Radiosity

Global Illumination

Global Illumination is the term given to models which render a view of a scene by evaluating the light reflected from a point $x$ taking into account all the that arrives at that point. Consideration is give not only to light arriving directly from light sources but from all indirect illumination due to light interacting with other objects.

Local reflection models deal with direct illumination only, ignoring interactions with other objects and required add-on algorithms to handle effects such as shadows, reflections and transparency. Global methods can handle these phenomena inherently.

The two established global algorithms are raytracing and radiosity. Neither is a complete solution. Raytracing attempts to render perfect^11.1 specular reflection. Radiosity deals with the more difficult problem of diffuse^11.2 interaction.

The essential difference between the implementation of the two methods is that raytracing traces ray from the pixel into the scene back to the light sources, while radiosity follows light from light sources through the scene as patch-to-patch diffuse interaction. The radiosity solution needs to be passed through a traditional visibility process to deal with projection and Hidden Surface Removal .

Radiosity

Radiosity was developed from systems designed to model the transfer of heat in closed systems, but was adapted to deal with light transfer. Radiosity considers the diffuse interaction between 'patches'(polygons) in the scene. Because diffuse reflection is not view-point dependant (unlike specular reflection), the radiosity solution is view-independent. This has two important consequences.

1. Radiosity needs to be calculated for all points in the scene rather than just the points visible to the viewer.
2. Once a solution is calculated, that solution remains valid for all viewpoints as long as the scene doesn't change.

Figure 10.1: Cornell Box, the "Hello World" of Radiosity

Radiance

Diffuse reflection occurs when light strikes surface and that some light is reflected (equally in all direction) This reflected light is called radiance. Any given surface in a scene is irradiated (receives light) and radiates light. The core of radiosity is calculating how light radiated from one surface illuminates another surface.

The Radiosity Process

Initially the scene is divided into a number of flat patches. Light sources are considered as light emitting patches. Light is 'shot' from the sources into the scene and 'stored' by different patches in varying amounts, depending on their distance and orientation.

Each patch will radiate some of the absorbed light back into the scene (the exact amount will depend on surface properties. The patch with the highest unradiated light then shots its light back into the scene to be stored by other patches. The patch with the next highest stored light is processed. This continues until a very high proportion on the original light has been distributed.

At any stage, some of the light will arrive back at patches which have already been considered. This implies that the process needs to be iterative. Between 20 & 500 iterations are needed.

The transfer of light between any two patches is calculated using the geometric relationship between the two patches, this relationship is known as the form factor. The form factor determine what proportion of light emitted by a patch will arrive at another patch. The form factor needs to be calculated for every pair of patches in the scene (i.e is a scene contains $n$ patches, $n^2$ form factors are needed. The form factor also needs to take into account the presence of any intervening patches.

Substructuring

The cost of radiosity depends on the square of number of patches in the scene ($O(n^2)$). To keep processing costs down, the patches are made large and the light intensity across a patch is assumed constant. However is introduces problems where there is an illumination discontinuity across a patch (e.g a shadow). To resolve this problem, a patch needs to be subdivided if there is a discontinuity across the patch.

Figure 10.2: Subdivision of the Cornell Box

In order to determine which patches need to be subdivided and by how much, a process known as progressive refinement is adopted. This process generates progressively accurate images. The progressive refinement procedure involved iterating the radiosity process subdividing patches each time. At each iteration new form factors need to be calculated and the radiosity begins again.

Hemicubes

To calculate the form factor between a patch and the remainder of the scene, a hemicube is placed onto the center of the patch. This hemicube is divided into a number of pixels^11.3. Other patches are projected onto the sides of this hemicube, with the center of the original patch acting as the center of projection. The number of 'pixels' onto which a patch has been projected will determine the form-factor. Where two or more patches project onto one pixel, a Z-buffer type approach is used to determine which is the nearest.

Figure 10.3: Projecting a patch onto a hemicube

Radiosity Problems

There are 3 significant problems with radiosity rendering.

1. Algorithm Artifacts Certain assumptions and approximations necessary for radiosity can cause visual problems such as Mach Banding in a scene.
2. Specular Reflection Radiosity deals only with diffuse reflections, hence does not render Specular reflection at all. Most radiosity systems, incorporate a final 'Raytracing pass' to overlay specular effects on the final image.
3. Rendering Time The calculations of forms factors and the iterative nature of radiosity make the method unsuitable for real-time rendering.