In computational geometry, different ways of space partitioning have been developed, including the Voronoi diagram of points and the power diagram of balls. In this article, a generalized Voronoi partition of overlapping d-dimensional balls, called the boundary-partition-based diagram, is proposed. The definition, properties and applications of this diagram are presented. Compared to the power diagram, this boundary-partition-based diagram is straightforward in the computation of the volume of overlapping balls, which avoids the possibly complicated construction of power cells. Furthermore, it can be applied to characterize singularities on molecular surfaces and to compute the medial axis that can potentially be used to classify molecular structures.