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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:


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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