Cornu spiral connection

I know this reply is a bit old, but I thought about implementing various clothoids awhile back in order to generate curves for producing Victorian scrolls with a v-cut router bit. The main issue here is to make an editable, very smooth curve with an inflection point. I also considered it for making "fair’ curves for boats. In my particular case, I came to the conclusion I needed a bit more flexibility which required piecewise clothoids like those used here for violin scrolls http://zhurnal.lib.ru/m/muratow_s_w/violin_design.shtml and didn’t feel ambitious enough to finish building a plug-in thinking I’d probably revisit the issue by specifying a smooth curvature graph as the piecewise function.

My stopping point ended up with fitting a curve to two endpoints, the tangents at those endpoints and an interior tangent vector that allowed including/excluding the inflection point. This doesn’t address fitting the minimum length curve to join a line and a circle, which I think is actually much easier, but if anyone is interested, I could probably be talked into finishing my train of thought in a couple months when I have spare time. The attached plot shows an example, and I should add that the number of turns as well as tightness to some degree is also settable.

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thats not true. transition curves, mainly clothoids, are used for roads and railways.