I need an automated way to find cusps in planar curves. Attached is a 3dm with some curves where I've manually marked each cusp with a green point.



The best approach I've thought of is something like a comb diagram where I array short teeth along the curve and look for places where the teeth cross the curve. Basically where the curve gets close to itself.



- Peer

Hi Peer, unfortunately the curve solvers available to me do not support curves with a tangent discontinuity internal to a span.

So I don't think I've got anything that could help with that.

Maybe some strategies here:
https://math.stackexchange.com/questions/1140778/b%C3%A9zier-curve-higher-order-detect-sharpness-serpentine-or-cusp-in-curve

- Michael

This is over my head, so I'll just give the link for uv.es pdf:
It concerns Nurbs curves and singularities, but mentions the beziers, and "extends" the (whatever).
At the end it mentions that one nurbs curve can have a singular point. (Which Moi can already do... I guess)

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C48&q=A+Property+on+Singularities+of+NURBS+Curves+Authors%3A++A.+Arnal+%2C++A.+Lluch+%2C++J.+Monterde&btnG=

- Brian

Michael: thanks for telling me there's no solver for this. That's good to know. The link was also pretty useful.

Brian: the paper you linked looks good, though haven't fully digested it yet.

Thanks to both of you I think I've got a solid basis for solving this.

- Peer