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paraboloid question

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Question about Jason Zink's Dual Paraboloid Mapping article:

Would the paraboloid mirror he suggests 0.5 - 0.5 (x^2 + y^2) work in real life?

I think it introduces a slight warp in the resulting texture, this is my attempt to show it:[{Tan[ArcTan[Cos[%28x*0.5%2B0.5%29+pi]%2FSin[%28x*0.5%2B0.5%29+pi]]0.5]%2C+-x}%2C+{x%2C+-1%2C+1}]

I understand that because the 2nd derivative of his mirror is 0 it will be perfectly smooth - but does that also mean all incident rays (to a point) will be reflected in the same direction?

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