• Global Illumination: we implemented simple path tracer to trace a number of bouncing rays from diffuse surface. Instead of tracing perfect reflected ray like in the previous project, we perturb the reflected rays (randomly pick rays in the upper hemisphere) and use Monte Carlo to find the color at a particular pixel. The path tracer runs much slower than the ray tracer.
• Environment Mapping: we added Environment class, ConstantEnvironment class that returns the constant color background and HDREnvironment class that stores the *.pfm environment file. When a ray misses all the objects, it will return the environment color instead of returning black background like the previous project.
• Motion Blur: we added time variable to each ray so that each ray will trace at different time. For a given interval, we find the (startTime + random * endTime) and set that time into a ray. This will make the moving objects look blur. 
• New Primitives: We use math methods to find out the intersections of the rays with the primitives (they are not made from triangles so we can save space storage and run faster)
• Box
• Cone 
• Cylinder

We also optimize our Kd tree acceleration. Now a 100,000 triangle Stanford Dragon scene runs in less than 60s and a thousand sphere scene runs in 0.3s!

We fixed our Refraction feature to output more realistic by using Fresnel equation and good approximation which is referenced in the book (Schlick, 1994a) Fundamentals of Computer Graphics 3rd Edition by Peter Shirley and Steve Marschner

Enough said, now here are our results: