In this paper, the collision prediction between polyhedra under screw motions and a static scene using a new K dimensional tree data structure (Multiresolution Kdtree, MKtree) is introduced. In a complex scene containing a high number of individual objects, the MKtree represents a hierarchical subdivision of the scene objects that guarantees a small space overlap between node regions. The proposed MKtree data structure succeeds in performing simultaneously space and scene subdivision. MKtrees are useful for broad phase collision and proximity detection tests and for time-critical rendering in large environments requiring external memory storage. The paper proposes an efficient broad phase collision prediction algorithm. Examples in ship design applications are presented and discussed.. Keywords Collision Prediction and Detection, Large Environments, Hierarchical Representations, Virtual Reality, Screw motions.