Arc-fibration kernels of arc-spline domains

Any star-shaped domain admits a polar parameterization with straight parameter lines originating from a center point in its kernel. Arc-fibrations use circular arcs instead of straight lines; specifically, an arc-fibration is a regular polar parameterization whose parameter lines are circular arcs. The existence of arc-fibrations has been studied recently for domains defined by -smooth boundary curves, and the arc-fibration kernel–the set of points that can serve as centers of an arc-fibration–has arisen in the investigation of arc-fibrations. We extend earlier results in two ways: (1) we generalize arc-fibrations to domains with boundary curves, including arc splines; and (2) we analyze the arc-fibration kernel for arc-spline domains and present an algorithm to compute it, demonstrating its performance on several examples. • Arc-Fibrations of arc-spline domains are introduced and investigated. • The arc-fibration kernel is the set of points that can serve as centers. • Arc-fibration kernels of arc-spline domains are shown to be arc-spline domains. • Algorithm AFKC computes arc-fibration kernels of arc-spline domains.