Algorithm for Clpping Arbitrary Polygons

Andreev, Rumen

doi:10.1111/j.1467-8659.1989.tb00484.x

Cited by 23 publications

(13 citation statements)

References 5 publications

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“…If so, it computes the intersections and inserts them into corresponding edges. It does in this way, until all Black: (1,1)(4,1)(4,3)(a)(2,4)(2,3)(a)(1,2) Read: (2,2)(5,2)(a)(6,1)(6,3)(4,5)(a)(2,4.5) (1,4) P1: (10,10), (40,10), (40,30), (20,40), (15,30), (15,15) P2: (20,20), (45,20),(55,30),(50,50), (30,45) edges of P 1 are processed. The rest of steps are to assign the entry-exit properties and to traverse, which are the same as the ones of our proposed method.…”

Section: A Methodologiesmentioning

confidence: 99%

“…The conic polygon has several special or degenerate cases: (i) the linear polygon (known as traditional polygon), whose boundaries consist of only linear curves, i.e., straight line segments; and (ii) the circular-arc polygon, whose boundaries consist of circular-arcs and/or straight line segments. The natural problem -boolean operation on traditional polygons -has been extensively investigated, see e.g., [1], [11], [13], [14], [15], [16], [17], [18], [20], [21], [22], [25]. However, in existing literature (almost) no article focuses on another natural problem -boolean operation on circular-arc polygons.…”

Section: Introductionmentioning

confidence: 99%

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A Simple Algorithm for Computing Several Sequences Synthesis

Wang

Qing

Feng

2000

Information Security for Global Information Infrastructures

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In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easyto-implement but without loss of efficiency. Given two circular-arc polygons with m and n edges respectively, our method runs in O(m + n + (l + k) log l) time, using O(m + n + k) space, where k is the number of intersections, and l is the number of edges. Our algorithm has the power to approximate to linear complexity when k and l are small. The superiority of the proposed algorithm is also validated through empirical study.

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Section: A Methodologiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Simple Algorithm for Computing Several Sequences Synthesis

Wang

Qing

Feng

2000

Information Security for Global Information Infrastructures

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“…Many available algorithms exist for boolean operations, but some of them have limitations on the shape of input polygons. For example, Andreev [21] required a rectangular clip polygon, while Rappoport [22] required a convex clip polygon. Greiner and Hormann [23] handled degenerate cases by perturbing the position of the vertex, but, by doing so, it required some additional computational overhead, which makes its running time undeterminable.…”

Section: Boolean Operationsmentioning

confidence: 99%

“…Greiner and Hormann [23] handled degenerate cases by perturbing the position of the vertex, but, by doing so, it required some additional computational overhead, which makes its running time undeterminable. Weiler [7], Weiler and Atherton [24], and Andreev [21] permitted any clip or subject polygons to be concave or with holes, but could not handle self-intersecting polygons. Vatti [25] and Greiner and Hormann [23] could perform boolean operations for any clip and subject polygons including those that are self-intersecting, concave, or with holes.…”

Section: Boolean Operationsmentioning

confidence: 99%

Optimal Reliable Point-in-Polygon Test and Differential Coding Boolean Operations on Polygons

et al. 2018

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This paper provides a full theoretical and experimental analysis of a serial algorithm for the point-in-polygon test, which requires less running time than previous algorithms and can handle all degenerate cases. The serial algorithm can quickly determine whether a point is inside or outside a polygon and accurately determine the contours of input polygon. It describes all degenerate cases and simultaneously provides a corresponding solution to each degenerate case to ensure the stability and reliability. This also creates the prerequisites and basis for our novel boolean operations algorithm that inherits all the benefits of the serial algorithm. Using geometric probability and straight-line equation, it optimizes our two algorithms that avoid the division operation and do not need to compute any intersection points. Our algorithms are applicable to any polygon that may be self-intersecting or with holes nested to any level of depth. They do not have to sort the vertices clockwise or counterclockwise beforehand. Consequently, they process all edges one by one in any order for input polygons. This allows a parallel implementation of each algorithm to be made very easily. We also prove several theorems guaranteeing the correctness of algorithms. To speed up the operations, we assign each vector a number code and derive two iterative formulas using differential calculus. However, the experimental results as well as the theoretical proof show that our serial algorithm for the point-in-polygon test is optimal and the time complexities of all algorithms are linear. Our methods can be extended to three-dimensional space, in particular, they can be applied to 3D printing to improve its performance.

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“…There are lesser known variants of the three most widely known line clipping algorithms (CS, LB, NLN), in addition to other algorithms. Improvements to the CS algorithm have been developed (Andreev 1989;Duvanenko et al 1990;Shi et al 1990;Blinn 1991), concentrating on speeding up the algorithm by minimizing the work involved in recomputing line segment endpoint encodings. In some work (Liang and Barsky 1990;) the original LB algorithm is improved by reducing the number of divisions in favour of more comparisons.…”

Section: Introductionmentioning

confidence: 99%

2D line and polygon clipping based on space subdivision

Slater

Barsky

1994

The Visual Computer

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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.

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Algorithm for Clpping Arbitrary Polygons

Cited by 23 publications

References 5 publications

A Simple Algorithm for Computing Several Sequences Synthesis

A Simple Algorithm for Computing Several Sequences Synthesis

Optimal Reliable Point-in-Polygon Test and Differential Coding Boolean Operations on Polygons

2D line and polygon clipping based on space subdivision

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