Information AboutRadiosity |
| CATEGORIES ABOUT RADIOSITY | |
| 3d computer graphics | |
As a rendering method, radiosity was introduced in 1984 by researchers at '', Vol. 18, No. 3. The theory had been in use in engineering to solve problems in radiative Heat Transfer since about 1950.
VISUAL CHARACTERISTICS The inclusion of radiosity calculations in the rendering process often lends an added element of realism to the finished scene, because of the way it mimics real-world phenomena. Consider a simple room scene. The image on the left was rendered with a typical direct illumination renderer. There are three types of lighting in this scene, chosen and placed by the artist in an attempt to create realistic lighting: Spot Lighting with Shadows (to create the light shining on the floor), Ambient Lighting (without which the rest of the room would be totally dark), and Omnidirectional lighting without shadows (to reduce the flatness of the ambient lighting). The image on the right was rendered using a radiosity algorithm. There is only one source of light, an image of the sky placed outside the window. The difference is marked. The room glows with light. Soft shadows are visible on the floor, and subtle lighting effects are noticeable around the room. Furthermore, the red color from the carpet has bled onto the grey walls, giving them a slightly warm appearance. None of these effects were specifically chosen or designed by the artist. OVERVIEW OF THE RADIOSITY ALGORITHM The surfaces of the scene to be rendered are each divided up into one or more smaller surfaces (patches). A form factor is computed for each pair of patches. Form factors are a coefficient describing how well the patches can see each other. Patches that are far away from each other, or oriented at oblique angles relative to one another, will have smaller form factors. If other patches are in the way, the form factor will be reduced or zero, depending on whether the occlusion is partial or total. The form factors are used as coefficients in a linearized form of the rendering equation, which yields a linear system of equations. Solving this system yields the radiosity, or brightness, of each patch, taking into account diffuse interreflections and soft shadows. Progressive radiosity solves the system iteratively in such a way that after each iteration we have intermediate radiosity values for the patch. These intermediate values correspond to bounce levels. That is, after one iteration, we know how the scene looks after one light bounce, after two passes, two bounces, and so forth. Progressive radiosity is useful for getting an interactive preview of the scene. Also, the user can stop the iterations once the image looks good enough, rather than wait for the computation to numerically converge. Another common method for solving the radiosity equation is "shooting radiosity," which iteratively solves the radiosity equation by "shooting" light from the patch with the most error at each step. After the first pass, only those patches which are in direct line of sight of a light-emitting patch will be illuminated. After the second pass, more patches will become illuminated as the light begins to bounce around the scene. The scene continues to grow brighter and eventually reaches a steady state. MATHEMATICAL FORMULATION The basic radiosity method has its basis in the theory of Thermal Radiation , since radiosity relies on computing the amount of light energy transferred among surfaces. In order to simplify computations, the method assumes that all scattering is Perfectly Diffuse . Surfaces are typically discretized into quadrilateral or triangular Elements over which a piecewise polynomial function is defined. After this breakdown, the amount of light energy transfer can be computed by using the known reflectivity of the reflecting patch, combined with the ''form factor'' of the two patches. This Dimensionless Quantity is computed from the geometric orientation of two patches, and can be thought of as the fraction of the total possible emitting area of the first patch which is covered by the second patch. More correctly, radiosity is the energy leaving the patch surface per discrete time interval and is the combination of emitted and reflected energy: : where:
e i) in the rendered environment are integrated for ''BjFji'' ''dAj'', to determine the energy leaving each patch ''j'' that arrives at patch ''i''.
The reciprocity: : gives: : For ease of use the Integral is replaced and constant radiosity is assumed over the patch, creating the simpler: : This equation can then be applied to each patch. The equation is monochromatic, so color radiosity rendering requires calculation for each of the required colors. The constant Fji can be calculated in a number of ways. Early methods used a '' Hemicube '' (an imaginary cube centered upon the first surface to which the second surface was projected, devised by Cohen and Greenberg in 1985) to approximate the form factor, which also solved the intervening patch problem. This is quite Computation ally expensive, because ideally Form Factor s must be derived for every possible pair of patches, leading to a Quadratic increase in computation with added geometry. REDUCING COMPUTATION TIME Although in its basic form, radiosity is assumed to have a quadratic increase in computation time with added geometry (surfaces and patches), this need not be the case. The radiosity problem can be rephrased as a problem of rendering a Texture Mapped scene. In this case, the computation time increases only linearly with the number of patches (ignoring complex issues like Cache use). Using a Binary Space Partitioning Tree can massively reduce the amount of time spent determining which patches are completely hidden from others, in complex scenes. Since radiosity can be computed using standard texture mapping algorithms, it lends itself to acceleration using standard Graphics Acceleration Hardware , available for a standard PC. ADVANTAGES One of the advantages of the Radiosity algorithm is that it is relatively simple to explain and implement. This makes it a useful algorithm for teaching students about global illumination algorithms. A typical direct illumination renderer already contains nearly all of the algorithms ( Perspective Transform ations, Texture Mapping , Hidden Surface Removal ) required to implement radiosity. A strong grasp of mathematics is not required to understand or implement this algorithm. LIMITATIONS
Basic radiosity also has trouble resolving sudden changes in visibility (e.g., hard-edged shadows) because coarse, regular discretization into piecewise constant elements corresponds to a low-pass box filter of the spatial domain. Discontinuity meshing {Link without Title} uses knowledge of visibility events to generate a more intelligent discretization. CONFUSION ABOUT TERMINOLOGY Radiosity was perhaps the first rendering algorithm in widespread use which accounted for diffuse indirect lighting. Earlier rendering algorithms, such as Whitted-style Ray Tracing were capable of computing effects such as reflections, refractions, and shadows, but despite being highly global phenomena these effects were not commonly referred to as "global illumination." As a consequence, the term "global illumination" became confused with "diffuse interreflection," and "Radiosity" became confused with "global illumination" in popular parlance. However, the three are distinct concepts. (This confusion frequently shows up in marketing jargon for commercial software packages - for instance, LightWave has a "radiosity" option for global illumination that is actually more akin to Irradiance Caching .) Yet another source of confusion is the radiometric term "radiosity." In a radiometric context, "radiosity" is the power per unit area (W/m^2) leaving a surface. This term is uncommon outside of computer graphics, and is more typically called " Radiant Exitance ." REFERENCES EXTERNAL LINKS
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