The automatic reconstruction of 3D models from image sequences is still a very active field of research. All existing methods are designed for a given camera model, and a new (and ambitious) challenge is 3D modeling with a method which is exploitable for any kind of camera. A similar approach was recently suggested for structure-from-motion thanks to the use of generic camera models. In this paper, we first introduce geometric tools designed for 3D scene modeling with a generic camera model. Then, these tools are used to solve many issues: matching errors, wide range of point depths, depth discontinuities, and viewpoint selection for reconstruction. Experiments are provided for perspective and catadioptric cameras.