In order to enable multi-scale urban visualization, multiple model representations at different levels of detail (LoDs) need to be produced (like by generalization) in advance or on the fly. At local scale, building groups are involved and at least medium LoD is needed in terms of visual perception. Motivated by such demands, this article proposes a novel method for generalizing 3D building groups at medium LoD (the idea was firstly presented in the work of He et al. \cite{He2012a}). The goal is to reduce both geometric complexity and information density. The emphasis is placed on converting 3D generalization tasks into 2D issues via buildings' footprints. The challenge is how to do the mapping from 3D to 2D without losing the information for going back to 3D, especially for a non-prismatic model at medium LoD. Instead of treating such model as a whole, two preprocessing steps (model partition and unit division) are introduced to decompose a model into suitable structures for footprint-based generalization. As a result, basic generalizations units are obtained, and each of them is divided into $Top+Body$. The $Body$ part must be a prism for footprint projection. The $Top$ part can include roofs and upper walls, and it can be transplanted onto the extruded model by displacement or be generalized with adjacent $Top$ parts. Two common types of building groups are studied and different algorithms are developed for their generalization. Experimental results validate the effectiveness of our approach.