Divide curve by curvature with control over segment size

I am trying to make some toolpaths more efficient by dividing the path up based on the curvature of that path. It is also important that I can control the maximum and minimum length of the curve segments.

So far I have been able to divide the curve based on curvature and define a maximum length for each segment but defining a minimum length has proven much more difficult. I have a slider (highlighted in red in the definition) which does control the density of the points, but it is not normalized to the world, so I cannot give a specific dimension and the density changes based on the length of the curve being divided.

Any help, specific or general is appreciated. I know there must be a mathematical relationship between the slider controlling the density and the minimum length of the segments but I have not been able to identify that relationship. Thanks!

Attachments:

curvedensitytest.gh, 13 KB
curvedensitytest.3dm, 30 KB

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Permalink Reply by Steve Moody on February 2, 2017 at 5:08pm

After spending the day trying to recall how to do trigonometry, I finally figured out the math needed to (approximately) control the minimum division distance. It's not perfect and there's a couple mysteries in there (for some reason it doesn't work properly unless the the start of the curve has no curvature, my workaround is to simply force a zero into the beginning of the list) but it'll be good enough for my purposes.

Just wanted to share my progress in case anyone else runs across this topic in the future looking for a solution.

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