## A unified hierarchical algorithm for global illumination with scattering volumes and object clusters (1995)

Venue: | IEEE Trans. Vis. Comput. Graph |

Citations: | 108 - 22 self |

### BibTeX

@ARTICLE{Sillion95aunified,

author = {François X. Sillion},

title = {A unified hierarchical algorithm for global illumination with scattering volumes and object clusters},

journal = {IEEE Trans. Vis. Comput. Graph},

year = {1995},

pages = {240--254}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract — This paper presents a new radiosity algorithm that allows the simultaneous computation of energy exchanges between surface elements, scattering volume distributions, and groups of surfaces, or object clusters. The new technique is based on a hierarchical formulation of the zonal method, and efficiently integrates volumes and surfaces. In particular no initial linking stage is needed, even for inhomogeneous volumes, thanks to the construction of a global spatial hierarchy. An analogy between object clusters and scattering volumes results in a powerful clustering radiosity algorithm, with no initial linking between surfaces and fast computation of average visibility information through a cluster. We show that the accurate distribution of the energy emitted or received at the cluster level can produce even better results than isotropic clustering at a marginal cost. The resulting algorithm is fast and, more importantly, truly progressive as it allows the quick calculation of approximate solutions with a smooth convergence towards very accurate simulations. I.

### Citations

1271 |
The Design and Analysis of Spatial Data Structures
- Samet
(Show Context)
Citation Context ...e factors. used to represent this subdivision. For volumes a variety of structures are possible, including octrees and binary trees. In our implementation we have used a tri-dimensional k-d tree [4], =-=[27]-=-. In the remainder of this paper we will refer to portions of surfaces and volumes as generic Hierarchical Elements or H-elements. We now show that the hierarchical radiosity algorithm of Hanrahan et ... |

1257 |
Multidimensional binary search trees used for associative searching
- Bentley
- 1975
(Show Context)
Citation Context ...volume factors. used to represent this subdivision. For volumes a variety of structures are possible, including octrees and binary trees. In our implementation we have used a tri-dimensional k-d tree =-=[4]-=-, [27]. In the remainder of this paper we will refer to portions of surfaces and volumes as generic Hierarchical Elements or H-elements. We now show that the hierarchical radiosity algorithm of Hanrah... |

470 | Footprint Evaluation for Volume Rendering
- Westover
- 1990
(Show Context)
Citation Context ...g any volume rendering package. A ray-casting based technique is likely to provide the best results in general. In our implementation we have chosen to use a direct projection ("splatting") =-=algorithm [36]-=-, [17] in order to maintain the short rendering times necessary for interactive simulation: Surfaces are rendered first using a conventional z-bu#er. The leaf H-elements of all volumes are then compos... |

411 | Volume rendering
- Drebin, Carpenter, et al.
- 1988
(Show Context)
Citation Context ...tegral. This derivation also provides a justification for the simple fog models commonly found in rendering packages (and in special-purpose hardware accelerators) and for volume rendering algorithms =-=[7]-=-. This formal manipulation suggests that if the source radiancesJ can be computed in a first pass, the final radiance can then be obtained using for example a ray tracing pass based on Equation 7. B.2... |

254 |
Hierarchical splatting: A progressive refinement algorithm for volume rendering
- Laur, Hanrahan
- 1991
(Show Context)
Citation Context ...volume rendering package. A ray-casting based technique is likely to provide the best results in general. In our implementation we have chosen to use a direct projection ("splatting") algori=-=thm [36], [17]-=- in order to maintain the short rendering times necessary for interactive simulation: Surfaces are rendered first using a conventional z-bu#er. The leaf H-elements of all volumes are then composited i... |

193 |
Thermal radiation of heat transfer
- Siegel, Howell
(Show Context)
Citation Context ...ength. . # a L e represents the increase in radiance due to emission by the medium. L e is the emitted radiance, and the presence of # a is a consequence of reciprocity principles from thermodynamics =-=[28]-=-. . The integral term represents the increase in radiance due to in-scattering, that is the e#ect of light coming from all directions and scattered into the direction of interest. f(#) is the phase fu... |

174 |
Automatic Creation of Object Hierarchies for Ray Tracing
- Goldsmith, Salmon
- 1987
(Show Context)
Citation Context ...culations [37], [8], is to attach surfaces only to leaves of the hierarchical volume description. This can be accomplished for instance by building a hierarchy of bounding volumes around the surfaces =-=[10]-=-, [34]. However traditional methods for such a construction do not produce suitable clusters, and current research focuses on their improvement [31]. In the implementation described here, surfaces are... |

164 |
Radiosity and Global Illumination
- Sillion, Puech
- 1994
(Show Context)
Citation Context ... of an isotropically scattering medium: that is, a medium with a constant phase function f isotropic # 1 4# . This is done in a typical finite-element way, similar to the traditional radiosity method =-=[33]-=-, by first breaking up the volume containing the participating medium into discrete elements, used in addition to the usual surface patches. Radiosities are defined for both surfaces (with B i = #L i ... |

150 |
A Global Illumination Solution for General Reflectance Distributions
- SILLION, ARVO, et al.
- 1991
(Show Context)
Citation Context ...te results. One possibility to avoid this di#culty, is to represent directional information at the cluster level. Several data structures have been developed for the simulation of nondi #use surfaces =-=[30]-=- and could be used to store radiance distributions and scattering functions for each cluster. The benefit of this approach would be to maintain the constanttime linking operation, but the tradeo# with... |

135 |
The zonal method for calculating light intensities in the presence of a participating medium
- RUSHMEIER, TORRANCE
- 1987
(Show Context)
Citation Context ...c scattering volumes and di#use surfaces. We begin by presenting the governing equations for light transfer with participating media, and continue with a brief account of the traditional zonal method =-=[25]-=-. We then explain how to combine the zonal method and a hierarchical radiosity algorithm [12]. A similar combination, limited to homogeneous media, has been described elsewhere [5]. The algorithm desc... |

135 | A Clustering Algorithm for Radiosity in Complex Environments
- Smits, Arvo, et al.
- 1994
(Show Context)
Citation Context ..., [1], or manually constructed groups of patches used as representatives for their contents [24], [16]. Current research e#orts focus on the combination of clustering and hierarchical radiosity [29], =-=[34]-=- and automatic construction of clusters. In particular, independent work by Smits et al [34] suggested a clustering algorithm very similar to the one presented below. In this paper we propose a hierar... |

109 | Combining hierarchical radiosity and discontinuity meshing
- Lischinski, Tampieri, et al.
- 1993
(Show Context)
Citation Context ...flection e#ects, although it is not adequate for the direct computation of high-quality images. A "local" shading step can always be added to improve the illumination accuracy on the visible=-= surfaces [19]-=-. However such local computation is typically very expensive, and for many applications defeats the purpose of clustering, that is to quickly obtain approximate solutions while controlling accuracy. T... |

105 |
tracing volume densities
- Ray
- 1984
(Show Context)
Citation Context ...along a path at a particular di#erential volume element. where s is the path variable (a measure of the distance traveled along the path from the origin), and# denotes the entire sphere of directions =-=[15]-=-. The various terms of this equation correspond to the following physical phenomena: . -# t L represents the attenuation of radiance due to absorption or out-scattering. # t is called the extinction c... |

84 |
An importance-driven radiosity algorithm
- Smits, Arvo, et al.
- 1992
(Show Context)
Citation Context ... more accurate one. A natural extension of this work consists of developing better visibility algorithms that switch automatically from one description to the other. In particular, importance methods =-=[35]-=- should be used to select the appropriate representation for each surface. The hierarchy of clusters also provides the basis for a multi-resolution representation of visibility [31]. C. Results Fig. 9... |

70 | Efficient Light Propagation for Multiple Anisotropic Volume Scattering
- Max
- 1994
(Show Context)
Citation Context ...fer, including multiple scattering, in scenes containing both surfaces and isotropic volume scatterers. This approach complements previous ones based on ray casting or discrete ordinates methods [6], =-=[20]-=-. Fig. 6. Radiosity solution for a scene with volumes and surfaces. IV. Unification of surfaces and volumes using object clusters The analysis of the complexity of hierarchical radiosity algorithms sh... |

67 | Bounds and error estimates for radiosity
- Lischinski, Smits, et al.
- 1994
(Show Context)
Citation Context ...ding the radiosity transfer (BF refineSILLION: A UNIFIED HIERARCHICAL ALGORITHM FOR GLOBAL ILLUMINATION WITH SCATTERING VOLUMES... 5 ment) [12], or by estimating an error bound on the energy transfer =-=[18]-=-. Importance weighting of these bounds is also possible [35]. Our current implementation uses BF refinement. Thus the simulation procedure starts with an initial linkingsphase, where the potential int... |

64 | A Framework for the Analysis of Error in Global Illumination Algorithms
- ARVO, TORRANCE, et al.
- 1994
(Show Context)
Citation Context ...ION AND COMPUTER GRAPHICS, VOL. 1, NO. 3, SEPTEMBER 1995 will reflect more of this energy than others. Thus radiosity can not be simply pushed down the hierarchy. Using the terminology of Arvo et al. =-=[2]-=-, the local reflection operator must consider the inhomogeneous reflective character of the surface. Fortunately, this can be accomplished quite simply by using the underlying hierarchy to apply this ... |

58 |
Making radiosity usable: automatic preprocessing and meshing techniques for the generation of accurate radiosity solutions
- Baum, Mann, et al.
- 1991
(Show Context)
Citation Context ... the algorithm still depends on the quality of the mesh generated on the surfaces. Light leaks are possible whenever mesh boundaries are not properly positioned with respect to the radiosity function =-=[3]-=-. Using importance weighting with clustering will help directing the computational e#ort to visible areas, while other areas can be treated as large clusters. Fig. 11 shows some sample links for the s... |

56 |
Radiative transfer
- Hottel, Sarofim
- 1967
(Show Context)
Citation Context ...cipating medium, light can interact with matter at any point in space. Thus radiance must be defined everywhere, and a general integrodi #erential equation is used to express the local energy balance =-=[14]-=-. This equation expresses the rate of change in radiance along a path as: dL ds = -# t L + # a L e + # s Z# L i (#)f(#)d# , (1) emission absorption in-scattering out-scattering Fig. 1. Processes contr... |

55 | A clustering algorithm for radiance calculation in general environments
- Sillion, Drettakis, et al.
- 1995
(Show Context)
Citation Context ...each cluster. The benefit of this approach would be to maintain the constanttime linking operation, but the tradeo# with the important cost of the directional structure must be carefully investigated =-=[32]-=-. Smits et al. showed that clustering remains attractive even if more work is performed for each link, as long as the total cost of a link is linear in the total number of surfaces in the clusters bei... |

54 | A Rendering Algorithm for Discrete Volume Density Objects
- Blasi, Le, et al.
- 1993
(Show Context)
Citation Context ...transfer, including multiple scattering, in scenes containing both surfaces and isotropic volume scatterers. This approach complements previous ones based on ray casting or discrete ordinates methods =-=[6]-=-, [20]. Fig. 6. Radiosity solution for a scene with volumes and surfaces. IV. Unification of surfaces and volumes using object clusters The analysis of the complexity of hierarchical radiosity algorit... |

47 | Clustering and volume scattering for hierarchical radiosity calculations
- Sillion
- 1994
(Show Context)
Citation Context ...h [37], [1], or manually constructed groups of patches used as representatives for their contents [24], [16]. Current research e#orts focus on the combination of clustering and hierarchical radiosity =-=[29]-=-, [34] and automatic construction of clusters. In particular, independent work by Smits et al [34] suggested a clustering algorithm very similar to the one presented below. In this paper we propose a ... |

40 |
Aravindan Veerasamy. Geometric simplification for indirect illumination calculations
- Rushmeier, Patterson
- 1993
(Show Context)
Citation Context ...ithm have either attempted to treat subsets of the scene independently in a divide-and-conquer approach [37], [1], or manually constructed groups of patches used as representatives for their contents =-=[24]-=-, [16]. Current research e#orts focus on the combination of clustering and hierarchical radiosity [29], [34] and automatic construction of clusters. In particular, independent work by Smits et al [34]... |

39 | Textures and radiosity: Controlling emission and reflection with texture maps
- Gershbein, Schröder, et al.
- 1994
(Show Context)
Citation Context ...nce down the hierarchy, transform irradiance into radiosity at leaf H-elements, then pull radiosity up the hierarchy. A similar algorithm was described by Gershbein et al. for wavelet-based radiosity =-=[9]. Note that in the c-=-ase of volume elements, the "area"- averaging performed when pulling up radiosity values uses the "area factor" described above, thereby ensuring proper distribution of energy for ... |

38 | Feature-based control of visibility error: A multi-resolution clustering algorithm for global illumination
- Sillion, F, et al.
- 1995
(Show Context)
Citation Context ...a hierarchy of bounding volumes around the surfaces [10], [34]. However traditional methods for such a construction do not produce suitable clusters, and current research focuses on their improvement =-=[31]-=-. In the implementation described here, surfaces are attached at the lowest level of the volume hierarchy that contains them entirely. This avoids potential problems when a surface straddles a subdivi... |

29 |
A rapid hierarchical radiosity algorithm for unoccluded environments
- Hanrahan, Salzman
- 1990
(Show Context)
Citation Context ... each of the new components. The benefit of hierarchical radiosity methods is that the number of links created in the adaptive procedure is linear with respect to the final number of surface elements =-=[11]. This is -=-a major advantage compared to the quadratic matrix of form factors needed to completely represent the possible energy transfers with "conventional" radiosity. However, typical hierarchical r... |

27 |
Grouping of patches in progressive radiosity
- Kok
- 1993
(Show Context)
Citation Context ...ave either attempted to treat subsets of the scene independently in a divide-and-conquer approach [37], [1], or manually constructed groups of patches used as representatives for their contents [24], =-=[16]-=-. Current research e#orts focus on the combination of clustering and hierarchical radiosity [29], [34] and automatic construction of clusters. In particular, independent work by Smits et al [34] sugge... |

23 |
On the division of environments by virtual walls for radiosity computation
- ARNALDI, PUEYO, et al.
- 1994
(Show Context)
Citation Context ...of abstract entities that exchange energy. Previous e#orts to simplify the radiosity algorithm have either attempted to treat subsets of the scene independently in a divide-and-conquer approach [37], =-=[1]-=-, or manually constructed groups of patches used as representatives for their contents [24], [16]. Current research e#orts focus on the combination of clustering and hierarchical radiosity [29], [34] ... |

23 | Sampling and anti-aliasing of discrete 3-D volume density textures - Sakas, Gerth - 1991 |

21 |
Accelerated radiosity method for complex environments
- Xu, Peng, et al.
- 1990
(Show Context)
Citation Context ...a set of abstract entities that exchange energy. Previous e#orts to simplify the radiosity algorithm have either attempted to treat subsets of the scene independently in a divide-and-conquer approach =-=[37]-=-, [1], or manually constructed groups of patches used as representatives for their contents [24], [16]. Current research e#orts focus on the combination of clustering and hierarchical radiosity [29], ... |

17 |
A rapid hierarchical radiosity algorithm. Comput Graphics
- Hanrahan, Salzman, et al.
- 1991
(Show Context)
Citation Context ...ous work Hierarchical algorithms attempt to limit the amount of subdivision of surfaces by selecting the proper level of detail needed to represent each energy transfer within a given error tolerance =-=[12]-=-. The exchange of energy between a pair of surfaces is represented using a hierarchy of links that connect some of their components. Links are created in an adaptive refinement procedure that recursiv... |

9 |
Illumination of dense foliage models
- Patmore
- 1993
(Show Context)
Citation Context ...em. A. Creating a volume model We first consider the case of a large number of "small" objects. This model can be used to represent a number of natural situations such as foliage, as noted b=-=y Patmore [22]-=-. The value of this model is that, as objects become smaller, the behaviour of the medium resembles more and more that of a density distribution. In this section we therefore model the radiative prope... |

8 |
Application of rapid hierarchical radiosity to participating media
- Bhate
- 1993
(Show Context)
Citation Context ...ional zonal method [25]. We then explain how to combine the zonal method and a hierarchical radiosity algorithm [12]. A similar combination, limited to homogeneous media, has been described elsewhere =-=[5]-=-. The algorithm described here is more general in that it accommodates arbitrary density distributions as shown in Section III. A. Energy transfer in volume densities The presence of a participating m... |

8 | Eihachiro Nakamae. A shading model for atmospheric scattering considering luminous distribution of light sources - Nishita, Miyawaki - 1987 |

5 |
Fiat lux
- Fournier, Fiume, et al.
- 1990
(Show Context)
Citation Context ...is a di#cult problem, since it has a direct impact on the quality and performance of the simulation. One possibility, similar to the idea of "virtual walls" to accelerate radiosity calculati=-=ons [37], [8]-=-, is to attach surfaces only to leaves of the hierarchical volume description. This can be accomplished for instance by building a hierarchy of bounding volumes around the surfaces [10], [34]. However... |

2 |
Solution methods for radiatively participating media
- Rushmeier
- 1992
(Show Context)
Citation Context ...volume element 1 . As in the traditional radiosity method, the zonal method proceeds by setting up a linear system of equations to express the coupling between all variables based on Equation 1 [25], =-=[23]-=-: B p = E p + # p X q F pq B q . (10) Here the summation is carried out both over a set of surface patches, and a set of volume elements, each of which is assumed to possess a uniform radiosity value.... |