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Originally Posted by Malekos
Hmmm...
C++,
GDI
Algebra...
That's all?
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Sure, to start, but for high-performance graphics, you will need to move beyond GDI, and since Windows does not allow arbitrary direct hardware access, that leaves DirectX as the lowest-level method available to you.
I would recommend starting with a 2D engine first (like a tile-based game). Don't forget you can mix polygons with plain 2D stuff. In fact, a polygon is a 2D shape, so all 3D accelerators can be used in 2D engines (for example, to rapidly blit texture-mapped tiles to the screen). Then, when you're comfortable with that, move on to some pseudo-3D stuff, like a slivering engine. If you don't know what that is, it's an engine that builds up a 3D view from multiple verticle 'slivers' which are scaled in height according to how far they are from the camera location. Old games like Heretic, Hexen, and the original DOOM used this technique. This approach should yield satisfactory performance on modern machines, even if you're using GDI. After you've gotten that down, you can move on to DirectX and a pure-polygon 3D engine.