  A novel static algorithm is proposed for numerical reparametrization of
periodic planar curves. The method identifies a monitor function of the
arclength variable with the true curvature of an open planar curve and
considers a simple interpolation between the object and the unit circle at the
curvature level. Since a convenient formula is known for tangential velocity
that maintains the equidistribution rule with curvature-type monitor functions,
the strategy enables to compute the correspondence between the arclength and
another spatial variable by evolving the interpolated curve. With a certain
normalization, velocity information in the motion is obtained with spectral
accuracy while the resulting parametrization remains unchanged. Then, the
algorithm extracts a refined representation of the input curve by sampling its
arclength parametrization whose Fourier coefficients are directly accessed
through a simple change of variables. As a validation, improvements to spatial
resolution are evaluated by approximating the invariant coefficients from
downsampled data and observing faster global convergence to the original shape.
