### Abstract

This paper is concerned with robustness problems in computational geometry. To solve geometric problems, numerical computations by floating-point arithmetic are preferred in terms of computational performance. However, when the rounding errors of floating-point computations accumulate, meaningless results of the problems may be obtained. It is called robustness problem in computational geometry. Recently, several verified algorithms for a two-dimensional orientation problem have been developed. By applying these algorithms, we develop an algorithm which overcomes this problem. Finally, we present numerical examples for a convex hull for a set of points on two-dimensional spaces to illustrate an efficiency of the proposed algorithm.

Original language | English |
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Title of host publication | Asia Simulation Conference 2009, JSST 2009 |

Publisher | Japan Society for Simulation Technology, JSST |

Publication status | Published - 2009 |

Event | Asia Simulation Conference 2009, JSST 2009 - Shiga Duration: 2009 Oct 7 → 2009 Oct 9 |

### Other

Other | Asia Simulation Conference 2009, JSST 2009 |
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City | Shiga |

Period | 09/10/7 → 09/10/9 |

### Fingerprint

### Keywords

- Accurate numerical computation
- Computational geometry

### ASJC Scopus subject areas

- Modelling and Simulation

### Cite this

*Asia Simulation Conference 2009, JSST 2009*Japan Society for Simulation Technology, JSST.

**Robustness problems and verified computations for computational geometry.** / Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shinichi.

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

*Asia Simulation Conference 2009, JSST 2009.*Japan Society for Simulation Technology, JSST, Asia Simulation Conference 2009, JSST 2009, Shiga, 09/10/7.

}

TY - GEN

T1 - Robustness problems and verified computations for computational geometry

AU - Ozaki, Katsuhisa

AU - Ogita, Takeshi

AU - Oishi, Shinichi

PY - 2009

Y1 - 2009

N2 - This paper is concerned with robustness problems in computational geometry. To solve geometric problems, numerical computations by floating-point arithmetic are preferred in terms of computational performance. However, when the rounding errors of floating-point computations accumulate, meaningless results of the problems may be obtained. It is called robustness problem in computational geometry. Recently, several verified algorithms for a two-dimensional orientation problem have been developed. By applying these algorithms, we develop an algorithm which overcomes this problem. Finally, we present numerical examples for a convex hull for a set of points on two-dimensional spaces to illustrate an efficiency of the proposed algorithm.

AB - This paper is concerned with robustness problems in computational geometry. To solve geometric problems, numerical computations by floating-point arithmetic are preferred in terms of computational performance. However, when the rounding errors of floating-point computations accumulate, meaningless results of the problems may be obtained. It is called robustness problem in computational geometry. Recently, several verified algorithms for a two-dimensional orientation problem have been developed. By applying these algorithms, we develop an algorithm which overcomes this problem. Finally, we present numerical examples for a convex hull for a set of points on two-dimensional spaces to illustrate an efficiency of the proposed algorithm.

KW - Accurate numerical computation

KW - Computational geometry

UR - http://www.scopus.com/inward/record.url?scp=84903827733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903827733&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84903827733

BT - Asia Simulation Conference 2009, JSST 2009

PB - Japan Society for Simulation Technology, JSST

ER -