For the displaying 3D Polygon Animations section of the assignment you don’t need to get to technical. Just research and have a base understanding of how 3D images/animations are displayed on screen.
Microsoft Direct3D: Part of the DirectX package and a competitor to openGL. It is an application programming interface (API) which renders 3D objects. Designed to speed up 3D rendering within Windows. All mainstream graphics cards support it.
Direct X Graphics Pipeline: https://msdn.microsoft.com/en-us/library/windows/desktop/ff476882%28v=vs.85%29.aspx?f=255&MSPPError=-2147217396
Render Engines: https://yellowdog.co/2016/01/28/which-is-the-best-render-engine/
Pixel & Vertex Shaders: Pixel & Vertex