The Lienard--Wiechert field of an arbitrarily moving charge can be visualized with the aid of electric and magnetic field lines. The system of such lines is Lorentz-invariant if a specified motion along Poynting vectors is ascribed to them. In this note the field lines are parametrized by light signals emitted from the trajectory. Ordinary differential equations are obtained describing the instantaneous configuration of electric and magnetic field lines. These equations have been solved in a general form for the magnetic field, and for the electric field in the case when the quantity $\tau/\kappa\gamma$ is constant where $\gamma$ is the Lorentz factor of the charge, and $\kappa$ and $\tau$ are the curvature and torsion of the trajectory.