This thesis explores different approaches for the acceleration of raytracing calculations on the graphics processing unit (GPU). For that a voxel grid is used and extended by the linespace data structure. The linespace consists of direction based shafts and stores the objects located in those shafts in a candidate list. Different methods for the sorting and traversal of the linespace are presented and evaluated. The shown methods cannot provide a speed up of the frame rate without resulting in a loss of image quality.