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What do you mean GPUs don't support them? Most opengl tutorials I've read have people building triangles in 2d to learn fragment shaders and vertices before going 3d. Most of them also support parametric curves, so even hardware accelerated bezier curves should be possible.
Wait, why do you say GPUs support parametric curves? GPUs are based on triangles mostly.
You can builds all kinds on top of pixels and triangles.