Line Segment Clipping using Quadrilateral Concavity and Convexity

2026-04-30

AI Summary

This work proposes a novel line-clipping algorithm that overcomes limitations of traditional methods, which often treat clip-window boundaries or input segments as infinite lines, thereby computing spurious intersections and performing redundant divisions. The proposed approach instead models both the clipping window edges and the input segment as finite line segments and leverages the convexity or concavity of the quadrilateral formed by their endpoints to efficiently determine whether a genuine intersection exists. This geometric insight enables a “test-then-intersect” paradigm that uniformly handles line segments in arbitrary configurations while eliminating unnecessary intersection computations. Experimental results demonstrate that the algorithm outperforms classical techniques—including Cohen-Sutherland, Liang-Barsky, Nicholl-Lee-Nicholl, and Skala—in terms of execution efficiency on randomly generated line segments.

Abstract

This paper proposes an algorithm for clipping line segment against an axis-aligned rectangular window. The conventional algorithms for line segment clipping treat the clipping boundary and/or the line segment to be clipped as line. The present algorithm treats the clipping boundary and the line segment to be clipped as line segment and using this strategy, it succeeds to avoid computation of false intersection points. A quadrilateral is constructed using the end points of a clipping boundary segment and the end points of the line segment to be clipped as its vertices. The concavity and convexity of the quadrilateral dictates whether a line segment actually intersects the clipping boundary. If the quadrilateral is found to be concave then the line segment is rejected, otherwise the point of intersection of the line segment with the clipping boundary is computed. Since a 'test & intersect' approach is used instead of a 'intersect & test', hence the proposed algorithm does not compute false intersection point thereby reducing the number of divisions required to obtain a clipped line segment. Only one routine can process line segments at any position. Improved performance is observed with respect to the Nicholl-Lee-Nicholl, Liang-Barsky, Cohen-Sutherland and Skala's algorithm through experiments with random line segments using a metric based on execution time.

Problem

• line segment clipping
• false intersection
• clipping algorithm
• axis-aligned rectangle
• computational geometry

Innovation

• line segment clipping
• quadrilateral concavity
• convexity test
• false intersection avoidance
• axis-aligned rectangle