*The following is a transcription of one of my independent projects while I was a student at SCAD. The original page is still available here. With RPS 17 and beyond, most of these features are standard, and I haven't continued development as I no longer have a RenderMan license at home. I hope this information is useful!*

Understanding various specular models was one of the main goals of this project. First, I implemented several specular models with punctual/point light sources. At that point, the difference between the specular models is just slight changes to the shape of the fake specular ping. However, I implemented these models in the following order so that I might better understand the underlying concepts before trying to grasp a full physically-based material. All of these models are explained in great detail else on the web, so I will stick with very short descriptions.

I first started with the most basic specular model, Phong [1]. The Phong model attempts to address that surfaces do not simply reflect in one direction, but tend to spread out as an indication of roughness. Phong reflection is one simple equation, where the angle between the reflection and view vectors is raised to some power. The value of the poewr determines the sharpness of the highlight. Below are a couple of examples. This shader is not energy conserving in any way, so as the highlight becomes more blurred, the specular multiplier must be lowered to keep values realistic.

Jim Blinn made a key change to the Phong model by introducing the concept of a*half vector* [2]. The half-vector is the angle halfway between the view and light vectors. Phong requires the reflection vector to be computed, which is a more expensive operation. Blinn observed that if the half-vector is computed and compared to the surface normal, this was roughly equivalent to comparing the view and reflection vectors. The resulting exponent value is different, but the overall look is very similar to Phong but much cheaper to compute.

The next models I attempted to implement were the Ward isotropic and anisotropic models. Ward sought to create the simplest formula possible to match real-world measurements and as such the Ward model is more complex than the previous Phong and Blinn models. The isotropic version was very straightforward to implement from Ward's 1992 paper [3], but the anisotropic version requires tangent and bitangent vectors orthogonal to the surface normal. This is not straight- forward to compute using built in RenderMan functions, as the shading point only has a dPdu and dPdv function. This only provides predictable numbers with parameterized surfaces, so I used a piece of code from Ali Seiffouri's website to compute the tangent and bitangent vectors. I look forward to spending more time developing my own solution to this problem when I have an opportunity.

Finally, I implemented the Cook-Torrance specular model, or more specifically the modified Cook-Torrance present in Walter et al's 2007 paper. Cook-Torrance is a proper microfacet BRDF specular model, and is of the form described in the BRDF overview section. Unlike the other specular models mentioned before, the Cook-Torrance specular correctly dims out as the roughness increases.

I have opted to leave out the maths for the above specular models, but more detail can be found in the references if interested.

### REFERENCES

[1] - The Phong Reflection model

[2] - Models of light reflection for computer synthesized pictures

[3] - Measuring and Modeling Anisotropic Reflection

Some slides from Cornell about MIS