A comparison of a new algorithm for line clipping in E2 and E3 by convex polygon and/or polyhedron with O(1) processing complexity and Cyrus- Beck algorithm is presented. The new algorithm in E2 is based on dual space representation and space subdivision technique. The principle of algorithm in E3 is based on the projection of polyhedron to three orthogonal E2 coordinate systems. Algorithms have optimal complexities O(1) and demonstrates that preprocessing can be used to speed up the line clipping significantly. Obvious applications are for one polygon and/or polyhedron and many clipped lines. Detailed theoretical estimations and experimental results are also presented.