  The method of regularized Stokeslets (MRS) is a numerical approach using
regularized fundamental solutions to compute the flow due to an object in a
viscous fluid where inertial effects can be neglected. The elastic object is
represented as a Lagrangian structure, exerting point forces on the fluid. The
forces on the structure are often determined by a bending or tension model,
previously calculated using finite difference approximations. In this paper, we
study Spherical Basis Function (SBF), Radial Basis Function (RBF) and
Lagrange-Chebyshev parametric models to represent and calculate forces on
elastic structures that can be represented by an open curve, motivated by the
study of cilia and flagella. The evaluation error for static open curves for
the different interpolants, as well as errors for calculating normals and
second derivatives using different types of clustered parametric nodes, are
given for the case of an open planar curve. We determine that SBF and RBF
interpolants built on clustered nodes are competitive with Lagrange-Chebyshev
interpolants for modeling twice-differentiable open planar curves. We propose
using SBF and RBF parametric models within the MRS for evaluating and updating
the elastic structure. Results for open and closed elastic structures immersed
in a 2D fluid are presented, showing the efficacy of the RBF-Stokeslets method.
