Ray tracing is a fundamental technique in computer graphics used for rendering realistic

images. Answer the following questions:

b$)$ Explain the concept of ray$-$object intersection in ray tracing. How is this intersection point

calculated for common geometric objects such as spheres and planes?

c$)$ Describe the difference between a bounding volume hierarchy $($BVH$)$ and a k$-$d tree. When

would you choose to use one over the other in a ray tracing application?

d$)$ Implement the basic ray$-$sphere intersection algorithm using pseudo$-$code. Discuss its

limitations and possible optimizations