  Region extraction is a very common task in both Computer Science and
Engineering with several applications in object recognition and motion
analysis, among others. Most of the literature focuses on regions delimited by
straight lines, often in the special case of intersection detection among two
unstructured meshes. While classical region extraction algorithms for line
drawings and mesh intersection algorithms have proved to be able to deal with
many applications, the advances in Isogeometric Analysis require a
generalization of such problem to the case in which the regions to be extracted
are bounded by an arbitrary number of curved segments. In this work we present
a novel region extraction algorithm that allows a precise numerical integration
of functions defined in different spline spaces. The presented algorithm has
several interesting applications in contact problems, mortar methods, and
quasi-interpolation problems.
