Even if you load OpenGL quadrants, the triangle is executed by the driver on the processor side before it even gets on the GPU. Modern GPUs these days eat nothing but triangles. (Well, the lines and dots.) So, something will triangulate, whether you or the driver - it does not really matter where this happens.
This will be less efficient if, say, you do not reuse vertex buffers, and instead re-fill them again with quads (in this case, the driver will have to re-initialize each vertex buffer), instead of the pre-processed triangles, but this is rather far-fetched (and the problem you have to fix in this case is only that you replenish vertex buffers).
I would say, if you have a choice, stick to the triangles, since this is that most content pipelines are laid out anyway, and you are less likely to encounter problems with non-planar ATVs and the like. If you want to choose the format that your content is in, then for sure use triangles, and the triangulation step will be skipped altogether.
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