Add distance-to-curve sections

[behdad]

For quadratics, it's solvable, eg:

http://blog.gludion.com/2009/08/distance-to-quadratic-bezier-curve.html

For cubics, perhaps introduce a couple approximations.

[Pomax]

yeah, it pretty much involves (for any curve order) finding all points that have a normal that pass through the off-curve point. I can probably write up a bit on iteratively finding those and then picking the result(s) that have minimal distance. For quadratic that solution can be found directly, cubic and higher will be a little more work although in terms of "what we do", pretty much identical

[Pomax]

and interesting shortcut might be to arc-approximate the curve and then do a quick "point close to which arc?" and then us that to restrict the search. No idea if that'd be faster than LUT iteration, but perhaps worth testing?

[deanm]

There is a paper worth reading on this topic:

Improved Algebraic Algorithm On Point Projection For Bézier Curves Xiao-Diao Chen, Yin Zhou, Zhenyu Shu, Hua Su, Jean-Claude Paul

https://hal.archives-ouvertes.fr/inria-00518379/document

Basically it just discusses some details in the root finding approaches, and their contribution is an additional check to filter out / skip calculating some roots that can't be a minimum distance.

[adrientetar]

Improved Algebraic Algorithm On Point Projection For Bézier Curves

FWIW there's a C++ implementation here: https://github.com/nrtaylor/CubicSplineClosestPoint