The most common solution to solve imprecision problems introduced by the arithmetic of computers is to use exact arithmetic. In the first part of this thesis, we suggest an extremely efficient optimization of rational arithmetic : the lazy rational arithmetic. The originality of this arithmetic is to postpone exact computations until they are either useless or inevitable. In that way, unnecessary exact computations are never made. Lazy arithmetic is an autonomous library which solves imprecision problems by itself, independently of computer programs using it. The second part of this thesis describes a modelling tool using photographs of objects to model them in a constructive solid geometry description. It is an interactive tool with which the user may build what he needs with the most adapted detail level for his own application. Proposed extensions for image synthesis may be used to solve image incrustation consistently with shadows, lights and environment reflections.
