A Comparison of O(1) and Cyrus-Beck Line Clipping Algorithms in E2 and E3

TL;DR

This paper compares a new O(1) line clipping algorithm with the traditional Cyrus-Beck method in 2D and 3D, demonstrating significant speed improvements through preprocessing and innovative geometric techniques.

Contribution

It introduces a novel O(1) complexity line clipping algorithm for convex polygons and polyhedra in E2 and E3, utilizing dual space and projection methods, with theoretical and experimental validation.

Findings

The new algorithm achieves O(1) processing complexity.

Preprocessing significantly accelerates line clipping.

Experimental results confirm the efficiency of the proposed method.

Abstract

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.