## Sampling Implicit Objects With Physically-Based Particle Systems (1996)

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Venue: | Computers & Graphics |

Citations: | 9 - 7 self |

### BibTeX

@ARTICLE{Figueiredo96samplingimplicit,

author = {Luiz Henrique De Figueiredo and Jonas Gomes},

title = {Sampling Implicit Objects With Physically-Based Particle Systems},

journal = {Computers & Graphics},

year = {1996},

volume = {20},

pages = {365--375}

}

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### Abstract

. After reviewing three classical sampling methods for implicit objects, we describe a new sampling method that is not based on scanning the ambient space. In this method, samples are "randomly" generated using physically-based particle systems. Introduction In computer graphics, an object is described either by a set of sample points or by an analytic scheme that uses mathematical equations to define its geometry and topology. Descriptions based on samples occur in areas such as medical images and terrain models. Analytical descriptions are usually found in applications of geometric modeling, such computeraided design and manufacture. When an object is described by samples, a reconstruction scheme is needed to recover its geometry and topology from the samples. This problem, called structuring, consists of providing a combinatorial structure to the samples in order to (ideally) recover the exact topology of the object and an approximation of its geometry. When the object is describe...

### Citations

224 | S.: Using particles to sample and control implicit surfaces
- WITKIN, HECKBERT
- 1994
(Show Context)
Citation Context ...ystems that are integrated to simulate Newtonian mechanics. Discrete models for physical systems are well suited for computer simulation and have recently been successfully used in geometric modeling =-=[10,11]-=-. In the kinematic interpretation, the field F describes velocity in terms of position. The equation of motion corresponding to this interpretation is dx dt + sign(h)#h = 0. to appear in Computer & Gr... |

200 | D.: Surface modeling with oriented particle systems
- SZELISKI, TONNESEN
- 1992
(Show Context)
Citation Context ...ystems that are integrated to simulate Newtonian mechanics. Discrete models for physical systems are well suited for computer simulation and have recently been successfully used in geometric modeling =-=[10,11]-=-. In the kinematic interpretation, the field F describes velocity in terms of position. The equation of motion corresponding to this interpretation is dx dt + sign(h)#h = 0. to appear in Computer & Gr... |

134 |
Numerical continuation methods : an introduction
- Allgower, Georg
- 1990
(Show Context)
Citation Context ...One way to use this additional information to help stabilize the integration is to do a few iterations of Newton's method for the solution of nonlinear equations as a correction after each prediction =-=[1]-=-: if p is the current point on the curve, then Euler's prediction of the next point is p+ #H(h)(p), which is possibly on a di#erent level curve; we use Newton's method to bring the point p back to the... |

128 | Interactive Techniques for Implicit Modeling
- BLOOMENTHAL, WYVILLE
- 1990
(Show Context)
Citation Context ...od does not need a predefined region of interest because the particles will track V wherever it is in the ambient space. Related work The scattering method briefly described by Bloomenthal and Wyvill =-=[15]-=- also uses particles to sample implicit surfaces defined by skeletons. This method is essentially our kinematic sampling method, except that their initial samples lie on the skeleton and on its cross ... |

96 |
Interval arithmetic and recursive subdivision for implicit functions and constructive solid geometry
- Duff
- 1992
(Show Context)
Citation Context ...ll undersh is computed. This estimate is an interval; if it does not contain zero, then the cell does not contain zeros of h. Interval arithmetic is the natural technique for computing such estimates =-=[7]-=- (Fig. 5). Figure 5: Adaptive enumeration with interval arithmetic;sh(x; y) = x 2 + y 2 + xy \Gamma (xy) 2 =2 \Gamma 1=4. The estimates provided by interval arithmetic are too conservative; in complex... |

66 | Affine arithmetic and its applications to computer graphics
- Comba, Stolfi
- 1993
(Show Context)
Citation Context ... expressions having many coupled sub-expressions, these estimates can quickly become useless. An alternative to interval arithmetic, called a#ne arithmetic, has been proposed to overcome this problem =-=[8]-=-. A#ne arithmetic does handle coupling in expressions and is therefore able to provide better estimates. Adaptive enumeration of implicit objects using a#ne arithmetic is a promising technique, specia... |

44 |
Adaptive polygonalization of implicitly defined surfaces
- Hall, Warren
- 1990
(Show Context)
Citation Context ...rcome this problem is to exploit the geometry of the object and use adaptive cellular decompositions, which reduce the total number of cells to be scanned by concentrating small cells around features =-=[3,4,5]-=- (see below for an alternative method). Enumeration methods can be very expensive because only a few cells intersect the object, especially in high co-dimension. Nevertheless, enumeration methods are ... |

35 | Physically-based methods for polygonization of implicit surfaces
- Figueiredo, Gomes, et al.
(Show Context)
Citation Context ...le concentration near high curvature zones can be exploited for enhancing visual perception of surface geometry. A brief description of the sampling method presented here appeared in a previous paper =-=[16]-=-. Conclusion We have described a new method for sampling implicit objects that uses equilibrium configurations of simulated physical motions of particles. This method is in some aspects more robust th... |

30 | Adaptive enumeration of implicit surfaces with affine arithmetic, Comput. Graphics Forum 15 (5
- Figueiredo, Stolfi
- 1996
(Show Context)
Citation Context ...does handle coupling in expressions and is therefore able to provide better estimates. Adaptive enumeration of implicit objects using a#ne arithmetic is a promising technique, specially for rendering =-=[9] (Fig. 6).-=- to appear in Computer & Graphics 20 #3 (1996) (special issue "Computer Graphics in Brazil") 4 Figure 6: Adaptive enumeration with a#ne arithmetic;sh(x, y) = x 2 + y 2 + xy - (xy) 2 /2 - 1/4... |

25 |
Contour tracing by piecewise linear approximation
- Dobkin, Levy, et al.
- 1990
(Show Context)
Citation Context ...adient Figure 3: Sampling by continuation. Sampling by enumeration Instead of computing an approximation of the level sets of the exact h, we can compute the exact level sets of an approximation of h =-=[2]-=-. If this is to be easier than dealing with the exact h, then the approximation should be su#ciently simple so that its exact level sets are easy to compute. This is achieved by taking a piecewise smo... |

17 |
Adaptive polygonization of implicit surfaces using simplicial decomposition and boundary constraints
- Velho
- 1990
(Show Context)
Citation Context ...rcome this problem is to exploit the geometry of the object and use adaptive cellular decompositions, which reduce the total number of cells to be scanned by concentrating small cells around features =-=[3,4,5]-=- (see below for an alternative method). Enumeration methods can be very expensive because only a few cells intersect the object, especially in high co-dimension. Nevertheless, enumeration methods are ... |

15 |
Interval arithmetic and recursive subdivision for implicit functions and constructive solid geometry
- Du
- 1992
(Show Context)
Citation Context ...ll undersh is computed. This estimate is an interval; if it does not contain zero, then the cell does not contain zeros of h. Interval arithmetic is the natural technique for computing such estimates =-=[7]-=- (Fig. 5). Figure 5: Adaptive enumeration with interval arithmetic;sh(x, y) = x 2 + y 2 + xy - (xy) 2 /2 - 1/4. The estimates provided by interval arithmetic are too conservative; in complex expressio... |

8 |
A new method for solving nonlinear simultaneous equations
- Incerti, Parisi, et al.
- 1979
(Show Context)
Citation Context ...d-order dynamical system can have additional spurious attractors, other than the ones described above. Friction also provides additional control over the sampling process. Incerti, Parisi and Zirilli =-=[12]-=- proposed a similar di#erential equation for finding zeros of functions R n # R n ; however, they were interested in finding any one solution, not many, as required in sampling for geometric modeling.... |

8 |
Computational morphology of curvesâ€ť, Visual Computer
- Figueiredo, Gomes
- 1995
(Show Context)
Citation Context ...is not too expensive in a workstation, the geometric computations needed for structuring are usually tightly coupled (we have proposed a structuring method for curves that uses minimal spanning trees =-=[13,14]-=-). Moreover, the samples provided by the physically-based method usually contain many almost coincident points; such concentrations occur at regions of high curvature and on spurious attractors, as me... |

7 |
A simple and relatively efficient triangulation of the n-cube, Discrete and Computational Geometry 6
- Haiman
- 1991
(Show Context)
Citation Context ...ecause, when the cells are simplices, the total number of cells grows exponentially with the dimension: a simplicial decomposition of a hypercube in dimensionsn needs \Omega\Gamma c n p n!) simplices =-=[6]-=-. Independently of how the cells are chosen, the sample provided by the full scan described above is only structured locally at each cell; global structuring, such as the correct glueing of pieces and... |

3 |
de Figueiredo, Computational Morphology of Implicit Curves
- H
- 1992
(Show Context)
Citation Context ...is not too expensive in a workstation, the geometric computations needed for structuring are usually tightly coupled (we have proposed a structuring method for curves that uses minimal spanning trees =-=[13,14]-=-). Moreover, the samples provided by the physically-based method usually contain many almost coincident points; such concentrations occur at regions of high curvature and on spurious attractors, as me... |

2 |
A simple and relatively e#cient triangulation of the n-cube, Discrete and Computational Geometry 6
- Haiman
- 1991
(Show Context)
Citation Context ...s problem because, when the cells are simplices, the total number of cells grows exponentially with the dimension: a simplicial decomposition of a hypercube in dimensionsn needs## c n # n!) simplices =-=[6]-=-. Independently of how the cells are chosen, the sample provided by the full scan described above is only structured locally at each cell; global structuring, such as the correct glueing of pieces and... |

1 |
Polygonization of implicit surfaces, Comp. Aided Geometric Design 5
- Bloomenthal
- 1988
(Show Context)
Citation Context ...rcome this problem is to exploit the geometry of the object and use adaptive cellular decompositions, which reduce the total number of cells to be scanned by concentrating small cells around features =-=[3,4,5]-=- (see below for an alternative method). Enumeration methods can be very expensive because only a few cells intersect the object, especially in high co-dimension. Nevertheless, enumeration methods are ... |