Radiosity was first developed in the field of thermal engineering (Siegel & Howell, 1984) to account for radiative heat transfer between elements in furnaces. This research was first applied to computer graphics in 1984 at both Cornell and Hiroshima University yielding the radiosity rendering method. Its basis rests on the notion of conservation of radiative energy in a closed environment .Heat transfer theory describes radiation as the transfer of energy from a surfaces when that surfaces has been thermally excited.

This "thermal radiation" theory can be used to described the transfer of many kinds of energy between surfaces, including light energy.

As in thermal heat transfer, the basic radiosity method for computer image generation makes the assumption that surfaces are diffuse emitters and reflector of energy, emitting and reflecting energy uniformly over their entire area. It also assumes that an equilibrium solution can be reached, that all of the energy in an environment is accounted for, through absorbtion and reflection

Radiosity rendering is a method that calculates the lighting effects of ideal diffuse reflections. Other rendering techniques do not consider diffuse reflection as accurately as radiosity methods and rather use a directionless "ambient lighting " term to provide a very crude approximation. This ambient term is usually constant over the entire surface and does not depend of the presence of abscence of nearby objects. Thus leading to poor results with regard to diffuse reflections [see Pic 3.].

Pic 3. Diffuse Reflectance Comparison

The radiosity equation describes the amount of energy which can be emitted from a surfaces, as the sum of the energy inherent in the surfaces (a light sources, for example) and energy which strikes the surfaces, being emitted from some other surfaces. The energy which leaves a surfaces (surfaces "j") and strikes another surfaces (surfaces"i") is attentuated by two factors:

• the "form factor" between surfaces "i" and "j", which accounts for the physical relationship between the two surfaces
• the reflectivity of surfaces "i", which will absorb a certain percentage of light energy which strikes the surfaces

Pic 4. Radiosity Equation

Such an equation exists for each discrete patch, the complete environmet produces a set of N simultaneous equations that can be represented in a matrix form [see Pic 6.].

Pic 5. Radiosity Equation

These simultaneous equations can be solved in an iterartive fashion using a method called Gauss-Seidel iteration.

The form factor is defined as the fraction of energy leaving one surface that reaches another surfaces. It is a purely geometric relationship, indepedent of viewpoint or surfaces attribute. (see Pic 6)

Pic 6. Radiosity Calculation of Form Factors

Differentiation of the basic form factor equation is difficult even for simple surfaces, as the result a researcher by the name of Nusselt developed a geometric analogy which allows a relatively simple and accurate calculation of the form factor between a surface and a point on a second surface.

The "Nusselt analog" involves placing a hemispherical projection body, with unit radius, at a point on a surface. The second surface is spherically projected onto the projection body, then projected onto the base of the hemisphere. The form factor is, then, the area projected on the base of the hemisphere divided by the area of the base of the hemisphere [see Pic 7.].

Pic 7. Hemisphere approach to Form Factors

Looking for an even more efficient method, Cohen and Greenberg, developed an alternate method for computing form factors. This method involves placing the center of a cube at a point on a surface, and using the upper half of the cube (the "hemicube" wh ich is visible above the surface) as a projection body. Each face of the 5 faces of the hemicube are subdivided into a set of discrete areas. Each of these new discrete areas have a pre-computed form factor value. A given surface is then projected onto the hemicube; next the pre-computed form factors are summed from the discrete areas that have been projected on, yielding an approximation to the true form factor [see Pic 8.].

Pic 8. Hemicube approach to Form Factors

Radiosity Substructuring

To start the radiosity process, the virtual modeled world is broken into a finite number of N discrete patches [see Pic 9.].

Pic 9. Discrete Patches

As previously mentioned the virtual modeled world is initially broken into a finite number of N discrete patches. If we create a finer mesh by uniformly increasing the number of discrete patches we will get better results. However, this will come at a very high increase in computational cost. Cohen, Greenberg, Immel & Brock created a substructuring method that adaptively sub-divides the original N patches only at locations where a high radiosity gradient (or difference) was found minimizing the amount of new patches necessary to create better results [see Pic 10.]. I won�t go into the details, just know that this has been addressed with research and a solution .

Figure 10. Substructuring

Application for Radiosity Techniques

In general, radiosity is most useful in application where ideal diffuse interreflection is important and the geometry is static. The view independent approach is particularly valuable when the exploration of the 3D model is required, rather than the production of the single static image

The application of radiosity in many field :

• Architectural Dessign
• Lighting Design
• Theatrical Design
• Lighting Optimization
• Remote Sensing
• Visual Shape Understanding
• Infrared Signature Analysis
• Fine Arts

Radiosity Images

Japanese Room Modelling and Rendering using Maya's software from�@Alias Created by Yanuar

Brick Style Room Modelling and Rendering using Maya's software from�@Alias Created by Yanuar

Stone Style Room Modelling and Rendering using Maya's software from�@Alias Created by Yanuar

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