## Discontinuity Meshing for Radiosity (1992)

Venue: | Third Eurographics Workshop on Rendering |

Citations: | 92 - 2 self |

### BibTeX

@INPROCEEDINGS{Heckbert92discontinuitymeshing,

author = {Paul S. Heckbert},

title = {Discontinuity Meshing for Radiosity},

booktitle = {Third Eurographics Workshop on Rendering},

year = {1992},

pages = {203--226}

}

### Years of Citing Articles

### OpenURL

### Abstract

The radiosity method is the most popular algorithm for simulating interreflection of light between diffuse surfaces. Most existing radiosity algorithms employ simple meshes and piecewise constant approximations, thereby constraining the radiosity function to be constant across each polygonal element. Much more accurate simulations are possible if linear, quadratic, or higher degree approximations are used. In order to realize the potential accuracy of higher-degree approximations, however, it is necessary for the radiosity mesh to resolve discontinuities such as shadow edges in the radiosity function. A discontinuity meshing algorithm is presented that places mesh boundaries directly along discontinuities. Such algorithms offer the potential of faster, more accurate simulations. Results are shown for three-dimensional scenes. Keywords: global illumination, diffuse interreflection, adaptive mesh, shadow. 1 Introduction One of the most challenging tasks of image synthesis in computer ...

### Citations

760 | T.: The rendering equation
- Kajiya
(Show Context)
Citation Context ...e scene in one of two directions: either from the lights into the scene or from the eye into the scene. With the addition of Monte Carlo techniques, it is possible to simulate diffuse interreflection =-=[Kajiya86]-=-. This can be done efficiently by caching the slowly-varying diffuse component of radiance [Ward et al. 88]. 1.1.1 Radiosity Algorithms Radiosity methods have their roots in the simulation of thermal ... |

385 | A rapid hierarchical radiosity algorithm - HANRAHAN, SALZMAN, et al. - 1991 |

288 |
The HemiCube: A Radiosity Solution for Complex Environments
- Cohen, Greenberg
- 1985
(Show Context)
Citation Context ...of standard radiosity algorithms, except for the non-constant basis functions. The most difficult factor in these integrations is the visibility function v, but this can be evaluated using a hemicube =-=[Cohen-Greenberg85]-=- or ray tracing. Hemicube algorithms can be generalized to evaluate linear basis functions using Gouraud shading [Max-Allison92]. Discontinuity Meshing for Radiosity 11 A variety of system solution me... |

252 | A progressive refinement approach to fast radiosity image generation - Cohen, Chen, et al. - 1988 |

243 | A Ray Tracing Solution for Diffuse Interreflection - J, Rubinstein, et al. - 1988 |

141 |
Geometric modeling for computer vision
- Baumgart
(Show Context)
Citation Context ...s, faces with any number of sides, vertices of arbitrary degree, ordering of edges and faces around a vertex, and fast access to adjacent objects. An extended winged edge data structure was used here =-=[Baumgart74]-=-. BSP trees could also be used to represent the arrangement of critical lines on each face, but they split polygons unnecessarily, constraining the space of meshes, and lead to poorer quality meshes. ... |

109 |
Computational Methods for Integral Equations
- Delves, Mohamed
- 1985
(Show Context)
Citation Context ...oblem to a linear system of equations, a system solution method, and a display algorithm. For general references on finite element methods and integral equations, see the texts [Becker et al. 81] and =-=[Delves-Mohamed85]-=-, respectively. Radiosity obeys the integral equation [Heckbert-Winget91,Kajiya86]: b(x) = e(x) + Z \Gamma dx 0 (x; x 0 )b(x 0 ) where b(x) denotes the radiosity at 3-D point x, e(x) is radiant emitte... |

103 | An efficient radiosity approach for realistic image synthesis - Cohen, Greenberg, et al. - 1986 |

85 | Computing the aspect graph for line drawings of polyhedral objects
- Gigus, Malik
- 1990
(Show Context)
Citation Context ...along critical curves where these surfaces intersect the faces (polygons) of the scene. For a scene of polygons, there are two types of events: vertex-edge (VE) events and edge-edge-edge (EEE) events =-=[Gigus-Malik90]-=-. VE events result from an inter-visible vertex v and edge e. The critical surface for this event is a subset of the plane containing the vertex and the edge. More precisely, it is the set of points c... |

81 | Near real-time shadow generation using BSP trees
- Chin, Feiner
- 1989
(Show Context)
Citation Context ...est shadow algorithms simulate only point light sources, computing the shadowed and unshadowed polygons using "cookie cutter" algorithms [Atherton et al. 78], or binary space partitioning (B=-=SP) trees [Chin-Feiner90]-=-. Nishita went further, computing penumbra boundaries from area light sources [Nishita-Nakamae83], thereby producing some amazingly realistic pictures without simulating interreflection. Chin has rece... |

78 |
Simulating Global Illumination Using Adaptive Meshing
- Heckbert
- 1991
(Show Context)
Citation Context ... curve. Shadow edges from point, linear, and area light sources are in general of degree 0, 1, and 2, respectively, but when two discontinuities coincide, the degree of the discontinuity can decrease =-=[Heckbert91]-=-. The lowest degree discontinuities generally cause the greatest error, if not resolved by an approximation. Many of the characteristics of VE discontinuities are shown in figure 5. A top view of thes... |

71 | Computing the antipenumbra of an area light source
- Teller
- 1992
(Show Context)
Citation Context ...critical curves to be generated: those due to touching or intersecting surfaces, VE critical lines, and EEE critical curves. We discuss VE lines in this paper. EEE curves are more difficult to handle =-=[Teller92]-=-. Baum discussed touching and intersecting surfaces in [Baum et al. 91]. Figure 5 suggests an algorithm for determining all VE critical line segments. Half of the critical segments can be generated by... |

64 |
Fast Object-Precision Shadow Generation for Area Light Sources Using BSP Trees
- Chin, Feiner
- 1992
(Show Context)
Citation Context ...enumbra boundaries from area light sources [Nishita-Nakamae83], thereby producing some amazingly realistic pictures without simulating interreflection. Chin has recently done the same using BSP trees =-=[Chin-Feiner92]-=-. 1.2 Motivation Current radiosity algorithms work well for some scenes: the progressive radiosity algorithm [Cohen et al. 88] is relatively fast and its artifacts are often imperceptible. Sometimes, ... |

57 | Making radiosity usable: automatic preprocessing and meshing techniques for the generation of accurate radiosity solutions - Baum, Mann, et al. - 1991 |

49 |
Adaptive mesh generation for global diffuse illumination
- Campbell, Fussell
- 1990
(Show Context)
Citation Context ...tructed accordingly, and a solution found. Campbell's a priori meshing split the scene with planes through light source points and edges of occluding polygons, thereby approximating some shadow edges =-=[Campbell-Fussell90]-=-. A later improvement by Campbell found the discontinuities along the boundaries of the penumbra [Campbell91]. Baum split surfaces where they intersected or touched to resolve the most severe disconti... |

43 | Polygon shadow generation - Atherton, Weiler, et al. - 1978 |

30 | Radiosity in Flatland - Heckbert - 1992 |

29 |
Finite element methods for global illumination
- Heckbert, Winget
- 1991
(Show Context)
Citation Context ...ization of radiosity methods to arbitrary basis functions. 2.4 Finite Element Methods for Radiosity There are a variety of finite element methods for solving the integral equation governing radiosity =-=[Heckbert-Winget91]-=-. Figure 12 shows some of the available options for radiosity simulation using a finite 10 Discontinuity Meshing for Radiosity integral equation approximation problem integration problem linear system... |

24 | A progressive renement approach to fast radiosity image generation - COHEN, CHEN, et al. - 1988 |

22 |
Polygon comparison using a graph representation
- Weiler
- 1980
(Show Context)
Citation Context ...nto regions of homogeneous visibility bounded by critical lines or edges of the original polygon (figure 9, right). This is done with a 2-D sweepline algorithm similar to a polygon clipping algorithm =-=[Weiler80]-=-. This step creates a winged edge data structure. As the sweepline passes across each vertex or intersection point, the order of the emanating edges is found by a radial sort of the geometry. This ord... |

21 | Modeling global diffuse illumination for image synthesis
- Campbell
- 1992
(Show Context)
Citation Context ...ce points and edges of occluding polygons, thereby approximating some shadow edges [Campbell-Fussell90]. A later improvement by Campbell found the discontinuities along the boundaries of the penumbra =-=[Campbell91]-=-. Baum split surfaces where they intersected or touched to resolve the most severe discontinuities [Baum et al. 91]. Rigorous meshing of 2-D scenes has also been explored [Heckbert91,Heckbert92,Lischi... |

13 |
Adaptive mesh generation for global diuse illumination
- Campbell, Fussell
- 1990
(Show Context)
Citation Context ...tructed accordingly, and a solution found. Campbell's a priori meshing split the scene with planes through light source points and edges of occluding polygons, thereby approximating some shadow edges =-=[Campbell-Fussell90]-=-. A later improvement by Campbell found the discontinuities along the boundaries of the penumbra [Campbell91]. Baum split surfaces where they intersected or touched to resolve the most severe disconti... |

13 | A ray tracing solution for di use interre ection - Ward, Rubinstein, et al. - 1988 |

12 | Finite Elements: An Introduction, volume 1 - Becker, Cary, et al. - 1981 |

11 |
On the calculation of radiant interchange between surfaces
- Sparrow
- 1963
(Show Context)
Citation Context ...ching the slowly-varying diffuse component of radiance [Ward et al. 88]. 1.1.1 Radiosity Algorithms Radiosity methods have their roots in the simulation of thermal radiation in mechanical engineering =-=[Sparrow63]-=-, and were extended and optimized for the simulation of complex scenes in computer graphics [Cohen-Greenberg85,Cohen et al. 88]. The radiosity method subdivides the scene into elements (subsurfaces) a... |

9 |
Linear Radiosity Approximations using Vertex-to-Vertex Form Factors, Graphics Gems III
- Max, Allison
- 1992
(Show Context)
Citation Context ...ree elements in 3-D is straightforward, if no discontinuity meshing is done. In fact, it is possible to compute the form factors for linear element radiosity using a variant of the hemicube algorithm =-=[Max-Allison92]-=-. Since discontinuity meshing seems much more challenging than the use of higher degree elements, we devote the bulk of our attention to discontinuity meshing. 2 Discontinuity Meshing in 3-D Discontin... |

8 |
The constant radiosity assumption syndrome
- Tampieri, Lischinski
- 1991
(Show Context)
Citation Context ...radiosity is not taken into account during form factor calculation, with a few exceptions [Max-Allison92,Heckbert-Winget91]. The true radiosity function is not constant across each element, of course =-=[Tampieri-Lischinski91]-=-. Meshes with constant elements result in jaggy shadow boundaries and other artifacts. Better meshes can be created by user intervention, a posteriori methods, and a priori methods. A posteriori meshi... |

8 | An efficient radiosity approach for realistic image synthesis - S, Brock - 1986 |

7 | Improving sampling and reconstruction techniques for radiosity - Lischinski, Tampieri, et al. - 1991 |

4 |
Modeling Global Diuse Illumination for Image Synthesis
- Campbell
- 1991
(Show Context)
Citation Context ...ce points and edges of occluding polygons, thereby approximating some shadow edges [Campbell-Fussell90]. A later improvement by Campbell found the discontinuities along the boundaries of the penumbra =-=[Campbell91]-=-. Baum split surfaces where they intersected or touched to resolve the most severe discontinuities [Baum et al. 91]. Rigorous meshing of 2-D scenes has also been explored [Heckbert91,Heckbert92,Lischi... |

4 | A Progressive Re Approach to Fast Radiosity Image Generation - Cohen, Chen, et al. - 1988 |

3 | Finite Elements: An Introduction, volume 1. Prentice-Hall, Englewood Cli s - Becker, Cary, et al. - 1981 |

3 | A ray tracing solution for diuse interre - Ward, Rubinstein, et al. - 1988 |

2 |
Finite Element Mesh Generation from CSG Models
- Boender
- 1992
(Show Context)
Citation Context ...on can be concave, with holes. The final step subdivides these regions according to a user-selected maximum element size (figures 10 and 11). Delaunay triangulation and mesh relaxation were used here =-=[Boender92]-=-, but it appears that there is considerable flexibility in this last step. Once the mesh is constructed, basis functions are chosen for each element. If constant elements are used, then each element h... |

2 | Radiosity in - Heckbert - 1992 |

1 | Radiosity in atland - Heckbert - 1992 |

1 |
comparison using a graph representation
- Polygon
- 1980
(Show Context)
Citation Context ...into regions of homogeneous visibility bounded by critical lines or edges of the original polygon (gure 9, right). This is done with a 2-D sweepline algorithm similar to a polygon clipping algorithm =-=[Weiler80]-=-. This step creates a winged edge data structure. As the sweepline passes across each vertex or intersection point, the order of the emanating edges is found by a radial sort of the geometry. This ord... |