https://fgiesen.wordpress.com/2013/02/17/optimizing-sw-occlu...
(articles 6, 7, 8, others are not closely related)
As far as I know modern hardware has been non-scanline-based for ages btw.
For a 3D renderer, I recommend fgiesen's series as linked above, and the older series by Nicolas Capens: http://forum.devmaster.net/t/advanced-rasterization/6145
In terms of a software rasterizer, which can often be faster, it's just a matter of elbow grease and engineering. Use SIMD. Implement tons of special cases.
Write a simple polygon plotter to get you started -- just fill a triangle with white with simple edge functions. Then work your way up to arbitrary polygons. And then look into the theory behind antialiasing and such.
Whoa, I want to hear about this. I have a couple of DSP firmware images I've shied away from reverse engineering as I don't know the platforms.
* Compression (lossless, lossy, image, audio, texture, video)
* Languages (bytecode interpreter, AST interpreter, parser/lexer for a simple language, simple JIT, understanding instruction scheduling)
* DSP programming (writing programs for fast, branchless math)
* Comfort with binary and binary formats (start with packfiles .zip/.tar, move onto reverse engineering simple formats for e.g. games)
* Understanding the difference between RAM and address spaces (e.g. understanding virtual memory, mmap, memory-mapped IO, dynamic linking, the VDSO, page faulting, shared memory)
* Device drivers (easier on Linux, understanding userspace/kernel interaction, ioctls, how hardware and registers work, how to read spec sheets and hardware manuals)
* Graphics (modern software rasterizer that's not scanline-based, understanding 3D and projective transforms, GPU programming and shaders, basic lighting (reflection and illumination) models, what "GPU memory" is, what scanout is, how full scenes are accumulated all along the stack)
I could go heavily into depth for any one of these. Ask me questions if you're interested! They're all fun and I always have more to learn.
Also, the longer you get into any given track, the more you realize they all connect in the end.