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This paper surveys two methods for designing numerically robust geometric algorithms. The first method is the exact-arithmetic method, in which numerical computations are done in sufficiently high precision so that all the topological judgements can be done correctly. This method is usually accompanied with lazy evaluation and symbolic perturbation in order to reduce the computational cost and the implementation cost. The second method is the topology-oriented method, in which the consistency of the topological structure is considered as higher-priority information than numerical computation, and thus inconsistency is avoided. Both of the methods are described with the implementation examples.

- Publication
- IEICE TRANSACTIONS on Information Vol.E83-D No.3 pp.447-454

- Publication Date
- 2000/03/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- INVITED SURVEY PAPER

- Category
- Algorithms for Geometric Problems

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Kokichi SUGIHARA, "How to Make Geometric Algorithms Robust" in IEICE TRANSACTIONS on Information,
vol. E83-D, no. 3, pp. 447-454, March 2000, doi: .

Abstract: This paper surveys two methods for designing numerically robust geometric algorithms. The first method is the exact-arithmetic method, in which numerical computations are done in sufficiently high precision so that all the topological judgements can be done correctly. This method is usually accompanied with lazy evaluation and symbolic perturbation in order to reduce the computational cost and the implementation cost. The second method is the topology-oriented method, in which the consistency of the topological structure is considered as higher-priority information than numerical computation, and thus inconsistency is avoided. Both of the methods are described with the implementation examples.

URL: https://global.ieice.org/en_transactions/information/10.1587/e83-d_3_447/_p

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@ARTICLE{e83-d_3_447,

author={Kokichi SUGIHARA, },

journal={IEICE TRANSACTIONS on Information},

title={How to Make Geometric Algorithms Robust},

year={2000},

volume={E83-D},

number={3},

pages={447-454},

abstract={This paper surveys two methods for designing numerically robust geometric algorithms. The first method is the exact-arithmetic method, in which numerical computations are done in sufficiently high precision so that all the topological judgements can be done correctly. This method is usually accompanied with lazy evaluation and symbolic perturbation in order to reduce the computational cost and the implementation cost. The second method is the topology-oriented method, in which the consistency of the topological structure is considered as higher-priority information than numerical computation, and thus inconsistency is avoided. Both of the methods are described with the implementation examples.},

keywords={},

doi={},

ISSN={},

month={March},}

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TY - JOUR

TI - How to Make Geometric Algorithms Robust

T2 - IEICE TRANSACTIONS on Information

SP - 447

EP - 454

AU - Kokichi SUGIHARA

PY - 2000

DO -

JO - IEICE TRANSACTIONS on Information

SN -

VL - E83-D

IS - 3

JA - IEICE TRANSACTIONS on Information

Y1 - March 2000

AB - This paper surveys two methods for designing numerically robust geometric algorithms. The first method is the exact-arithmetic method, in which numerical computations are done in sufficiently high precision so that all the topological judgements can be done correctly. This method is usually accompanied with lazy evaluation and symbolic perturbation in order to reduce the computational cost and the implementation cost. The second method is the topology-oriented method, in which the consistency of the topological structure is considered as higher-priority information than numerical computation, and thus inconsistency is avoided. Both of the methods are described with the implementation examples.

ER -