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Hardware Interpolation

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Hi, everybody, I've a problem about interpolation. As we know, when data are transformed from vertex shader to pixel shader, hardware will automatically interpolate attributes of the vertices to produce pixels' attributes. Furthermore, this interpolation is linear with 1/z. My question is that, if I apply a transform M for each vertex P. what's the requirement for M such that hardware can guarantee the following interpolation is still linear? for example, M11 = x^2 + 3y + 4/z, M12 = x, M13 = y^3, M14 = z; M21 = ..... M31 = ..... M41 = ..... can hardware guarantee the following interpolation is linear (after M*P)? thanks very much!

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