2D line and polygon clipping based on space subdivision

Abstract

This paper introduces a new approach to 2D line and polygon clipping against a rectangular clipping region, using space subdivision into cells, with the clipping region as the central cell. The line segment path is traced through the cells, and entries into and out of the cell corresponding to the clipping region enable computation of the intersection of the line segment with crossed cell edges. Tracing the line segment path is computationally very simple, leading to an algorithm that only computes intersections that are part of the clipped line segment. The new algorithm is compared to other standard line clipping algorithms with simulations and operation counts.

A Brief Survey of Clipping and Intersection Algorithms with a List of References (including Triangle-Triangle Intersections)

“…Other proposed modifications of algorithms can be found in Bui (1999), Andreev and Sofianska (1991), Bao and Peng (1996), Devai (2005Devai ( , 2006Devai ( , 1998, Duvalenko et al (1990Duvalenko et al ( , 1993Duvalenko et al ( , 1996, Cai et al (2001), Day (1992aDay ( , 1992b, Evangeline and Anitha (2014), Kaijian et al (1990), Kodituwakku et al (2013), Kong and Yin (2001), Maillot (1992), Wei et al (2013), Slater and Barsky (1994), Ray (2012aRay ( , 2012bRay ( , 2014Ray ( , 2015, Li (2016), Singh and Lumar (2016), Dev and Saharan (2019).…”

“…As the edges of the convex polygon are ordered, the algorithm with the O(lg N) complexity was derived by Skala (1994). An algorithm based on space subdivision was described in Slater and Barsky (1994).…”

Another Simple but Faster Method for 2D Line Clipping

“…There are four primary methods for line clipping: Cohen-Sutherland, Cyrus-Beck [2], Liang-Barsky [15] and Nicholl-Lee-Nicholl [18]. Over the years, other algorithms for line clipping appeared, like Fast Clipping [29], Dörr [5], Andreev and Sofianska [1], Day [3], Sharma and Manohar [24], Skala [25] [26] [27], Slater and Barsky [28], Ray [23], [22] but many of them are variations of the first two ones; see [21] or [14] for a different approach. In general, the existing line-clipping algorithms can be classified into three types: the encoding approach (with the Cohen-Sutherland algorithm as a representative), the parametric approach (with the Liang-Barsky and the Cyrus-Beck algorithms as representatives) and the Midpoint Subdivision algorithms.…”