Project 3d points or NURB curve onto NURB surface parameter space

Question

I have a NURB surface bounded by NURB curves, how do I find their parameterization wrt to the NURB surface? I am using openNurbs by McNeel and Associates to evaluate the NURB entities themselves, but have no tool to project the points, or transform their parameterization. My current solution is to use steepest descent to approximate 3d points along the curve, but this is very inefficient.

Answer 1

I am using the solution proposed by http://www.geometrie.tugraz.at/wallner/sproj.pdf A second order algorithm for orthogonal projection onto curves and surfaces by Hu and Wallner.