@raphlinus i have heard that @Keavon might be interested in this being in a kurbo release… thoughts?

I've fixed the merge conflict. @Keavon can you confirm this is still useful, and that review comments have been addressed to your satisfaction?

@raphlinus This is still useful and the code/comments indeed look good!

It would also be useful to have a normal_to_point function as well, and add support for quadratic and linear segments in addition to cubic. (For linear, only normal is applicable and it will only return a single t value.) But I wouldn't suggest delaying this until those can be included, because this is useful in its own right.

For some context surrounding Graphite and Bezier-rs:

In Graphite, we're preparing to begin replacing some Bezier-rs functionality with Kurbo because it has better robustness, so this will be helpful to have. Our motivation for making Bezier-rs was twofold:

• Needing more features/algorithms (normals/tangents to point is an example of one). But our scope also includes more sophisticated ones like Poisson-disk point sampling that would be out of scope for Kurbo. Rapid implementation mattered more than robustness/correctness in the short term for us, but now we're getting towards desiring more robustness. Kurbo's performance is likely also considerably better and that's starting to matter to us a lot more too.
• Needing to represent the data structure as "manipulator groups" (anchor + that anchor's 0/1/2 handles) rather than SVG d path command style segments (0/1 outward handle, 0/1/ inward handle, and anchor) so our tools didn't need to pay the performance penalty for translating between Kurbo SVG-style and our tools' manipulator group style; but this requirement has changed and is no longer a factor, which means Kurbo would be just as efficient for us, leaving only point 1 above regarding features. Hence, the desire to have these tangent/normal to point algorithms implemented.

Maintenance and the future of Bezier-rs is still up in the air but I'm envisioning it as a possible wrapper for Kurbo that could use those algorithms that exist and augment it with our additional features that Kurbo currently lacks (or always will), such as the Poisson-disk point sampling linked above. Downside: Bezier-rs would no longer be a zero-dependency crate. Upside: we can reduce our maintenance burden through deleting a lot of our code by wrapping Kurbo's algorithms, provide better robustness and performance, and probably continue to use Bezier-rs as a testbed or incubator for more complex algorithms instead of needing to officially abandon our maintenance for the crate if we fully switched to Kurbo in Graphite.

Unless I hear otherwise or someone else merges this, I will merge this during or after office hours today.

I'm merging it now. Sounds like there's a good discussion to be had about future coevolution of bezier-rs and kurbo. The poisson disk feature looks quite interesting, but as you say it's probably not in scope for kurbo.

I'm very excited about bezier-rs moving some things into Kurbo!

I should go through and create a comparison chart about which algorithms each of our libraries implement in order to focus attention towards those which may be useful in Kurbo. But I need to emphasize that our algorithms are somewhat janky and probably aren't fast or robust enough for the standards of Kurbo. Though it would still be a useful way to evaluate what may be worth reimplementing in Kurbo with better attention towards those fine details.