Get the latest tech news
Closed form arc length parametrization is impossible for quadratic Bézier curves
Bézier curves are widely used for defining vector graphics. They are basically polynomial parametric curves, but given in the Bernstein basis, which enables us to define the curve using control points.
The arc length parametrization of a quadratic Bézier is also generally accepted to have no closed form solution, but I’ve also not seen a proof for that before. Don’t worry if you’re not so deep into abstract math, I’m basically applying some substitutions to bring the relevant expression into a form where I can use a known result. I’ve learned some Galois theory, which enables you to prove that a polynomial has no solution in radicals (the nth roots), but that is clearly not immediately applicable here.
Or read this on Hacker News