### Abstract

Exact geometric computation (EGC) is a general approach for achieving robust numerical algorithms that satisfy geometric constraints. At the heart of EGC are various Zero Problems, some of which are not-known to be decidable and others have high computational complexity. Our current goal is to introduce notions of “soft- correctness” in order to avoid Zero Problems. We give a bird’s eye view of our recent work with collaborators in two principle areas: computing zero sets and robot path planning. They share a common Subdivision Framework. Such algorithms (a) have adaptive complexity, (b) are practical, and (c) are effective. Here, “effective algorithm” means it is easily and correctly implementable from standardized algorithmic components. Our goals are to outline these components and to suggest new components to be developed. We discuss a systematic pathway to go from the abstract algorithmic description to an effective algorithm in the subdivision framework.

Original language | English (US) |
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Title of host publication | Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings |

Editors | Evgenii V. Vorozhtsov, Timur M. Sadykov, Werner M. Seiler, Wolfram Koepf, Matthew England |

Publisher | Springer-Verlag |

Pages | 12-36 |

Number of pages | 25 |

ISBN (Print) | 9783030268305 |

DOIs | |

State | Published - Jan 1 2019 |

Event | 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019 - Moscow, Russian Federation Duration: Aug 26 2019 → Aug 30 2019 |

### 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 | 11661 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019 |
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Country | Russian Federation |

City | Moscow |

Period | 8/26/19 → 8/30/19 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings*(pp. 12-36). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11661 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-030-26831-2_2

**Towards Soft Exact Computation (Invited Talk).** / Yap, Chee.

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

*Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11661 LNCS, Springer-Verlag, pp. 12-36, 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019, Moscow, Russian Federation, 8/26/19. https://doi.org/10.1007/978-3-030-26831-2_2

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T1 - Towards Soft Exact Computation (Invited Talk)

AU - Yap, Chee

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Exact geometric computation (EGC) is a general approach for achieving robust numerical algorithms that satisfy geometric constraints. At the heart of EGC are various Zero Problems, some of which are not-known to be decidable and others have high computational complexity. Our current goal is to introduce notions of “soft- correctness” in order to avoid Zero Problems. We give a bird’s eye view of our recent work with collaborators in two principle areas: computing zero sets and robot path planning. They share a common Subdivision Framework. Such algorithms (a) have adaptive complexity, (b) are practical, and (c) are effective. Here, “effective algorithm” means it is easily and correctly implementable from standardized algorithmic components. Our goals are to outline these components and to suggest new components to be developed. We discuss a systematic pathway to go from the abstract algorithmic description to an effective algorithm in the subdivision framework.

AB - Exact geometric computation (EGC) is a general approach for achieving robust numerical algorithms that satisfy geometric constraints. At the heart of EGC are various Zero Problems, some of which are not-known to be decidable and others have high computational complexity. Our current goal is to introduce notions of “soft- correctness” in order to avoid Zero Problems. We give a bird’s eye view of our recent work with collaborators in two principle areas: computing zero sets and robot path planning. They share a common Subdivision Framework. Such algorithms (a) have adaptive complexity, (b) are practical, and (c) are effective. Here, “effective algorithm” means it is easily and correctly implementable from standardized algorithmic components. Our goals are to outline these components and to suggest new components to be developed. We discuss a systematic pathway to go from the abstract algorithmic description to an effective algorithm in the subdivision framework.

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U2 - 10.1007/978-3-030-26831-2_2

DO - 10.1007/978-3-030-26831-2_2

M3 - Conference contribution

AN - SCOPUS:85071445752

SN - 9783030268305

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

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EP - 36

BT - Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings

A2 - Vorozhtsov, Evgenii V.

A2 - Sadykov, Timur M.

A2 - Seiler, Werner M.

A2 - Koepf, Wolfram

A2 - England, Matthew

PB - Springer-Verlag

ER -