### Abstract

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. In this paper, we address this problem without the restriction that P is fixed inside Q and consider the variation where Q is a circle and the cuts are line cuts. We show that if P can be placed inside Q such that P does not contain the center of Q, then placing P in a most cornered position inside Q gives a cutting cost of 6.48 times the optimal. We also give an O(n ^{2})-time algorithm for finding such a position of P, a problem that may be of independent interest. When any placement of P must contain the center of Q, we show that P can be cut of Q with cost 6.054 times the optimal.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 252-262 |

Number of pages | 11 |

Volume | 5942 LNCS |

DOIs | |

Publication status | Published - 25 Mar 2010 |

Event | 4th International Workshop on Algorithms and Computation, WALCOM 2010 - Dhaka Duration: 10 Feb 2010 → 12 Feb 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5942 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 4th International Workshop on Algorithms and Computation, WALCOM 2010 |
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City | Dhaka |

Period | 10/2/10 → 12/2/10 |

### Fingerprint

### Keywords

- Cornerable and non-cornerable polygon
- Cutting cost
- Line cut
- Most cornered position
- Polygon cutting

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 5942 LNCS, pp. 252-262). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5942 LNCS). https://doi.org/10.1007/978-3-642-11440-3_23

**On finding a better position of a convex polygon inside a circle to minimize the cutting cost.** / Ahmed, Syed Ishtiaque; Bhuiyan, Md Mansurul Alam; Hasan, Masud; Khan, Ishita Kamal.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 5942 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5942 LNCS, pp. 252-262, 4th International Workshop on Algorithms and Computation, WALCOM 2010, Dhaka, 10/2/10. https://doi.org/10.1007/978-3-642-11440-3_23

}

TY - GEN

T1 - On finding a better position of a convex polygon inside a circle to minimize the cutting cost

AU - Ahmed, Syed Ishtiaque

AU - Bhuiyan, Md Mansurul Alam

AU - Hasan, Masud

AU - Khan, Ishita Kamal

PY - 2010/3/25

Y1 - 2010/3/25

N2 - 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. In this paper, we address this problem without the restriction that P is fixed inside Q and consider the variation where Q is a circle and the cuts are line cuts. We show that if P can be placed inside Q such that P does not contain the center of Q, then placing P in a most cornered position inside Q gives a cutting cost of 6.48 times the optimal. We also give an O(n 2)-time algorithm for finding such a position of P, a problem that may be of independent interest. When any placement of P must contain the center of Q, we show that P can be cut of Q with cost 6.054 times the optimal.

AB - 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. In this paper, we address this problem without the restriction that P is fixed inside Q and consider the variation where Q is a circle and the cuts are line cuts. We show that if P can be placed inside Q such that P does not contain the center of Q, then placing P in a most cornered position inside Q gives a cutting cost of 6.48 times the optimal. We also give an O(n 2)-time algorithm for finding such a position of P, a problem that may be of independent interest. When any placement of P must contain the center of Q, we show that P can be cut of Q with cost 6.054 times the optimal.

KW - Cornerable and non-cornerable polygon

KW - Cutting cost

KW - Line cut

KW - Most cornered position

KW - Polygon cutting

UR - http://www.scopus.com/inward/record.url?scp=77949604377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949604377&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-11440-3_23

DO - 10.1007/978-3-642-11440-3_23

M3 - Conference contribution

SN - 3642114393

SN - 9783642114397

VL - 5942 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 252

EP - 262

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -