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On Finding a Better Position of a Convex Polygon Inside a Circle to Minimize the Cutting Cost [chapter]

Syed Ishtiaque Ahmed, Md. Mansurul Alam Bhuiyan, Masud Hasan, Ishita Kamal Khan
2010 Lecture Notes in Computer Science  
The problem of cutting a convex polygon P out of a planar piece of material Q (P is already drawn on Q) with minimum total cutting cost is a well studied problem in computational geometry that has been  ...  studied with several variations such as P and Q are convex or non-convex polygons, Q is a circle, and the cuts are line cuts or ray cuts.  ...  We consider the problem of finding a position of P inside Q so that the total cost of cutting P out of Q by using line cuts is minimum.  ... 
doi:10.1007/978-3-642-11440-3_23 fatcat:lqg4aihk2bgflhxfu3czvm3usm

On Calculating the Packing Efficiency for Embedding Hexagonal and Dodecagonal Sensors in a Circular Container

Marina Prvan, Julije Ožegović, Arijana Burazin Mišura
2019 Mathematical Problems in Engineering  
We concentrate on the sensor manufacturing application, where sensors need to be produced from a circular wafer with maximal silicon efficiency (SE) and minimal number of sensor cuts.  ...  Even though packing problems are common in many fields of research, not many authors concentrate on packing polygons of known dimensions into a circular shape to optimize a certain objective.  ...  Conflicts of Interest The authors declare that there are no conflicts of interest regarding the publication of this paper.  ... 
doi:10.1155/2019/9624751 fatcat:qey5qwf7djavhcihxvl4t4ikda

A subdivision algorithm in configuration space for findpath with rotation

Rodney A. Brooks, Tomas Lozano-Perez
1985 IEEE Transactions on Systems, Man and Cybernetics  
The algorithm will find a path from a given initial position and orientation to a goal position and orientation if such a path exists, subject only to a user-specified resolution limit on displacements  ...  A circle of that radius, centered at b,, completes the construction. Note that both the inside and outside regions are convex.  ... 
doi:10.1109/tsmc.1985.6313352 fatcat:e6evbdetw5bljlekfoiqlubmsy

Circle Covering using Medial Axis*

Pedro Rocha, Rui Rodrigues, Franklina M.B. Toledo, A. Miguel Gomes
2013 IFAC Proceedings Volumes  
This paper presents a method to achieve a complete Circle Covering Representation of a simple polygon, through a topological skeleton, the Medial Axis.  ...  The aim is to produce an efficient circle representation of irregular pieces, while considering the approximation error and the resulting complexity, i.e. the number of circles.  ...  INTRODUCTION Problems that deal with the positioning of pieces in a given region without overlap, while having the objective of finding the best placement positions in order to minimize waste, require  ... 
doi:10.3182/20130522-3-br-4036.00081 fatcat:evz7jvql6bgebdnqbgzngl76p4

Optimal Online Escape Path Against a Certificate

Elmar Langetepe, David Kübel, Marc Herbstritt
2016 Scandinavian Workshop on Algorithm Theory  
Up to now such a fixed ultimate optimal escape path for a known shape for any starting position is only known for some special convex shapes (i.e., circles, strips of a given width, fat convex bodies,  ...  This escape path depends on the starting position s and takes the distances from s to the outer boundary of the environment into account.  ...  We would like to thank the anonymous referees for their helpful comments and suggestions.  ... 
doi:10.4230/lipics.swat.2016.19 dblp:conf/swat/LangetepeK16 fatcat:6vdxzew2ezcctcyzhech65vefm

Parallelized ear clipping for the triangulation and constrained Delaunay triangulation of polygons

Günther Eder, Martin Held, Peter Palfrader
2018 Computational geometry  
As usual, we call three consecutive vertices of a (planar) polygon an ear if the triangle that is spanned by them is completely inside the polygon.  ...  We report on our experimental findings, which show that the most promising method achieves an average speedup of 2-3 on a quad-core processor.  ...  We thank an anonymous reviewer for suggesting a simplified description of the re-triangulation of a hole in the divide-and-conquer algorithm.  ... 
doi:10.1016/j.comgeo.2018.01.004 fatcat:yis2ce3kevbzpbxuw4fllmjtyu

Optimal online escape path against a certificate [article]

Elmar Langetepe, David Kübel
2016 arXiv   pre-print
Up to now such a fixed ultimate optimal escape path for a known shape for any starting position is only known for some special convex shapes (i.e., circles, strips of a given width, fat convex bodies,  ...  This escape path depends on the starting position s and takes the distances from s to the outer boundary of the environment into account.  ...  Acknowledgements: We would like to thank all anonymous referees for their helpful comments and suggestions.  ... 
arXiv:1604.05972v1 fatcat:7xgiwjevy5gzxl5i3wcmrrgyie

Solving Geometric Optimization Problems using Graphics Hardware

Markus Denny
2003 Computer graphics forum (Print)  
Given a set S of n point in the plane, the first two problems are to determine the smallest homothetic scaling of a star shaped polygon P enclosing S and to find the largest empty homothetic scaling of  ...  Given the Voronoi diagram VoD´Sµ of the n points, we try to position another point p in the plane, such that the resulting Voronoi region of p has maximal area.  ...  Furthermore, we thank the computer graphics group of Philipp Slusallek, especially Georg Demme.  ... 
doi:10.1111/1467-8659.00692 fatcat:p7qtrbywobfejdc6gyflbw4y2e

New Results on Stabbing Segments with a Polygon [chapter]

José Miguel Díaz-Báñez, Matias Korman, Pablo Pérez-Lantero, Alexander Pilz, Carlos Seara, Rodrigo I. Silveira
2013 Lecture Notes in Computer Science  
We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment  ...  Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized.  ...  Moreover, our proof shows that the problem remains NP-hard even if the endpoints of all the segments are in convex position or lie on a circle.  ... 
doi:10.1007/978-3-642-38233-8_13 fatcat:kuhadftsa5hslenht4vagcvr5i

New results on stabbing segments with a polygon

José Miguel Díaz-Báñez, Matias Korman, Pablo Pérez-Lantero, Alexander Pilz, Carlos Seara, Rodrigo I. Silveira
2015 Computational geometry  
We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment  ...  Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized.  ...  Moreover, our proof shows that the problem remains NP-hard even if the endpoints of all the segments are in convex position or lie on a circle.  ... 
doi:10.1016/j.comgeo.2014.06.002 fatcat:kftaavnejnab5ff4mnsl5et7n4

New results on stabbing segments with a polygon [article]

José Miguel Díaz-Báñez and Matias Korman and Pablo Pérez-Lantero and Alexander Pilz and Carlos Seara and Rodrigo I. Silveira
2014 arXiv   pre-print
We consider a natural variation of the concept of stabbing a segment by a simple polygon: a segment is stabbed by a simple polygon P if at least one of its two endpoints is contained in P.  ...  Further, an adaptation of our polynomial-time algorithm solves an open problem posed by Löffler and van Kreveld [Algorithmica 56(2), 236--269 (2010)] about finding a maximum perimeter convex hull for a  ...  Moreover, our proof shows that the problem remains NP-hard even if the endpoints of all the segments are in convex position or lie on a circle.  ... 
arXiv:1211.1490v3 fatcat:5632zhtkxzgwpltzlzpilvrzae

Method of sentinels for packing items within arbitrary convex regions

E G Birgin, J M Martínez, W F Mascarenhas, D P Ronconi
2006 Journal of the Operational Research Society  
Sentinels sets are finite subsets of the items to be packed such that, when two items are superposed, at least one sentinel of one item is in the interior of the other.  ...  A new method is introduced for packing items in convex regions of the Euclidian ndimensional space.  ...  Acknowledgement: The authors are indebted to three anonymous referees whose comments helped a lot to improve this paper.  ... 
doi:10.1057/palgrave.jors.2602067 fatcat:abplmgqisvg5nbesshsbfsl7ga

A Parallel Biased Random-Key Genetic Algorithm with Multiple Populations Applied to Irregular Strip Packing Problems

Bonfim Amaro Júnior, Plácido Rogério Pinheiro, Pedro Veras Coelho
2017 Mathematical Problems in Engineering  
The aim of this work is to minimize the area needed to accommodate the given demand.  ...  The irregular strip packing problem (ISPP) is a class of cutting and packing problem (C&P) in which a set of items with arbitrary formats must be placed in a container with a variable length.  ...  Acknowledgments The authors are thankful to Coordination for the Improvement of Higher Level Education Personnel (CAPES), National Counsel of Technological and Scientific Development (CNPq), via Grant  ... 
doi:10.1155/2017/1670709 fatcat:aoesktaxjbfpvkzqj2axd3pyca

Convex partitioning of a polygon into smaller number of pieces with lowest memory consumption

K. R. Wijeweera, S. R. Kodituwakku
2017 Ceylon Journal of Science  
This paper proposes an algorithm for partitioning a concave polygon into smaller number of convex pieces.  ...  Hertel Mehlhorn algorithm is the most efficient algorithm, but it does not minimize the number of convex pieces satisfactorily.  ...  The projections on x-axis and y-axis are considered to find the positions of points.  ... 
doi:10.4038/cjs.v46i1.7418 fatcat:dalxxvtwkzbydfavevre5sdsm4

On Equal Point Separation by Planar Cell Decompositions [article]

Nikhil Marda
2017 arXiv   pre-print
We consider a property of curves called the stabbing number, defined to be the maximum countable number of intersections possible between the curve and a line in the plane.  ...  We show that large subsets of X lying on Jordan curves of low stabbing number are an obstacle to equal separation. We further discuss Jordan curves of minimal stabbing number containing X.  ...  Minimal stabbing number Jordan curve through X We want to find the minimal stabbing number Jordan curve containing X in order to strengthen the lower bound on the cutting number from Lemma 3.1.  ... 
arXiv:1701.04529v1 fatcat:uhqyjysz65c5xih7f6yukdobym
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