# Linear 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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I'm slightly confused by the question. You seem to be talking about a matrix made up of variables in x, y and z. Normally speaking transformations are done with matrices of constants which can handle all the usual rotation/translation/projection.

However I'm gonna guess that you're using a vertex shader to do some kind of non-linear transformation. This means that a straight line transformed in this way (mathematically speaking) would not be transformed to a straight line, but since vertex shaders only transform the end points of lines (vertices of triangles) which are then treated as though they are joined by a straight line. In other words to get the correct effect with such a transformation all of your triangles have to be small to get a good approximation to the non-linear result, which means using linear interpolation locally is a good approximation. As far as I know the standard projective space linear transform (i.e. 4x4 matrix) can be used to do all transformations which can be linearly interpolated correctly in view space.

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