Interrogating witnesses for geometric constraint solving

Dominique Michelucci, Sebti Foufou

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Classically, geometric constraint solvers use graph-based methods to analyze systems of geometric constraints. These methods have intrinsic limitations, which the witness method overcomes. This paper details the computation of a basis of the vector space of the free infinitesimal motions of a typical witness, and explains how to use this basis to interrogate the witness for detecting all dependencies between constraints: structural dependencies already detectable by graph-based methods, and also non-structural dependencies, due to known or unknown geometric theorems, which are undetectable with graph-based methods. The paper also discusses how to decide about the rigidity of a witness.

    Original languageEnglish (US)
    Title of host publicationProceedings - SPM 2009
    Subtitle of host publicationSIAM/ACM Joint Conference on Geometric and Physical Modeling
    Pages343-348
    Number of pages6
    DOIs
    StatePublished - Nov 9 2009
    EventSPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling - San Francisco, CA, United States
    Duration: Oct 5 2009Oct 8 2009

    Other

    OtherSPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling
    CountryUnited States
    CitySan Francisco, CA
    Period10/5/0910/8/09

    Fingerprint

    Geometric Constraint Solving
    Vector spaces
    Rigidity
    Geometric Constraints
    Graph in graph theory
    Geometric theorem
    Vector space
    Unknown
    Motion

    Keywords

    • Dependency detection
    • Geometric constraint solving

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Computer Science Applications
    • Computer Vision and Pattern Recognition
    • Mathematics(all)

    Cite this

    Michelucci, D., & Foufou, S. (2009). Interrogating witnesses for geometric constraint solving. In Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling (pp. 343-348). [1629301] https://doi.org/10.1145/1629255.1629301

    Interrogating witnesses for geometric constraint solving. / Michelucci, Dominique; Foufou, Sebti.

    Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling. 2009. p. 343-348 1629301.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Michelucci, D & Foufou, S 2009, Interrogating witnesses for geometric constraint solving. in Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling., 1629301, pp. 343-348, SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling, San Francisco, CA, United States, 10/5/09. https://doi.org/10.1145/1629255.1629301
    Michelucci D, Foufou S. Interrogating witnesses for geometric constraint solving. In Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling. 2009. p. 343-348. 1629301 https://doi.org/10.1145/1629255.1629301
    Michelucci, Dominique ; Foufou, Sebti. / Interrogating witnesses for geometric constraint solving. Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling. 2009. pp. 343-348
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