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    Form-finding with polyhedral meshes made simple

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    formfinding2.pdf
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    7.282Mb
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    PDF
    Description:
    Accepted Manuscript
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    Type
    Conference Paper
    Authors
    Tang, Chengcheng cc
    Sun, Xiang cc
    Gomes, Maria Alexandra
    Wallner, Johannes
    Pottmann, Helmut cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Date
    2014-07-27
    Permanent link to this record
    http://hdl.handle.net/10754/555978
    
    Metadata
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    Abstract
    We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of user-specified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.
    Citation
    Form-finding with polyhedral meshes made simple 2014, 33 (4):1 ACM Transactions on Graphics
    Publisher
    Association for Computing Machinery (ACM)
    Conference/Event name
    41st International Conference and Exhibition on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2014
    DOI
    10.1145/2601097.2601213
    Additional Links
    http://dl.acm.org/citation.cfm?doid=2601097.2601213
    ae974a485f413a2113503eed53cd6c53
    10.1145/2601097.2601213
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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