### Abstract

The calculation of the overlap volume of half-spheres or ellipsoids is of direct interest in structural bioinformatics, which is concerned with the computational study of biological macromolecules on a genomic scale. We present an algorithm for computing the Delaunay graph and the overlap volume of a set of half-balls using exact predicates that detect the disjointness or non-disjointness of two half-balls and the validity of the generalized Voronoi vertex of four half-balls using geometric invariants and action (multiplication map) matrices. We prove the correctness of the algorithm and the optimality of the degree of the predicates by using geometric invariants and GroÂ¿bner bases. The main application of these certified computations is to predict the 3D structure of proteins.

Original language | English |
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Title of host publication | Proceedings of the Sixth International Symposium on Voronoi Diagrams in Science and Engineering |

Number of pages | 278 |

Place of Publication | DTU-Informatics |

Publisher | IEEE Computer Society Press |

Publication date | 2009 |

Pages | 263-264 |

ISBN (Print) | 978-97-643-0497-8 |

DOIs | |

Publication status | Published - 2009 |

Event | 6th International Symposium on Voronoi Diagrams in Science and Engineering - Technical University of Denmark, Kgs. Lyngby, Denmark Duration: 23 Jun 2009 → 26 Jun 2009 Conference number: 6 http://www2.imm.dtu.dk/projects/ISVD/ |

### Conference

Conference | 6th International Symposium on Voronoi Diagrams in Science and Engineering |
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Number | 6 |

Location | Technical University of Denmark |

Country | Denmark |

City | Kgs. Lyngby |

Period | 23/06/2009 → 26/06/2009 |

Internet address |

### Bibliographical note

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Anton, F., & Hamelryck, T. (2009). The Voronoi diagram of half-balls and its application to the prediction of the 3D structure of proteins. In

*Proceedings of the Sixth International Symposium on Voronoi Diagrams in Science and Engineering*(pp. 263-264). IEEE Computer Society Press. https://doi.org/10.1109/ISVD.2009.40