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## Robust Particle Systems for Curvature Dependent Sampling of Implicit Surfaces (2005)

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Venue: | In SMI ’05: Proceedings of the International Conference on Shape Modeling and Applications 2005 (SMI’ 05 |

Citations: | 40 - 5 self |

### Citations

3106 |
Numerical recipes in C – The art of scientific computing
- Press, Flannery, et al.
- 1989
(Show Context)
Citation Context ...the surface is a nonlinear optimization problem, and the inverse-Hessian techniques, such as the Levenberg-Marquardt algorithm, are often very effective at producing stable results in a timely manner =-=[15]-=-. Levenberg-Marquardt (L-M) works by varying between an inverse-Hessian when the energy is locally quadratic or a gradient descent when the inverse-Hessian fails. We begin with an expression for the H... |

466 |
A Generalization of Algebraic Surface Drawing.
- Blinn
- 1982
(Show Context)
Citation Context ...e, efficient, and controllable mechanisms for distributing particles that sample implicit surfaces within a locally adaptive framework. 1. Introduction Implicit surfaces are used for surface modeling =-=[2]-=-, point set reconstruction [7], animation [5], and visualization [22]. The widespread use of implicit surfaces is due to several desirable features of the surface representation, such as a simple, hom... |

445 | Re-tiling polygonal surfaces.
- Turk
- 1992
(Show Context)
Citation Context ...gy function from the molecular dynamics literature, which causes particles to exert short-range repulsion and long-range attraction, keeping particles at an appropriate distance from each other. Turk =-=[21]-=- uses repelling particles to re-sample polygonalized static surfaces using curvature measurements, while De Figueiredo et al. [4] proposes a physically-based particle method to polygonalize implicit s... |

256 | Using particles to sample and control implicit surfaces”
- Witkin, Heckbert
- 1994
(Show Context)
Citation Context ...ens.fr Ross T. Whitaker School of Computing University of Utah whitaker@sci.utah.edu Figure 1. A curvature dependent sampling of the dragon (Figure 5 in the color plate). In 1994, Witkin and Heckbert =-=[23]-=- introduced a novel approach to sampling and controlling implicit surfaces in which they constrain a system of interacting particles to lie on the implicit surface. Each particle repels nearby particl... |

221 | Computing and rendering point set surfaces.
- Alexa, Behr, et al.
- 2003
(Show Context)
Citation Context ...sampling unbounded surfaces and singularities. Similarly, Crossno et al. [3] propose modifying the W-H scheme to accommodate local curvature of extracted isosurfaces. Research in pointbased graphics, =-=[1, 14, 7]-=- builds, in part, upon ideas from particle systems. Point-based methods fit an implicit surface to a point cloud and then utilize particle system techniques to refine the point representation. 3. The ... |

216 | Surface modeling with oriented particle systems. Computer Graphics,
- Szeliski, Tonnesen
- 1992
(Show Context)
Citation Context ...e particle density, the efficiency of the computation, or update and rendering times. 2. Related Work Modeling surfaces with particles was first proposed in computer graphics by Szeliski and Tonnesen =-=[18, 19]-=-, by developing an oriented particle system to sample deformable surface models. They employ an energy function from the molecular dynamics literature, which causes particles to exert short-range repu... |

201 | Shape modeling with pointsampled geometry.
- Pauly, Keiser, et al.
- 2003
(Show Context)
Citation Context ...sampling unbounded surfaces and singularities. Similarly, Crossno et al. [3] propose modifying the W-H scheme to accommodate local curvature of extracted isosurfaces. Research in pointbased graphics, =-=[1, 14, 7]-=- builds, in part, upon ideas from particle systems. Point-based methods fit an implicit surface to a point cloud and then utilize particle system techniques to refine the point representation. 3. The ... |

157 | Curvature-based transfer functions for direct volume rendering: Methods and applications. In:
- Kindlmann, Whitaker, et al.
- 2003
(Show Context)
Citation Context ...an be increase in (14), or to smooth out the dependency, d < 1 can be used. We calculate the curvature of the implicit surface from the derivatives of F using the method described by Kindlmann et al. =-=[12]-=-. By adding αi into the energy, force, and Hessian equations, the influence of particles in regions of high curvature is reduced, causing particles to form denser configurations near these surface fea... |

157 |
Distributing many points on a sphere
- Saff, Kuijlaars
- 1997
(Show Context)
Citation Context ...it surfaces for animation [6] and texture mapping [24]. Also, a large body of work has been developed in the mathematics community that studies the discretization of surfaces via energy minimizations =-=[17, 8]-=-. Heckbert [10] extends the original W-H method by developing a spatial binning optimization that determines the radius of influence of a particle and only calculates forces for neighboring particles ... |

94 | Animating soft substances with implicit surfaces
- Desbrun, Gascuel
- 1995
(Show Context)
Citation Context ... distributing particles that sample implicit surfaces within a locally adaptive framework. 1. Introduction Implicit surfaces are used for surface modeling [2], point set reconstruction [7], animation =-=[5]-=-, and visualization [22]. The widespread use of implicit surfaces is due to several desirable features of the surface representation, such as a simple, homogeneous representation (e.g. volumes), the a... |

79 |
Modeling surfaces of arbitrary topology with dynamic particles.
- Szeliski, Tonnesen, et al.
- 1993
(Show Context)
Citation Context ...e particle density, the efficiency of the computation, or update and rendering times. 2. Related Work Modeling surfaces with particles was first proposed in computer graphics by Szeliski and Tonnesen =-=[18, 19]-=-, by developing an oriented particle system to sample deformable surface models. They employ an energy function from the molecular dynamics literature, which causes particles to exert short-range repu... |

67 | Discretizing manifolds via minimum energy points
- Hardin, Saff
(Show Context)
Citation Context ...it surfaces for animation [6] and texture mapping [24]. Also, a large body of work has been developed in the mathematics community that studies the discretization of surfaces via energy minimizations =-=[17, 8]-=-. Heckbert [10] extends the original W-H method by developing a spatial binning optimization that determines the radius of influence of a particle and only calculates forces for neighboring particles ... |

59 | An algorithm for computing Fekete points in the triangle,
- Taylor, Wingate, et al.
- 2000
(Show Context)
Citation Context ..., we put a soft minimum and maximum on this scaling: αi = γ + κ d i 1 . (14) + ν The upper bound on αi is 1/ν, and the lower bound is γ. We find that ν = 0.75, γ = 0.1, d = 2 and a curvaturesrange of =-=[0, 20]-=- works well and distributes particles with a strong curvature dependence. To increase the curvature dependence, d can be increase in (14), or to smooth out the dependency, d < 1 can be used. We calcul... |

48 | Isosurface extraction using particle systems
- CROSSNO, ANGEL
- 1997
(Show Context)
Citation Context ...es on the surface. Many applications, however, require inhomogeneous distributions based on curvature, such as using particles to polygonalize [11] or to parametrize [24] the surface. Several authors =-=[16, 3]-=- have attempted to enhance the W-H method for locally adaptive sampling , but have noted the difficulty of tuning such a complicated system of parameters.sThe difficulty with the W-H method is twofold... |

37 | Physicallybased methods for polygonization of implicit surfaces
- FIGUEIREDO, GOMEZ, et al.
- 1992
(Show Context)
Citation Context ...n, keeping particles at an appropriate distance from each other. Turk [21] uses repelling particles to re-sample polygonalized static surfaces using curvature measurements, while De Figueiredo et al. =-=[4]-=- proposes a physically-based particle method to polygonalize implicit surfaces by modeling particles with a mass-spring system. Building on these ideas, Witkin and Heckbert [23] propose a novel, physi... |

35 |
Curvature-dependent triangulation of implicit surfaces
- KARKANIS, STEWART
(Show Context)
Citation Context ...ing system produces a homogeneous distribution of particles on the surface. Many applications, however, require inhomogeneous distributions based on curvature, such as using particles to polygonalize =-=[11]-=- or to parametrize [24] the surface. Several authors [16, 3] have attempted to enhance the W-H method for locally adaptive sampling , but have noted the difficulty of tuning such a complicated system ... |

30 | Adaptive sampling of implicit surfaces for interactive modelling and animation.
- Desbrun, Tsingos, et al.
- 1996
(Show Context)
Citation Context ...] propose a novel, physically-based system that uses repulsive particles to not only sample, but also deform, implicit surfaces. Other work presents ideas for sampling implicit surfaces for animation =-=[6]-=- and texture mapping [24]. Also, a large body of work has been developed in the mathematics community that studies the discretization of surfaces via energy minimizations [17, 8]. Heckbert [10] extend... |

25 | Ray-tracing polymorphic multidomain spectral/hp elements for isosurface rendering.
- NELSON, KIRBY
- 2006
(Show Context)
Citation Context ... a point based surface splatter, finite element data can benefit from the nature of the surface constrained particle system to improve the accuracy and efficiency of visualizing higher order surfaces =-=[13]-=-. Acknowledgments The authors wish to thank David Breen of Drexel University and the Stanford 3D Scanning Repository for the dragon and griffin distance fields. We also wish to thank the anonymous rev... |

17 | Interactive Visualization of Implicit Surfaces with Singularities," Implicit Surfaces '96
- R6sch, Ruhl, et al.
(Show Context)
Citation Context ...es on the surface. Many applications, however, require inhomogeneous distributions based on curvature, such as using particles to polygonalize [11] or to parametrize [24] the surface. Several authors =-=[16, 3]-=- have attempted to enhance the W-H method for locally adaptive sampling , but have noted the difficulty of tuning such a complicated system of parameters.sThe difficulty with the W-H method is twofold... |

16 |
Using particles to sample and control more complex implicit surfaces. 11 Full resolution reconstruction. (c) Attributes level
- Hart, Bachta, et al.
(Show Context)
Citation Context ...hboring particles within this radius. The radius of influence varies from particle to particle, so the bounding sphere must be computed for each particle. Another extension is proposed by Hart et al. =-=[9]-=- to sample more complex surfaces. They describe an object-oriented system that numerically differentiates implicit surfaces comprised of large numbers of control parameters. Rösch et al. [16] introduc... |

15 | Fast Surface Particle Repulsion
- Heckbert
- 1997
(Show Context)
Citation Context ...imation [6] and texture mapping [24]. Also, a large body of work has been developed in the mathematics community that studies the discretization of surfaces via energy minimizations [17, 8]. Heckbert =-=[10]-=- extends the original W-H method by developing a spatial binning optimization that determines the radius of influence of a particle and only calculates forces for neighboring particles within this rad... |

14 | Segmentation of biological volume datasets using a level-set framework
- Whitaker, Breen, et al.
(Show Context)
Citation Context ... that sample implicit surfaces within a locally adaptive framework. 1. Introduction Implicit surfaces are used for surface modeling [2], point set reconstruction [7], animation [5], and visualization =-=[22]-=-. The widespread use of implicit surfaces is due to several desirable features of the surface representation, such as a simple, homogeneous representation (e.g. volumes), the ability to model deformat... |

10 |
Dynamic sculpting and deformation of point set surfaces
- GUO, QUIN
(Show Context)
Citation Context ... mechanisms for distributing particles that sample implicit surfaces within a locally adaptive framework. 1. Introduction Implicit surfaces are used for surface modeling [2], point set reconstruction =-=[7]-=-, animation [5], and visualization [22]. The widespread use of implicit surfaces is due to several desirable features of the surface representation, such as a simple, homogeneous representation (e.g. ... |

3 | de Figueiredo. Controlling texture mapping onto implicit surfaces with particle systems - Zonenschein, Gomes, et al. - 1998 |