## Bounded Clustering -- Finding Good Bounds on Clustered Light Transport (1998)

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Venue: | IN PACIFIC GRAPHICS ’98 |

Citations: | 9 - 3 self |

### BibTeX

@TECHREPORT{Stamminger98boundedclustering,

author = {Marc Stamminger and Philipp Slusallek and Hans-Peter Seidel},

title = {Bounded Clustering -- Finding Good Bounds on Clustered Light Transport},

institution = {IN PACIFIC GRAPHICS ’98},

year = {1998}

}

### Years of Citing Articles

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### Abstract

Clustering is a very efficient technique to apply finite element methods to the computation of radiosity solutions of complex scenes. Both computation time and memory consumption can be reduced dramatically by grouping the primitives of the input scene into a hierarchy of clusters and allowing for light exchange between all levels of this hierarchy. However, problems can arise due to clustering, when gross approximations about a cluster's content result in unsatisfactory solutions or unnecessary computations. In the clustering approach for diffuse global illumination described in this paper, light exchange between two objects --- patches or clusters --- is bounded by using geometrical and shading information provided by every object through a uniform interface. With this uniform view of various kinds of objects, comparable and reliable error bounds on the light exchange can be computed, which then guide a standard hierarchical radiosity algorithm.

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Citation Context ...ense, \computing hSi" means nding an upper andalower bound on S and a proper approximation. The de nition of addition, multiplication and division on the min/max-values is that of Interval Arithmetic =-=[10]-=-. Using Interval Arithmetic for our computations is certainly not optimal. We are optimistic that using A ne Artihmetic [3] instead may result in better range computations, as it has been shown for ot... |

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Citation Context ...tween objects in the environment. This resulted in a reduced computational complexity ofO(n) orO(n log n) compared to the quadratic nature of the original algorithm. For early hierarchical algorithms =-=[6, 5]-=- this speedup was restricted to adaptive subdivision of input primitives. In contrast, clustering algorithms group all primitives into a single hierarchy of clusters, which consist of other clusters, ... |

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Citation Context ...clusters, which consist of other clusters, surface elements, or subdivisions thereof. Applying the same idea of adaptive subdivision to this uni ed hierarchy extends the speedup to the complete scene =-=[16, 2,13,4, 1]-=-. There are two major issues with any hierarchical method: the design of an e cient re ner for the adaptive subdivision and of an accurate estimator to compute the actual interaction coe cients. The r... |

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Citation Context ... lifted by using spherical harmonics to represent the anisotropic radiance distribution of a cluster. A better re ner would estimate the range of illumination values on the receiver due to the sender =-=[16, 9]-=-. If the illumination on the receiving object varies strongly, sender and/or receiver have to be subdivided. Re ning the receiver decreases the error by allowing for a more accurate representation of ... |

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Citation Context ...clusters, which consist of other clusters, surface elements, or subdivisions thereof. Applying the same idea of adaptive subdivision to this uni ed hierarchy extends the speedup to the complete scene =-=[16, 2,13,4, 1]-=-. There are two major issues with any hierarchical method: the design of an e cient re ner for the adaptive subdivision and of an accurate estimator to compute the actual interaction coe cients. The r... |

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Citation Context ...the re ner in order to guide re nement properly. However, the oracle and form factor computation do not di erentiate between patches and clusters and even volumetric objects can be handled easily. In =-=[15]-=- the isotropy assumption is lifted by using spherical harmonics to represent the anisotropic radiance distribution of a cluster. A better re ner would estimate the range of illumination values on the ... |

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Citation Context ...ny two objects (clusters, surfaces, and surface elements), we need access to several values depending on both the sending and the receiving object, as for instance their bounding box, cone of normals =-=[12]-=- or exitant radiance in some direction. All objects allow to query these values using a common set of methods, abstracting from the concrete type of each object. In the following, we describe the comp... |

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Citation Context ...clusters, which consist of other clusters, surface elements, or subdivisions thereof. Applying the same idea of adaptive subdivision to this uni ed hierarchy extends the speedup to the complete scene =-=[16, 2,13,4, 1]-=-. There are two major issues with any hierarchical method: the design of an e cient re ner for the adaptive subdivision and of an accurate estimator to compute the actual interaction coe cients. The r... |

33 | Efficient hierarchical refinement and clustering for radiosity in complex environments - Gibson, Hubbold - 1996 |

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Citation Context ... for our computations is certainly not optimal. We are optimistic that using A ne Artihmetic [3] instead may result in better range computations, as it has been shown for other rendering applications =-=[8, 7]-=-. The algorithm described below should be easy to transform. In the following, we describe how the light transport between two objects can be computed using the above de nitions. We start by computing... |

22 | Bounded radiosity – Illumination on general surfaces and clusters
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Citation Context ..., this reasoning is based on computing upper and lower bounds on the light exchange and each of the individual terms used to compute these values. The algorithm is a continuation of work presented in =-=[18]-=-, where a simpler approach is used to uniformly handle arbitrarily shaped surfaces for di use radiosity computations. However, it turned out that a cluster's behaviour di ers strongly from that of an ... |

4 | Isotropic clustering for hierarchical radiosity — implementation and experiences
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Citation Context ...ement decision. Up to now, all computation have been made using strictly conservative bounds. This has the bene t that it can be assured that no light transport can be missed due to sampling problems =-=[17]-=-. Initial tessellation, which is necessary for other algorithms, can be completely omitted, the algorithm can work on all kind of input objects. Nevertheless it must be seen, that using interval arith... |

3 |
A uni ed hierarchical algorithm for global illumination with scattering volumes and object clusters
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Citation Context |

1 |
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Citation Context ...inally in previous publications. Our results showed that computing self-form factors by numerical integration using sampling does not deliver very useful results due to singularities in the integrand =-=[11]-=-. We use avery simple, but probably much more e ective method. Our approach is based on the fact that in closed scenes all form factors from an object sum up to one ( P j Fij = 1). If we sum up the fo... |

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Citation Context ...plication and division on the min/max-values is that of Interval Arithmetic [10]. Using Interval Arithmetic for our computations is certainly not optimal. We are optimistic that using A ne Artihmetic =-=[3]-=- instead may result in better range computations, as it has been shown for other rendering applications [8, 7]. The algorithm described below should be easy to transform. In the following, we describe... |

1 |
E cient hierarchical re nement and clustering for radiosity in complex environements
- Gibson, Hubbold
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(Show Context)
Citation Context |

1 |
Sampling procedural shaders using a ne arithmetic
- Heidrich, Slusallek, et al.
- 1998
(Show Context)
Citation Context ... for our computations is certainly not optimal. We are optimistic that using A ne Artihmetic [3] instead may result in better range computations, as it has been shown for other rendering applications =-=[8, 7]-=-. The algorithm described below should be easy to transform. In the following, we describe how the light transport between two objects can be computed using the above de nitions. We start by computing... |

1 |
Feature-based control of visibility error: Amulti-resolution clustering algorithm for global illumination
- Sillion, Drettakis
- 1995
(Show Context)
Citation Context ...relative error increase. 5.2. Visibility Accelleration In order to speed up visibility computation, we reuse the cluster hierarchy also as a hierarchical spatial density approximation, as proposed in =-=[14]-=-. If a rayistobe shot through the scene, the ray traverses the cluster hierarchy. When the ray does not intersect the bounding box of a cluster, the complete subtree can be skipped for intersection te... |