A 3D graphics system usually consists of two major subsystems: geometry subsystem and rendering subsystem. The geometry subsystem performs transformation, lighting, backface culling, and clipping. The clipping is to remove the part of a triangle that is outside of the view volume by calculating the intersections of the triangle edges with view planes. The clipping operation turns out to be a time-consuming procedure in the geometry subsystem. In this thesis, we present several clipping algorithms and their hardware implementations, and compare the performance in the geometry subsystem. Furthermore, a new pre-clipping algorithm is also proposed to reduce the number of triangles that need to go through the clipping operations in order to reduce the burden of clipping operations in the whole geometry subsystem. The whole geometry system including the pre-clipping and clipping hardware is verified in a complete 3G graphics system in the Versatile FPGA demonstration board.