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    Multi-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles

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    Type
    Article
    Authors
    Bobenko, Alexander I.
    Pottmann, Helmut cc
    Rörig, Thilo
    KAUST Department
    Applied Mathematics and Computational Science Program
    Visual Computing Center (VCC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-05-28
    Online Publication Date
    2019-05-28
    Print Publication Date
    2020-04
    Embargo End Date
    2020-01-01
    Permanent link to this record
    http://hdl.handle.net/10754/656384
    
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    Abstract
    We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on arbitrary parameter rectangles. For discrete planar quadrilateral nets, circular nets, Q∗-nets and conical nets we obtain a characterization of the corresponding discrete multi-nets. In the limit these discrete nets lead to some classical classes of smooth surfaces. Furthermore, we propose to use the characterized discrete nets as discrete extensions for the nets to obtain structure preserving subdivision schemes.
    Citation
    Bobenko, A. I., Pottmann, H., & Rörig, T. (2019). Multi-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles. Discrete & Computational Geometry. doi:10.1007/s00454-019-00101-1
    Sponsors
    We would like to thank Wolfgang Schief and Jan Techter for many fruitful discussions. This research was supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics.” – www.discretization.de. Helmut Pottmann was supported through Grant I 2978-N35 of the Austrian Science Fund (FWF).
    Publisher
    Springer Science and Business Media LLC
    Journal
    Discrete and Computational Geometry
    DOI
    10.1007/s00454-019-00101-1
    arXiv
    1802.05063
    Additional Links
    http://link.springer.com/10.1007/s00454-019-00101-1
    http://arxiv.org/pdf/1802.05063
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00454-019-00101-1
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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