This paper presents very high dynamic range VLBI observations of the quasar 3C345 at 18 cm wavelength at two epochs, 1981.11 and 1985.27. We find that the direction of the jet changes drastically and the surface brightness decreases with increasing distance from the core. We show that a true three-dimensional curvature of the jet in space is needed to obtain the observed decrease of intensity with distance from the core, both in an adiabatic expansion model as well as in a model where the comoving flux is constant. Our observations confirm the detection of a previously reported low surface brightness component, C0. In addition, there is a large component extended perpendicular to the jet axis which we associate with a stationary shock at a distance consistent with the expected position of the narrow line region. Models for the intensity of the jet fitted to the observed dependence of intensity with distance from the core suggests this shocked region to be the place where the jet is expanding adiabatically after having had a constant width closer to the core. A limit on the allowed viewing angle theta less-than-or-similar-to 40-degrees is derived from the lack of any detectable counterjet.