Laplacian mesh optimization

Andrew Nealen, Takeo Igarashi, Olga Sorkine, Marc Alexa

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    We introduce a framework for triangle shape optimization and feature preserving smoothing of triangular meshes that is guided by the vertex Laplacians, specifically, the uniformly weighted Laplacian and the discrete mean curvature normal. Vertices are relocated so that they approximate prescribed Laplacians and positions in a weighted least-squares sense; the resulting linear system leads to an efficient, non-iterative solution. We provide different weighting schemes and demonstrate the effectiveness of the framework on a number of detailed and highly irregular meshes; our technique successfully improves the quality of the triangulation while remaining faithful to the original surface geometry, and it is also capable of smoothing the surface while preserving geometric features.

    Original languageEnglish (US)
    Title of host publicationProceedings - GRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia
    Pages381-389
    Number of pages9
    DOIs
    StatePublished - 2006
    EventGRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia - Kuala Lumpur, Malaysia
    Duration: Nov 29 2006Dec 2 2006

    Other

    OtherGRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia
    CountryMalaysia
    CityKuala Lumpur
    Period11/29/0612/2/06

    Fingerprint

    Shape optimization
    Triangulation
    Linear systems
    Geometry

    Keywords

    • Discrete differential geometry
    • Fairing
    • Least squares
    • Remeshing
    • Smoothing
    • Triangle quality

    ASJC Scopus subject areas

    • Computer Graphics and Computer-Aided Design
    • Software

    Cite this

    Nealen, A., Igarashi, T., Sorkine, O., & Alexa, M. (2006). Laplacian mesh optimization. In Proceedings - GRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia (pp. 381-389) https://doi.org/10.1145/1174429.1174494

    Laplacian mesh optimization. / Nealen, Andrew; Igarashi, Takeo; Sorkine, Olga; Alexa, Marc.

    Proceedings - GRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia. 2006. p. 381-389.

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Nealen, A, Igarashi, T, Sorkine, O & Alexa, M 2006, Laplacian mesh optimization. in Proceedings - GRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia. pp. 381-389, GRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia, Kuala Lumpur, Malaysia, 11/29/06. https://doi.org/10.1145/1174429.1174494
    Nealen A, Igarashi T, Sorkine O, Alexa M. Laplacian mesh optimization. In Proceedings - GRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia. 2006. p. 381-389 https://doi.org/10.1145/1174429.1174494
    Nealen, Andrew ; Igarashi, Takeo ; Sorkine, Olga ; Alexa, Marc. / Laplacian mesh optimization. Proceedings - GRAPHITE 2006: 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia. 2006. pp. 381-389
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