The automatic recognition of geometric constraints during user interaction in virtual assembly and maintenance operations relies in the determination of intersecting surfaces between virtual prototypes. This is a central problem in many virtual prototype applications, where it is necessary to find collisions precisely and interactively. This paper presents an unified framework, for the broad and narrow phases of the collision detection problem, to determine precisely intersecting surfaces in a virtual prototyping environment. The proposed algorithm is based on R-tree structures and on the Overlapping Axis-Aligned Bounding Box (OAABB) for reducing the overall time complexity of the collision detection algorithm. We show that the OAABB concept used together with the R-tree data structure can be used effectively to eliminate the number of surfaces that cannot intersect and improve performance. The proposed architecture also facilitates the implementation using parallel computing methods.