BRDF(Bidirectional Reflectance Distribution Function) PBR(Physically Based Rendering) — 0. Basic

1. BRDF (Bidirectional Reflectance Distribution Function) PBR (Physically Based Rendering) data investigation

The purpose of PBR is to compute photorealistic light and surface reflections based on physics on 3D programs. However, due to these characteristics, PBR is expensive and is a burdensome technology for applications requiring real-time high-performance computing, such as games.

The factors considered in PBR are as follows:

• Subsurface Scattering
• Fresnel degree of the medium

First, subsurface scattering refers to the phenomenon where, when light comes into contact with an object, some of it is immediately reflected, while others penetrate into the object and cause scattering within. The form of scattering that occurs inside an object due to subsurface scattering is related to whether the object is a conductor. Figure 1 illustrates the actual interaction between light and conductors and insulators.

[Figure 1] Interaction of light between conductors (left) and insulators (right)

1.1. When Subsurface Scattering is applied to a conductor

In the case of conductors, the free electrons inside immediately absorb the energy of light that enters the object. Therefore, in the case of a perfect conductor, only pure direct reflected light exists.

1.2. When Subsurface Scattering is applied to an insulator

In the case of insulators, light interacts with internal atoms and bends, resulting in a mixture of light trapped inside and light escaping back to the outside of the object. Consequently, in the case of insulators, in addition to specular light, diffuse light that passes through the object and bounces back exists. Figure 2 illustrates the distinction between specular and diffuse light in the interaction between an insulator and light.

[Figure 2] Direct reflection and diffuse reflection

1.3. The relationship between light operations and pixels

Figure 3 shows a simplified model of the interaction between light and objects shown in Figure 2.

[Figure 3] Interaction between a simplified object and light. (Top left) When the pixel size is larger than the range of light traveling through the object, (Top right) in this case, it is acceptable to assume that all direct and diffuse reflections occur at the point where the light meets the object. (Bottom) However, when the pixel size is smaller than the range of light traveling through the object, simplification is impossible.

Since BRDF PBR is ultimately intended for use in 3D applications, the relationship between light calculations and the final pixel must be considered.

If the range of light moving inside an object is larger than the size of a single pixel, as shown in the top left of Figure 3, the actual location where diffuse light penetrates the surface may differ. However, since this occurs on a scale smaller than a single pixel, these subtle positional differences can be ignored, and calculations can be performed based on the point where the light first meets the object without affecting the result.

However, if the range of light moving inside an object is smaller than the size of a single pixel, as shown in the bottom of Figure 3, the light calculation applied to that pixel affects other pixels as well, making it difficult to perform a simplified approach.

In many cases, realistic processing for scenarios like the bottom of Figure 3 entails significant computation. Therefore, if a more lightweight lighting is implemented, a simplified model is applied in all cases, whereas if realistic lighting is implemented, models are applied separately for each case.

1.4. Microfacet

BRDF PBR is based on Microfacet theory.

The basic assumptions of microfacets are as follows:

• Surface inhomogeneities are smaller than the observable scale
• However, surface inhomogeneities are larger than the scale at which visible light interacts sufficiently

[Figure 4] Shadows at the microfacet level (left), light calculations ignored (center), and light paths in reality (right)

Generally, BRDF PBR assumes only a single reflection of light. In reality, even in environments where light can be seen through multiple reflections as shown on the right side of Figure 4, if it cannot be seen through a single reflection, it is ignored to reduce computational complexity. Reflecting multiple light reflections exists as a different technique called Ray-Tracing.

1.5. BRDF PBR formula

BRDF is a technique used to overcome the cost burden of PBR and is widely used in applications that must process tens to hundreds of frames per second, such as actual games. Therefore, the formula in Figure 5 also takes lightweighting into significant consideration.

[Figure 5] BRDF PBR Formula

f(l,v) takes l (Light Direction) and v (View Direction) at a microfacet scale and calculates the brightness at that location.

The main components constituting the formula consist of F(l, h), G(l, v, h), D(h), and 4(nl)(nv). The parameters l, v, h, and n used can be seen in Figure 6.

[Figure 6] Components of BRDF PBR operation