(This is more specifically referring to 3D LUT creations, incase there are other uses of tetrahedral interpolation, which I'm sure there are)
I've been reading about spline interpolation which visually has always been relatively intuitive to me, in regards to how we can use sample-source input and corresponding sample-target values to interpolate further non-sampled target values from other input values.
However, when I think about tetrahedral interpolation in 3D LUT creation, I can't seem to link the use of source sample data and target sample date aids in the interpolation.
To my understanding, we initially analyze which of the 6 tetrahedrons the input (r,g,b) triplet falls into and then proceed to use the 4 corners of these vertices to interpolate. To my knowledge this is usually done by implementing something such as barycentric coordinates.
However, aren't these vertices of the cubes just given the standard unit vectors (1,0,0), (0,1,0), (0,0,1) , (1,1,0) and so on. I don't see how the sample data of source and target comes into play to determine how the unsampled source data will be mapped to our target source.
I hope this makes sense and that this is the correct forum to post this in. Please leave feedback on how I can make this question easier to answer, although a
This is where my understanding,