Roger Breton wrote:
Is tetrahedral interpolation more involved, computationally?
It uses less computation. It uses dimension + 1 vertices of a grid cell. N-linear interpolation uses 2^dimension (ie. all of) the vertices of a grid cell. So that's a difference of 5 to 16 for CMYK->whatever, or 4 to 8 for RGB/Lab/XYZ->whatever
From a quality point of view the recommendation is to use simplex/tetrahedral interpolation for spaces that are "device like", ie. A->B tables typically, where neutral lightness changes are strongly correlated to equal changes in the input channels.
For spaces where a change in neutral lightness is correlated to one input channel while the the others remain about the same, the N-linear is recommended. This is the case for doing L*a*b*-> whatever, ie. a B->A table. For actual overall (optimised for speed) transforms, simplex/tetrahedral is usually used anyway, because it's the fastest (unless you are using GPU hardware texture mapping). Graeme Gill.