If one then tries to do some FEM analysis of e.g. the air flow around the body of the car, these small mismatches between the patches create big problems in the computation. The obvious way to solve this is to make sure that the designer is not allowed to make these kind of errors. One then gets what are known as G1 surfaces, but although this has been done, it is not in wide use because of, among other things, the lower degrees of freedom that the designer then has.
The problem thus remains of what to do with the existing CAD surfaces that exhibit these pathological mismatches. One has to find a method to decide whether two NURBS patches are "close enough" to fit together. In other words, one is looking for a computer algorithm to decide if two puzzle pieces that are incorrectly cut, are meant to fit together.
The aim of this project is to find a mathematical formula of a "metric" in the space of curves, that gives a measure of how "alike" two curves are. The general 3D problem is quite hard, but the hope is that the special case of a pair of 2D straight line elements can be done. The formula must then be implemented as a computer program in C++, evaluated and compared to other approaches.