Science of Rendering

Alright, after getting my nerves fried, let's tackle this shall we.
First off, math and science are involved in the process of rendering, and in a few different forms. Geometry is used due to it's involvement with the working of shapes, while coinciding with 3D coordinates, vectors, and matrices, to give off the illusion of space and depth.
Now from the stand point of differences between Rasterization and Ray Casting. First off, Rasterization is based on drawing points from the object to create the needed effect, aka Object Centric. Ray Casting is instead Image Centric, meaning it instead takes in consideration all images and where they are in comparison to the camera. Ray Casting also fixes some of the errors with Rasterization, such as fixing a visibility problem by taking the closest point if points intersected in a process called Z-Buffer. On top of this, Rasterization is not practical for things like shadows, reflections, and refractions, all of which needed to be done in Ray Casting.
With the topic of direct and indirect illumination, we need to know the differences first. Direct illumination is when light is reflecting directly from the source to the objects present in a scene. With indirect illumination, it simulates real world principles by having light bounce from everything present, giving a more realistic image. The issue that arose from this was that power of rendering was everything, and many who tried to use it, for example Pixar, didn't use indirect illumination until farther down the road. When it was used though, it created something truly realistic and special that gave life to what it was applied to.
The fact that in time, render time and power would improve is in part to Moore's law and Blinn's law. Moore's law involved the number of transistors in a dense integrated circuit will double every two years. However, Blinn's law starts that even with advances in technology, render time remains consistent. While Blinn's law may seem off, we have to think about how as technology advances, we are throwing more and more into this tech.
Really, CGI is an amazing art form, the fact that not everyone is capable should be proof enough to classify it as such. CGI allows filmmakers to build creative worlds of fantasy, loveable and memorable characters, and stunning stories that can only be brought to life through this method.
All and all, this video was really helpful when it comes to learning the work that goes behind this ever evolving form, and how far we've come in such a short time.