We discuss a new one-dimensional non-LTE time-dependent radiative-transfer technique for the simulation of supernova (SN) spectra and light curves. Starting from a hydrodynamical input characterizing the homologously-expanding ejecta at a chosen post-explosion time, we model the evolution of the entire ejecta, including gas and radiation. Non-LTE, which holds in all regions at and above the photosphere, is accounted for. The effects of line blanketing on the radiation field are explicitly included, using complex model atoms and solving for all ion level populations appearing in the statistical-equilibrium equations. Here, we present results for SN1987A, evolving the model "lm18a7Ad" of Woosley from 0.27 to 20.8d. The fastest evolution occurs prior to day 1, with a spectral energy distribution peaking in the range 300-2000A, subject to line blanketing from highly ionized metal and CNO species. After day 1, our synthetic multi-band light curve and spectra reproduce the observations to within 10-20% in flux in the optical, with a greater mismatch for the faint UV flux. We do not encounter any of the former discrepancies associated with the HeI and HI lines in the optical, which can be fitted well with a standard Blue-supergiant-star surface composition and no contribution from radioactive decay. The effects of time dependence on the ionization structure, discussed in Dessart & Hillier, are recovered, and thus nicely integrated in this new scheme. Despite the 1D nature of our approach, its high physical consistency and accuracy will allow reliable inferences to be made on explosion properties and pre-SN star evolution.