Mesh Editing Based on Discrete Laplace and Poisson Models

Marc Alexa, Andrew Nealen

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

    Abstract

    Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. This intrinsic representation could be derived from differential properties of the mesh, i.e. its Laplacian. The modeling process poses nonzero boundary constraints so that this idea results in a Poisson model. Different ways of representing the intrinsic geometry and the boundary constraints result in alternatives for the properties of the modeling system. In particular, the Laplacian is not invariant to scaling and rotations. Either the intrinsic representation is enhanced to be invariant to (linearized) transformations, or scaling and rotation are computed in a preprocess and are modeled as boundary constraints. Based on this representation, useful editing operations can be developed: Interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric detail between two surfaces, and transplanting of a partial surface mesh into another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of this approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.

    Original languageEnglish (US)
    Title of host publicationAdvances in Computer Graphics and Computer Vision - International Conferences VISAPP and GRAPP 2006, Revised Selected Papers
    PublisherSpringer Verlag
    Pages3-28
    Number of pages26
    Volume4 CCIS
    ISBN (Print)9783540752721
    DOIs
    StatePublished - 2007
    Event1st International Conferences on Computer Vision Theory and Applications, VISAPP 2006, and International Conference on Computer Graphics Theory and Applications, GRAPP 2006 - Setubal, Portugal
    Duration: Feb 25 2006Feb 28 2006

    Publication series

    NameCommunications in Computer and Information Science
    Volume4 CCIS
    ISSN (Print)18650929

    Other

    Other1st International Conferences on Computer Vision Theory and Applications, VISAPP 2006, and International Conference on Computer Graphics Theory and Applications, GRAPP 2006
    CountryPortugal
    CitySetubal
    Period2/25/062/28/06

    Fingerprint

    Linear systems
    Geometry

    Keywords

    • detail preservation
    • Mesh editing

    ASJC Scopus subject areas

    • Computer Science(all)

    Cite this

    Alexa, M., & Nealen, A. (2007). Mesh Editing Based on Discrete Laplace and Poisson Models. In Advances in Computer Graphics and Computer Vision - International Conferences VISAPP and GRAPP 2006, Revised Selected Papers (Vol. 4 CCIS, pp. 3-28). (Communications in Computer and Information Science; Vol. 4 CCIS). Springer Verlag. https://doi.org/10.1007/978-3-540-75274-5_1

    Mesh Editing Based on Discrete Laplace and Poisson Models. / Alexa, Marc; Nealen, Andrew.

    Advances in Computer Graphics and Computer Vision - International Conferences VISAPP and GRAPP 2006, Revised Selected Papers. Vol. 4 CCIS Springer Verlag, 2007. p. 3-28 (Communications in Computer and Information Science; Vol. 4 CCIS).

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

    Alexa, M & Nealen, A 2007, Mesh Editing Based on Discrete Laplace and Poisson Models. in Advances in Computer Graphics and Computer Vision - International Conferences VISAPP and GRAPP 2006, Revised Selected Papers. vol. 4 CCIS, Communications in Computer and Information Science, vol. 4 CCIS, Springer Verlag, pp. 3-28, 1st International Conferences on Computer Vision Theory and Applications, VISAPP 2006, and International Conference on Computer Graphics Theory and Applications, GRAPP 2006, Setubal, Portugal, 2/25/06. https://doi.org/10.1007/978-3-540-75274-5_1
    Alexa M, Nealen A. Mesh Editing Based on Discrete Laplace and Poisson Models. In Advances in Computer Graphics and Computer Vision - International Conferences VISAPP and GRAPP 2006, Revised Selected Papers. Vol. 4 CCIS. Springer Verlag. 2007. p. 3-28. (Communications in Computer and Information Science). https://doi.org/10.1007/978-3-540-75274-5_1
    Alexa, Marc ; Nealen, Andrew. / Mesh Editing Based on Discrete Laplace and Poisson Models. Advances in Computer Graphics and Computer Vision - International Conferences VISAPP and GRAPP 2006, Revised Selected Papers. Vol. 4 CCIS Springer Verlag, 2007. pp. 3-28 (Communications in Computer and Information Science).
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