This thesis presents the use of a local linespace data structure, which is designed and implemented on the basis of an existing GPU-based raytra- cer with a global linespace data structure. For each scene object, an N-tree is generated whose nodes each have a linespace. This saves informations about existing geometry in its shafts. A shaft represents a volume between two faces on the outside of the node. This allows a faster skipping of em- pty spaces during raytracing. Identical objects can access already calcula- ted linespaces, which can reduce the memory requirement by up to 94.13% and the initialization time of the datastructure by up to 97.15%. Due to the local access possibilities dynamic scenes can be visualized. An increase in quality can also be observed.