why is there a difference between per fragment lightning and per vertex ?


in per fragment lightning, we use the normal that has been interpolated between vertices to compute light factor,
in per vertex lightning, we use the per vertex normal but we let the lightning factor interpolate instead of normal

i am noob at maths and i don’t understand, why is there a difference ? in both cases the result depends on interpolated value, shouldn’t the interpolated lightning factor be the same as the lightning factor we would calculate with an interpolated normal ?


Because many of the equations involved in lighting would plot as curves if you drew graphs of them, meaning that they don’t linearly interpolate. For example, normalization involves taking a square root, and the graph of a square root is a curve.