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That used to be true, but right now you not only can, but have to control every pixel. The fixed pipeline is dead, now you have to write your own shaders and those can do literally anything. Or use CUDA/OpenCL for even more power.

Shaders still have plenty of limitations relative to a CPU (you can do virtually anything with them, but some tasks are too expensive to do efficiently). In particular, taking advantage of temporal and spacial coherence is much more tricky on a GPU - on a CPU the early 3D renderers could effectively use this stuff with scanline and fill tricks.

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