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<J1A8480>
inPhase some eastern ago i made these https://pasteboard.co/j1gRIga2IkO4.png which look similar but are mathematically different - not just variations but different constructions one has circle segments the other parabolas the other is scaled etc ..
<J1A8480>
the bottom row are similar and mosh eggs consisting of circle segments
<InPhase>
J1A8480: I should have saved the link I based mine on, because now I can't find it again, but some page had written a bunch of different options, and I looked for the one that appeared most prone to algebraic rearrangement plus parameterization. And one said: x^1.5-a^1.5x+y^2=0 showing that a set the horizontal length of the sideways egg. I swapped x and y to make it vertical, fixed a to 1, and
<InPhase>
recognized the real parameter was the deviation of the ^1.5 from 2, and started playing with that. I saw valid values ranged from 1 to infinity with 2 as symmetric, and therefore I introduced 1+exp(asym) so 0 on my asym would be symmetric.
<Guest42>
I am making a DN10, 15,20, 25,32 ISO flange... and the real measurements are 17.7mm, 22mm, 27mm... (no math relation) I need to make conversions based on the DN selection to optimize code. what is the best way you can think of?
<InPhase>
J1A8480: So basically made up, but with a hint from a bunch of options on some web page.
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<InPhase>
Guest42: "make conversions" as in what? You mean map 15 to 17.7, 20 to 22?
<InPhase>
Guest42: If you're used to thinking in Python terms or similar, here's some code I whipped up one day to produce dictionaries in OpenSCAD, along with some usage examples: https://bpa.st/AW6A Feel free to steal it. Consider it public domain or CC0 if you need a formal license.
<InPhase>
Guest42: Here I did lookup because it gives exact values for exact inputs, interpolates for intermediate values (out of standard), and I have it extrapolating based on the trailing relationship for past the end.
<InPhase>
There's a similar lookup table below that for the hex drive widths, although on reflection the interpolation is probably sketchier there and I should have done a round. (Not sure what I was thinking.)
<InPhase>
J1A8480: If you're interested, I morphed the equation a little more last night after sharing it to give a little more variability down in the saturated end. I thought it might be interesting to flatten out the ends a little more at the extreme that had stopped varying. I'm not sure if that corresponds to any real birds though, since I was finding good fits on the existing stuff, but I figured why not.