University of Pennsylvania, CIS 561: Advanced Computer Graphics, Homework 8

Yilin Liu

31955379

Here are some example screenshots of what your implementation should look like with varying amounts of roughness and metallicness:

• L_o is the light that exits point p along ray ω_o.
• L_e is the light inherently emitted by the surface at point p along ray ω_o.
• ∫_S is the integral over the sphere of ray directions from which light can reach point p. ω_o and ω_i are within this domain.
• f is the Bidirectional Scattering Distribution Function of the material at point p, which evaluates the proportion of energy received from ω_i at point p that is reflected along ω_o.
• L_i is the light energy that reaches point p from the ray ω_i. This is the recursive term of the LTE.
• V is a simple visibility test that determines if the surface point p' from which ω_i originates is visible to p. It returns 1 if there is no obstruction, and 0 is there is something between p and p'. This is really only included in the LTE when one generates ω_i by randomly choosing a point of origin in the scene rather than generating a ray and finding its intersection with the scene.
• The absolute-value dot product term accounts for Lambert's Law of Cosines.

In order to save space in your repository, we have uploaded a .zip file to Canvas containing the environment map .hdr files and .json scene files you can load into your program. Download this .zip and extract its contents into the same folder your .pro is in. We have also added a .gitignore that will ignore these folders when you push your code to Github. Make sure, then, that you explicitly git add any custom scene files you write as part of your extra credit.

Make sure that you fill out this README.md file with your name and PennKey, along with your example screenshots. For this assignment, you should take screenshots of your OpenGL window with the following configurations:

• 0% metallic, 0% rough, RBG = 1 1 1
• 100% metallic, 0% rough, RGB = 1 1 1
• 100% metallic, 25% rough, RGB = 1 1 1
• cerberus.json, with a camera angle that shows the model in profile

All code written for this point-light based PBR shader will be implemented in three different .glsl files:

• pbr.frag.glsl (same name as last assignment, different code)
• diffuseConvolution.frag.glsl
• glossyConvolution.frag.glsl

While we are implementing the paper Real Shading in Unreal 4, you can find an excellent in-depth tutorial on its implementation on LearnOpenGL.org. For this assignment, you will want to refer to the following two articles:

• Diffuse irradiance with image-based lighting
• Specular image-based lighting

While you are encouraged to refer to the articles on LearnOpenGL.org linked above, we want to make sure that you are doing more than simply copying the code listed there. As such, you must assign specific names to variables that serve particular purposes, as the code linked above uses different names:

• Name: wo | Purpose: The ray traveling from the point being shaded to the camera
• Name: wi | Purpose: The ray traveling from the point being shaded to the source of irradiance
• Name: wh | Purpose: The microfacet surface normal one would use to reflect wo in the direction of wi.
• Name: R | Purpose: The innate material color used in the Fresnel reflectance function

Please make sure to use this terminology in all three .glsl files where appropriate.

Implement the main function of diffuseConvolution.frag.glsl so that it takes samples of u_EnvironmentMap across the set of directions within the hemisphere aligned with the input surface normal. Please carefully read the comments in this shader file in order to determine what the surface normal is in the context of this shader.

When you have implemented the diffuse irradiance map, you can view it as your scene's background by modifying the code in MyGL::renderEnvironmentMap(). Below are two examples of what you should see (excluding the appearance of the sphere, as you have not yet implemented the PBR shader).

Default environment map:

Fireplace environment map:

Now that you have your diffuse Li term, you can implement one portion of pbr.frag.glsl. Using the surface normal direction in the shader, sample the diffuse irradiance cubemap (u_DiffuseIrradianceMap) and combine it with your material's albedo. If you set this as your output color, and set your material properties to the ones shown below, you should be able to match these screenshots (also, don't forget to apply the Reinhard operator and gamma correction):

Default environment map:

Fireplace environment map:

Fireplace environment map (viewed from another angle):

Implement the main function of glossyConvolution.frag.glsl so that it takes samples of u_EnvironmentMap via importance sampling based on the GGX normal distribution function. Please carefully read the comments in this shader file in order to determine how you should orient the glossy BRDF lobe you'll be importance sampling.

When you have implemented the glossy irradiance map, you can view it as your scene's background by modifying the code in MyGL::renderEnvironmentMap(), and uncommenting the invocation of textureLod in envMap.frag.glsl. Below are two examples of what you should see (excluding the appearance of the sphere, as you have not yet implemented the other portion of the PBR shader).

Default environment map:

Panorama environment map:

Now that you have your glossy Li term, you can implement the other portion of pbr.frag.glsl. You must compute the following attributes of your Cook-Torrance BRDF:

• Fresnel term using the Schlick approximation
• The combined D and G terms by sampling u_BRDFLookupTexture based on the absdot term and roughness.

Then, use wi to sample u_GlossyIrradianceMap using textureLod, along with roughness to determine the mip level.

You must also compute kD based on your kS term, and multiply it with your diffuse component.

If you combine your diffuse and glossy colors into your output, and set your material properties to the ones shown below, you should be able to match the screenshots shown in the very beginning of these instructions.

Modify pbr.frag.glsl and pbr.vert.glsl to do the following:

• Alter N to align with the direction given by u_NormalMap when u_UseNormalMap is true
• Alter displacedPos so that it is displaced along the surface normal by u_DisplacementMagnitude times a scalar obtained from u_DisplacementMap when u_UseDisplacementMap is true.

Create your own custom JSON scenes and load them into your project. Create texture maps for as many material attributes as you can for more interesting surface appearance. The more interesting and numerous your scenes are, the more points you'll receive. You'll also have created excellent material for your demo reel in the process!

Along with your project code, make sure that you fill out this README.md file with your name and PennKey, along with your test renders.

Rather than uploading a zip file to Canvas, you will simply submit a link to the committed version of your code you wish us to grade. If you click on the Commits tab of your repository on Github, you will be brought to a list of commits you've made. Simply click on the one you wish for us to grade, then copy and paste the URL of the page into the Canvas submission form.