Open AccessJournal Article10.1016/J.CAG.2004.11.001

Technical section: A new algorithm for Boolean operations on general polygons

- 01 Feb 2005

- Vol. 29, Iss: 1, pp 57-70

TL;DR: A new algorithm for Boolean operations on general planar polygons is presented, using the simplex theory to build the basic mathematical model of the new algorithm, and examples show that the running time required is less than one-third of that by the Rivero and Feito algorithm.

About: This article is published in Computers & Graphics. The article was published on 01 Feb 2005. and is currently open access. The article focuses on the topics: Boolean operations on polygons & Polygon.

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1. What are the contributions in "A new algorithm for boolean operations on general polygons" ?

In this paper, a new algorithm for Boolean operations on general planar polygons is presented, which uses simplex theory to solve the Boolean operation problem.

Fig. 5. An example of the subdivision process: (a) two polygons and their associated simplicial chains; (b) polygons after the subdivision process and their associated simplicial chains.

Table 5 Performance results using: the de Berg et al. algorithm, the Rivero and Feito algorithm and the new algorithm

Fig. 12. Performance chart using: the de Berg et al. algorithm, the Rivero and Feito algorithm and the new algorithm.

Fig. 1. Examples of general planar polygons: (a) two single polygons without inner contours; (b) a single polygon with two inner contours; (c) two single polygons with inner contours.

Fig. 7. Pseudo code for calculating the values of the characteristic functions.

Citations

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References

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Computer Graphics: Principles and Practice

James D. Foley

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TL;DR: This chapter discusses the development of Hardware and Software for Computer Graphics, and the design methodology of User-Computer Dialogues, which led to the creation of the Simple Raster Graphics Package.

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Computational Geometry: Algorithms and Applications

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Computational Geometry: An Introduction

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Journal Article•10.1145/360767.360802

Reentrant polygon clipping

Ivan E. Sutherland, +1 more

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- Communications of The ACM

TL;DR: A new family of clipping algorithms is described, able to clip polygons against irregular convex plane-faced volumes in three dimensions, removing the parts of the polygon which lie outside the volume.

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Technical section: A new algorithm for Boolean operations on general polygons

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Citations

Tool orientation optimization for 5-axis machining with C-space method

‘Moment of fluid’ interface reconstruction method in axisymmetric coordinates

New morphological methods to generate two-dimensional curve offsets

Re2l: An efficient output-sensitive algorithm for computing Boolean operations on circular-arc polygons and its applications

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

References

Computer Graphics: Principles and Practice

Computational Geometry: Algorithms and Applications

Computational Geometry: An Introduction

Computational Geometry

Reentrant polygon clipping

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