Decomposing a Polygon into Simpler Components

Keil, J. Mark

doi:10.1137/0214056

Cited by 148 publications

(83 citation statements)

References 15 publications

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“…An initial step of many algorithms on simple polygons is a decomposition into simpler components [21]. Keil and Snoeyink [22] devised an algorithm for computing the minimum convex decomposition of the interior of a given simple polygon.…”

Section: Simplementioning

confidence: 99%

Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-triangles

Aichholzer

Huemer

Kappes

et al. 2006

Lecture Notes in Computer Science

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Abstract. We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties and give combinatorial bounds on their complexity. Our upper bounds depend on new Ramsey-type results concerning disjoint empty convex k-gons in point sets.

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Section: Simplementioning

confidence: 99%

Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-triangles

Aichholzer

Huemer

Kappes

et al. 2006

Lecture Notes in Computer Science

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“…Hence, resolving k holes, which equals to join into a single entity without holes, takes O (nk+ Our framework has O (nr) time complexity as the same as that of ACD approach [5]. In contrast to other methods, such as Green's approach [22] has O ( 2 2 r n ) time complexity, Keil's approach [18] has O( 2 2 log r n n) time complexi-ty, our approach could be more efficient to generate more naturally visual partitions than other decomposing methods.…”

Section: Proofmentioning

confidence: 99%

“…So if we eliminate inessential diagonals of the triangulations obtained by both algorithms, we can obtain convex decompositions. For polygons with holes, the convex decomposition is NP-hard for both the minimum components criterion [17] and the shortest internal length criterion [18].…”

Section: Related Workmentioning

confidence: 99%

New Framework for Decomposing a Polygon with Zero or More Holes

Zhou¹,

Wang²

2015

TOCSJ

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Abstract:In this paper, we propose a unified framework for decomposition of a polygon with or without holes, enlightened by approximate convex decomposition. We transform target polygon containing holes into the polygon without holes by merging holes into external boundary, thus only need to partition the polygon without holes. Several constraints are enforced to ensure generate more visually meaningful decompositions, more elegant final components than that of other methods. Moreover, we estimate tolerance from geometry information of target polygon to obtain a naturally visual decomposition, a polished hierarchical representation. Our approach computes a decomposition of a polygon, containing zero or more holes, with n vertices and r notches in O(nr) time. In contrast, exact convex decomposition is NP-hard, or if the polygon has no holes, takes much more time. Many experimental results and applications are presented to show the superiority, applicability and flexibility of our approach.

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“…These techniques differ according to the expected purpose of the decomposition and the required properties of the components resulting from this decomposition. All these techniques aim to decompose a form into a finite number of simple parts and among the simple shapes targeted we find the convex shapes [7].…”

Section: Convex Decompositionmentioning

confidence: 99%

Novel Method to Generate and Optimize Reticulated Structures of a Non Convex Conception Domain

Bialleten¹,

Chiheb²,

Afia³

et al. 2017

IJSEIA

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Reticulated structures are increasingly represented in industry. They are lighter than traditional structures which allows weight saving. So they can be the best choice when material gain offsets the production cost which is an optimization purpose.In this paper, we propose an algorithm to generate automatically a reticulated structure. We particularly study non-convex conception domains which can be decomposed into a finite number of convex sub-domains, specially polygons. This solution generates a structure with an optimum form based on an algorithm that works on convex design domains.

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Decomposing a Polygon into Simpler Components

Cited by 148 publications

References 15 publications

Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-triangles

Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-triangles

New Framework for Decomposing a Polygon with Zero or More Holes

Novel Method to Generate and Optimize Reticulated Structures of a Non Convex Conception Domain

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