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#Engine Base (or, Unimaginatively Titled Engine Name, Uten)

I'm reading a book called "Tricks of the 3D Game Programming Gurus: Advanced 3D Graphics and Rasterization" by Andre Lamothe. The author defines a "Virtual Computer", which I'd describe as an abstraction layer on top of the OS, providing convenient functions for game programming without worrying about OS particulars like window creation, handling window events, etc. His code's all based on DirectX 8-9 era code on Windows (the book was released in 2003), C, and the odd C++-ism thrown in. I'm following the book on Linux in 2016, so I'd like an engine based on SFML and using more modern C++ constructs.

What's my purpose? Learn the math. Using it in some code seems like a good way to do that. Why do I want to know the math behind rasterization algorithms? Curiosity. What's the practical use? None, that I know of. How do I expect to make money from it? I think these questions are missing the point of learning something cool. OK, to be honest, it ties in slightly to my interest in the game Ultima Underworld. I'd like to have a better point of reference to understand some of the more classic rendering techniques, and in my mind, that means focusing on some math that I think I'm weak in and its application in the context of computer graphics.