This ends up being a minimization problem on a 6th-degree polynomial. If the user is tracking the nearest point over time, then starting the minimization from a nearby reference point could give quick convergence with a basic algorithm. Otherwise, we could find all roots of the derivative in [0, 1] using http://www.cemyuksel.com/research/polynomials/.
This ends up being a minimization problem on a 6th-degree polynomial. If the user is tracking the nearest point over time, then starting the minimization from a nearby reference point could give quick convergence with a basic algorithm. Otherwise, we could find all roots of the derivative in [0, 1] using http://www.cemyuksel.com/research/polynomials/.