Arc fibrations of planar domains

It is well known that star-shaped domains possess particularly simple polar parameterizations, which are formed by the line segments that connect a suitably chosen center with the points on the domain's boundary. The polar parameterization is valid (i.e., regular everywhere except for the center) if the center is located in the kernel of the domain. In the case of a domain with a smooth free-form boundary curve, the kernel is a convex region which is enclosed by the curve and (some of) the boundary's inflection tangents. These parameterizations possess numerous applications, most recently also including domain parameterization in isogeometric analysis.