  We present a variation of the method of regularized Stokeslet (MRS)
specialized for the case of forces and torques distributed over filaments in
three dimensions. The new formulation is based on the exact solution of Stokes
equation generated by a linear continuous distribution of regularized forces
along a line segment. Therefore, a straight filament with linearly varying
forces does not require discretization. A general filament is approximated by a
piecewise linear curve in three dimensions where the length of each line
segment is chosen only based on the variation of the force field and the
desired accuracy of its piecewise linear approximation. The most significant
advantage of this formulation is that the values of the regularization
parameter $\epsilon$ and the length of the segments $h$ are decoupled as long
as $\epsilon<h$ so that $\epsilon$ can be selected as a proxy for the radius of
the filament and $h$ is chosen to discretize the forces and torques. We analyze
the performance on test problems and present biological applications of sperm
motility based on existing models of swimming flagella in open space and near a
plane wall. The results show, for example, that because the forces along the
flagellum vary mildly, a flagellum can be approximated with as few as 11
segments of length $h$ while fixing the regularization parameter to
$\epsilon=h/30$, overcoming the need for hundreds of discretization nodes
required by the MRS when $\epsilon$ is small. The filament behaves like a
slender cylindrical tube of radius $\approx 0.97\epsilon$ so that the value of
$\epsilon$ influences the flagellum's swimming speed. For fixed regularization,
doubling the number of line segments does not affect the results significantly
as long as the force field is resolved. Examples that require rotlets and
potential dipoles along the filament are also presented.
