  Isogeometric analysis (IGA) is a numerical method that connects
computer-aided design (CAD) with finite element analysis (FEA). In CAD the
computational domain is usually represented by B-spline or NURBS patches. Given
a NURBS parameterization of the domain, an isogeometric discretization is
defined on the domain using the same NURBS basis as for the domain
parameterization. Ideally, such an isogeometric discretization allows an exact
representation of the underlying CAD model.
  CAD models usually represent only the boundary of the object, thus, for
planar domains, it is given as a collection of curves. Finding a suitable
parameterization of the interior is one of the major issues in IGA, similar to
the mesh generation process in FEA. The objective of this parameterization
problem is to obtain a set of patches, which exactly represent the boundary of
the domain and which are parameterized regularly and without
self-intersections. This can be achieved by segmenting the domain into patches
which are matching along interfaces, or by covering the domain with overlapping
patches. In this paper we follow the second approach.
  To construct from a given boundary a planar parameterization suitable for
IGA, we propose an offset-based domain parameterization algorithm. Given a
boundary curve, we obtain an inner curve by generalized offsetting. Those two
curves define a ring-shaped patch, which has a hole that can be covered by a
multi-cell domain. Consequently, the domain is represented as a union of two
overlapping subdomains which are both regularly parameterized. On such a
configuration, one can employ the overlapping multi-patch method introduced in
(Kargaran, J\"uttler, Kleiss, Mantzaflaris, Takacs; CMAME, 2019), to solve PDEs
on the given domain. The performance of the proposed method is reported in
several numerical examples, considering different shapes of the domain.
