## Comparison of two Methods of Global Illumination Analysis

Andrei Khodulev

 Contents  Introduction  Overview of Deterministic algorithm  Overview of Monte Carlo algorithm  Scenes used for comparison  Accuracy analysis  Results obtained  Conclusion  Acknowledgments

# 2. OVERVIEW OF DETERMINISTIC ALGORITHM

The task of global illumination algorithm is to solve the well known so called "Rendering equation" [Kaj86]. The equation describes light energy transfer in a very general situation.

TBT does not solve it in full generality. Our model of light-surface interaction accounts for:

• specular reflection (a reflected ray is a mirror image of an incoming ray);
• perfect diffuse reflection (a luminance of reflected light is a constant independent of the viewing direction and the direction of incoming light);
• specular refraction (a direction of a ray passing through a boundary of two materials is determined by the Snell law);
• perfect diffuse transmission (analogous to perfect diffuse reflection but for light crossing the surface).

It should be mentioned, however, that specular refraction is taken into account at the final stage (when a view-dependent image is generated by means of backward ray tracing). Thus, the global illumination algorithm (deterministic) does not account for light refraction (it assumes that light rays pass through transparent materials without change of direction); this is clearly seen in Figure 1a.

## 2.2 Method of solution

Our method of solving the rendering equation belongs to a group of progressive radiosity methods [CCWG88]. It is characterized by the following features:

• The scene patches considered as elementary light emitters / receivers are triangles. We assume uniform and Lambertian distribution of emitted light.
• The energy shooting scheme is used to solve the Radiosity system. At each iteration of energy shooting all emitters with energy higher than some threshold are considered, then the threshold is decreased according to some heuristics and the next iteration is processed. The boundary between "important" and "non-important" emitters becomes lower with each next iteration until it reaches user specified threshold at the final iteration.
• To treat energy transfer by specular reflections the method of virtual emitters is applied; see more detailed description in [MVK94]. A restriction of the method is that it accounts only for plane mirrors.
• Various speed-up techniques are applied. The most important is patches grouping when emitter and receiver are distant enough. Also ray tracing (used to compute visibility of one patch from another) is accelerated by means of the universal method: the uniform space subdivision [FTI86]. (This acceleration method is applied in TBT in all cases where ray tracing is used.)
• The reverse process of triangle subdivision is used when large gradients of illuminance are detected (the so called "adaptive triangle subdivision"). This essentially provide more accurate treatment of high-gradient areas thus increasing the overall accuracy / time factor.

A more detailed discussion of the TBT deterministic global illumination algorithm and some of its extensions can be found in [MK94].

## 2.3 Illumination maps

The result of global illumination analysis describes illuminance distribution in the scene. These data are kept in the form of the so called illumination maps (i-maps). During solution we assume uniform luminance / illuminance of each triangular patch. However, in i-maps (for better looking images) illuminance of each triangle is considered as linearly changing and continuous between adjacent triangles. Necessary recalculation (it is a sort of filtering) is done at the final stage of the global illumination algorithm.

Illumination maps can be later used to generate an accurate image by means of backward ray tracing. During this process DIRECT illumination of each visible point (that is illumination by light going directly from light sources, without intermediate diffuse scattering) is computed explicitly without use of i-maps while only indirect component of illumination is extracted from i-maps (i-maps in TBT keep thedirect and indirect components of illuminance separately). In this way we provide an accurate account for the direct illuminance (in many cases it is absolutely precise).

The direct component of illumination maps is also used in TBT in cases when we need fast display of images with no use of backward ray tracing (for real-time animation, say).

 Contents  Introduction  Overview of Deterministic algorithm  Overview of Monte Carlo algorithm  Scenes used for comparison  Accuracy analysis  Results obtained  Conclusion  Acknowledgments