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Algorithm/Numerical Approach for Computing CI (Contrast Index)

Recently I've been plotting my film test curves using R (sorry Bill), which I also use for smoothing them. I can calculate a myriad of gradients by getting a linear regression of any section of the fitted smooth curves, but I would like to code a procedure for calculating CI. I have used the hand-held technique, using the CI "ruler" with points marked off at 0.2 and 2.2 log E, and I think I understand the concept of the two concentric arcs described here. I have also seen discussions about automating curve-related plotting in several threads:

While there is a lot of discussion about curve fitting, that is not one of my issues—I find that R fits a good enough curve for me. It usually does it using LOESS, and the fitted curve is a *little* odd just to the left of the point where the toe takes off, but this is *not* my concern, as the search for CI takes place further to the right of that point anyway, in the section where the curve seems to look good. Besides, I am sure it wouldn't be too hard to fix the wonky section if needed, after all the smooth fit uses splines.

What I would like to ask for, please, is a pointer towards a suitable algorithm to use the just found curve to calculate the CI. I assume no weird curve shapes, and generally good inputs. If nothing can be found, then I will be resigned to writing a short loop, that "walks" the curve looking for the intersection of the 3 points on a straight line, first at x=FB+F, the other distant 0.2 and lying on the curve and the third, distant from the first 2.2, and also on the curve. But I am sure someone must have already coded that in a more elegant way than just doing a brute search along the curve.

FYI, example of plots, I'd be happy to share the few lines of R code if anyone cares:

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Many thanks.