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    Computing discrete shape operators on general meshes

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    v25i3pp547-556.pdf (2.860Mb)
    Date
    2006
    Author
    Grinspun, Eitan ORCID
    Gingold, Yotam ORCID
    Reisman, Jason
    Zorin, Denis
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    Abstract
    Discrete curvature and shape operators, which capture complete information about directional curvatures at a point, are essential in a variety of applications: simulation of deformable two-dimensional objects, variational modeling and geometric data processing. In many of these applications, objects are represented by meshes. Currently, a spectrum of approaches for formulating curvature operators for meshes exists, ranging from highly accurate but computationally expensive methods used in engineering applications to efficient but less accurate techniques popular in simulation for computer graphics.We propose a simple and efficient formulation for the shape operator for variational problems on general meshes, using degrees of freedom associated with normals. On the one hand, it is similar in its simplicity to some of the discrete curvature operators commonly used in graphics; on the other hand, it passes a number of important convergence tests and produces consistent results for different types of meshes and mesh refinement.
    BibTeX
    @article {10.1111:j.1467-8659.2006.00974.x,
    journal = {Computer Graphics Forum},
    title = {{Computing discrete shape operators on general meshes}},
    author = {Grinspun, Eitan and Gingold, Yotam and Reisman, Jason and Zorin, Denis},
    year = {2006},
    publisher = {The Eurographics Association and Blackwell Publishing, Inc},
    ISSN = {1467-8659},
    DOI = {10.1111/j.1467-8659.2006.00974.x}
    }
    URI
    http://dx.doi.org/10.1111/j.1467-8659.2006.00974.x
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    Eurographics Association copyright © 2013 - 2023 
    Send Feedback | Contact - Imprint | Data Privacy Policy | Disable Google Analytics
    Theme by @mire NV
    System hosted at  Graz University of Technology.
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