Project 3E - Physically Based Rendering

Compile the proj3E.cxx file, and run the executable by passing a .gltf file as a command line argument.

For the first part ( 8 points), all the work is to be done in the fragment shader. For the additional goals, you may need to modify the other files.

I would still recommend going through the display loop of the main program.

Instructions

• $p$ is the fragment position
• $V$ is the camera direction ( the direction of outgoing light )
• $L$ is the light direction ( the direction of incoming light )
• $N$ is the normal of the surface
• $\alpha$ is the roughness factor
• $H$ is the halfway vector, $H = normalize(L+V)$
• $F_0$ is the base reflectivity , $(0.4,0.4,0.4)$ for nonmetals, and the $albedo$ value for metals

For directional light, the amount of light recievced is equal to $f_r(p,N,V,L) * L_i(p,L) * (N \cdot L)$

Where $L_i$ is the light intensity function.

The Cook-Torrance Bidirectional Reflective Distribution Function $f_r$

$$f_r = \frac{K_d * albedo}{\pi} + K_s * f_\text{cook-torrance-specular}$$

$$f_\text{cook-torrance-specular} = \frac{DFG}{4 * (V \cdot N)(L \cdot N)}$$

In the above,

• $D = NDF_{TR-GGX}(n, h, \alpha) $
• $G = G_{Smiths-Method}(N,V,L,k)$
• $F = F_{Schlick}(H, V, F_0)$
• $K_s = F$
• $K_d = 1 - K_s$ (and 0 for all metals. multiply with (1-metallic)) $$NDF_{TR-GGX}(N, H, \alpha) = \frac{\alpha^2}{\pi((N \cdot H)^2 (\alpha^2 - 1) + 1)^2}$$

$$G_{Smiths-Method}(N,V,L,k) = G_{SchlickGGX}(N, V, k) * G_{SchlickGGX}(N, L, k) $$

$$G_{SchlickGGX}(N, incoming\_vec, k) = \frac{N \cdot incoming\_vec} {(N \cdot incoming\_vec)(1 - k) + k }$$

For directional light, $$k = \frac{(\alpha + 1)^2}{8}$$

$$F_{Schlick}(H, V, F_0) = F_0 + (1 - F_0) ( 1 - (H \cdot V))^5$$

It is a bunch of formulas, but all of them are relatively straightforward to implement.

For the Light Intensity function, we are going to use the light direction before normalization. The distance from light source to object is $length(L_{not \hspace{.2em} normalized})$. We then have an initial value (usually around $(30,30,30)$ to $(50,50,50)$ and divide it by the distance obtained.

gamma correction: (+0.5 points)

Apply gamma correction on the final color. Also, make sure to reverse the correction on the base albedo texture.

Ambient Occlusion (+0.5 points)

Read the texture from the AO map, and multiply with the albedo texture to get the final albedo color.

Normal Maps (+2 points)

Recommended: Without Normal Maps, your results won't look as good. Implement normal maps by first implementing the bitangent vector in the vertex shader using the following formula:

$bitangent = normalize( N \times tangent.xyz ) * tangent.w$

Then, create the TBN matrix ( a 3x3 matrix of tangent, bitangent and normal as rows) in the fragment shader. Read the value of the normal texture, normalize the value to be between -1 and 1 (when you read it, it will be between 0 and 1). Then, your new normal vector would be $TBN * normal_{texture}$

Displacement Maps and Parallax Occlusion Mapping (+3 points)

For some assets, displacement maps are provided. Use them to implement parallax occlusion mapping! Also have to modify the config file to load the displacement texture.

Add 3 more light sources (+2 points)

You have to have the intensity and color information in the config file, and figure out a way to pass the data to the fragment shaders using uniforms ( have to modify the main cxx file).

Note: The screenshots folder has helpful outputs showing just specific channel values as color for the default config parameters.

Note: The results of all dot products must be positive!