Robust line-convex polygon intersection computation in E² using projective space representation

Abstract

This paper describes modified robust algorithms for a line clipping by a convex polygon in E2 and a convex polyhedron in E3. The proposed algorithm is based on the Cyrus-Beck algorithm and uses homogeneous coordinates to increase the robustness of computation. The algorithm enables computation fully in the projective space using the homogeneous coordinates and the line can be given in the projective space, in general. If the result can remain in projective space, no division operation is needed. It supports the use of vector-vector operations, SSE/AVX instructions, and GPU.