A question that might be asked about this research is why it is so important to use a technique like spline interpolation? Does linear interpolation not suffice? From a mathematical perspective, I am trying to do justice to the fact that aurora colors are produced by the excitation of atmospheric oxygen and nitrogen. Because of the chemical properties of atomic and molecular oxygen and ionized nitrogen, each respond differently to excitation. Not only do these elements produce different colors, but they also have a varying excitation time--anywhere from 0.7s to 110s. This fact dictates that some colors can only have so much influence, because the photons they release do not contribute as much to how we perceive color as the more plentiful photons coming from excitations that last longer.
Since B-splines have local support at more than simply 2 points (or color vectors in our case), which allows us to reflect the contributions from multiple sources in a continuous way. Notice how, in the picture above, the top bar of each pair shows piecewise linear interpolation. We can see a line between the pieces, which is undesirable. In the bottom bar of each pair, we see that B-spline interpolation duplicates the gradient without any deficiency. The discontinuities are a consequence of the fact that linear interpolation has support only between two points and is not C2 continuous.
I realize it might be difficult to discern a difference on some monitors. What I am trying to get at is that there is a discontinuity in the top bar directly in the middle, and in the second bar from the bottom dividing it into thirds.
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