ATI cards follow DX9 specs. OpenGL requires higher Specs.
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This shows that Nvidia has better IQ than ATI.
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A trilinear filter is a linear interpolation between two bilinear samples, requiring a weight between 0 and 1. ATI allocate five bits for this weight, which matches Direct3D's reference rasterizer (however, higher precision is allowed by Direct3D and in fact desirable). In OpenGL, SGI - who spearheaded the inception of this API - use eight bits. That's also the standard that's followed by, eg, Nvidia's GeForce range that implements the 8 bit linear interpolation weight for both OpenGL and Direct3D.
This shows that Nvidia has better IQ than ATI.