The Voronoi diagram of half-balls and its application to the prediction of the 3D structure of proteins

François Anton (Invited author), Thomas Hamelryck (Invited author)

    Research output: Chapter in Book/Report/Conference proceedingConference abstract in proceedingsResearch

    1 Downloads (Pure)

    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 Gro¿bner bases. The main application of these certified computations is to predict the 3D structure of proteins.
    Original languageEnglish
    Title of host publicationProceedings of the Sixth International Symposium on Voronoi Diagrams in Science and Engineering
    Number of pages278
    Place of PublicationDTU-Informatics
    PublisherIEEE Computer Society Press
    Publication date2009
    Pages263-264
    ISBN (Print)978-97-643-0497-8
    DOIs
    Publication statusPublished - 2009
    Event6th International Symposium on Voronoi Diagrams in Science and Engineering - Technical University of Denmark, Kgs. Lyngby, Denmark
    Duration: 23 Jun 200926 Jun 2009
    Conference number: 6
    http://www2.imm.dtu.dk/projects/ISVD/

    Conference

    Conference6th International Symposium on Voronoi Diagrams in Science and Engineering
    Number6
    LocationTechnical University of Denmark
    CountryDenmark
    CityKgs. Lyngby
    Period23/06/200926/06/2009
    Internet address

    Bibliographical note

    Copyright 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

    Cite this

    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