Nothing in nature is truly uniform, so our auroras would be deficient if we did not somehow account for the variability of an aurora's thickness. To do this the quick and dirty way, I used--big surprise--another B-spline, where the control points have dimension one: they are simply distances measured in pixels.
The change to the rendering algorithm was simple. Instead using a maximum distance property for the aurora, I calculate where the ray from the pixel crosses the spline, saving the t-parameter value. That value is in the range [0, 1], so it is fed as an input into the distance spline function. The output of that is the maximum field distance. That distance is compared to the pixel's distance to the aurora skeleton spline, and the color interpolation is done according to that distance. It provides a nice sense that the spline dimensions are changing. In addition, it adds realism because the color bands no longer have a uniform shape as they blend into one another, so the geometric properties of the aurora appear to be more complicated than they actually are.
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