In this paper two improvements to speed up collision detection are described. Firstly, a method called oncollide sphere-tree, OCST for short, is presented. This approach works by detecting collisions among models with arbitrary geometry using the video card’s Graphics Processing Units, GPU. While candidate parts of colliding objects are being detected, the OCST is constructed for collision evaluation in parallel, at the same time. Thus, the OCST is created in real–time. Secondly, we have tested two kinds of triangulated representation models for the same original–objects. We have evaluated triangle–soup and triangle–strip models to speed up the algorithm response when computing collisions. The method has been described, implemented and tested for the two kinds of triangulated models, and the obtained results are shown.