Rectilinear Binary Space Partitioning (BSP) trees are often used for solving various types of range searching problems including ray shooting. We propose a novel method for construction of rectilinear BSP trees for a preferred set of ray shooting queries. Particularly, we study ray sets formed by fixing either the direction or the origin of rays. We analyse and discuss the properties of constructed trees. Theoretical considerations are followed by results obtained from the practical implementation. Keywords: ray shooting, ray casting, spatial data structures, BSP tree, clipping.