Non-Uniform Rational B-Splines are the dominant geometric representation format in Computer Aided Design. BRL-CAD's support for these primitives is relatively recent, and while we can raytrace them we do not have the ability to perform operations such as surface/surface intersection calculations. These abilities are fundamental to a wide variety of editing operations and essential to the process of converting implicit-primitive based boolean geometry trees to evaluated NURBS models.
This task would target the problem of implementing an algorithm to calculate surface/surface intersection for general NURBS surfaces. These guys implemented something very similar although their implementation was not robust: http://www.cs.unc.edu/~geom/CSG/boole.html These guys followed that work and implemented a robust solution, but killed performance: http://www.cs.unc.edu/~geom/ESOLID/ (Note that while the papers are excellent references from which to get ideas, the source code from these efforts is not license compatible with BRL-CAD.) You will need to be very careful about tolerances and tolerance tracking without resorting to fixed-precision arithmetic. There are a variety of other research papers on the surface/surface intersection problem - students interested in this topic should discuss it with developers on the IRC channel or via email.
- Familiarity with C++
- Solid mathematical foundations