  An effective solution to the problem of Hermite $G^1$ interpolation with a
clothoid curve is provided. At the beginning the problem is naturally
formulated as a system of nonlinear equations with multiple solutions that is
generally difficult to solve numerically. All the solutions of this nonlinear
system are reduced to the computation of the zeros of a single nonlinear
equation. A simple strategy, together with the use of a good and simple guess
function, permits to solve the single nonlinear equation with a few iterations
of the Newton--Raphson method.
  The computation of the clothoid curve requires the computation of Fresnel and
Fresnel related integrals. Such integrals need asymptotic expansions near
critical values to avoid loss of precision. This is necessary when, for
example, the solution of interpolation problem is close to a straight line or
an arc of circle. Moreover, some special recurrences are deduced for the
efficient computation of asymptotic expansion.
  The reduction of the problem to a single nonlinear function in one variable
and the use of asymptotic expansions make the solution algorithm fast and
robust.
