Диффузиялық шағылыс қолданатын компьютерлік графиканы көрсету әдісі

Computer graphics rendering method using diffuse reflection

In 3D computer graphics, radiosity is an application of the finite element method to solving the rendering equation for scenes with surfaces that reflect light diffusely. Unlike rendering methods that use Monte Carlo algorithms (such as path tracing), which handle all types of light paths, typical radiosity only account for paths (represented by the code "LD*E") which leave a light source and are reflected diffusely some number of times (possibly zero) before hitting the eye. Radiosity is a global illumination algorithm in the sense that the illumination arriving on a surface comes not just directly from the light sources, but also from other surfaces reflecting light. Radiosity is viewpoint independent, which increases the calculations involved, but makes them useful for all viewpoints. Radiosity methods were first developed in about 1950 in the engineering field of heat transfer. They were later refined specifically for the problem of rendering computer graphics in 1984 by researchers at Cornell University and Hiroshima University. Notable commercial radiosity engines are Enlighten by Geomerics (used for games including Battlefield 3 and Need for Speed: The Run); 3ds Max; form•Z; LightWave 3D and the Electric Image Animation System.

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 which have been specifically chosen and placed by the artist in an attempt to create realistic lighting: spot lighting with shadows (placed outside the window to create the light shining on the floor), ambient lighting (without which any part of the room not lit directly by a light source 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.

The surfaces of the scene to be rendered are each divided up into one or more smaller surfaces (patches). A view factor (also known as form factor) is computed for each pair of patches; it is 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 view factors. If other patches are in the way, the view factor will be reduced or zero, depending
on whether the occlusion is partial or total. The view factors are used as coefficients in a linear system of rendering 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 with intermediate radiosity values for the patch, corresponding to bounce levels. That is, after each iteration, we know how the scene looks after one light bounce, after two passes, two bounces, and so forth. This 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 energy 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.

The form factors Fij themselves are not in fact explicitly needed in either of the update equations; neither to estimate the total intensity Σj Fij Bj gathered from the whole view, nor to estimate how the power Aj Bj being radiated is distributed. Instead, these updates can be estimated by sampling methods, without ever having to calculate form factors explicitly. Since the mid 1990s such sampling approaches have been the methods most predominantly used for practical radiosity calculations. The gathered intensity can be estimated by generating a set of samples in the unit circle, lifting these onto the hemisphere, and then seeing what was the radiosity of the element that a ray incoming in that direction would have originated on. The estimate for the total gathered intensity is then just the average of the radiosities discovered by each ray. Similarly, in the power formulation, power can be distributed by generating a set of rays from the radiating element in the same way, and spreading the power to be distributed equally between each element a ray hits. This is essentially the same distribution that a path tracing program would sample in tracing back one diffuse reflection step; or that a bidirectional ray tracing program would sample to achieve one forward diffuse reflection step when light source mapping forwards. The sampling approach therefore to some extent represents a convergence between the two techniques, the key difference remaining that the radiosity technique aims to build up a sufficiently accurate map of the radiance of all the surfaces in the scene, rather than just a representation of the current view.

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). Following the commercial enthusiasm for radiosity enhanced imagery, but prior to the standardization of rapid radiosity calculation, many architects and graphic artists used a technique referred to loosely as false radiosity. By darkening areas of texture maps corresponding to corners, joints and recesses, and applying them via self illumination or diffuse mapping, a radiosity like effect of patch interaction could be created with a standard scanline renderer (cf. ambient occlusion). Static, pre computed radiosity may be displayed in realtime via Lightmaps on current desktop computers with standard graphics acceleration hardware.

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 transformations, texture mapping, hidden surface removal) required to implement radiosity. A strong grasp of mathematics is not required to understand or implement this algorithm.

Typical radiosity methods only account for light paths of the form LD*E, i. e. paths which start at a light source and make multiple diffuse bounces before reaching the eye. Although there are several approaches to integrating other illumination effects such as specular and glossy reflections, radiosity based methods are generally not used to solve the complete rendering equation. 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 uses knowledge of visibility events to generate a more intelligent discretization.

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 terms "diffuse interreflection" and "radiosity" both became confused with "global illumination" in popular parlance. However, the three are distinct concepts. The radiosity method, in the context of computer graphics, derives from (and is fundamentally the same as) the radiosity method in heat transfer. In this context, radiosity is the total radiative flux (both reflected and re radiated) leaving a surface; this is also sometimes known as radiant exitance. Calculation of radiosity, rather than surface temperatures, is a key aspect of the radiosity method that permits linear matrix methods to be applied to the problem.