Multi-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramVisual Computing Center (VCC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2019-05-28Online Publication Date
2019-05-28Print Publication Date
2020-04Embargo End Date
2020-01-01Permanent link to this record
http://hdl.handle.net/10754/656384
Metadata
Show full item recordAbstract
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/s00454-019-00101-1Sponsors
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 LLCarXiv
1802.05063ae974a485f413a2113503eed53cd6c53
10.1007/s00454-019-00101-1