How to Make Geometric Algorithms Robust

Kokichi SUGIHARA

How to Make Geometric Algorithms Robust

Kokichi SUGIHARA

Full Text Views

0

Cite this

Summary :

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

Cite this

Copy

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

Copy

@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},}

Copy

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 -