2018/02/14 by Alexander I. Bobenko, Helmut Pottmann, Bobenko, Alexander I. +3
Computer Science · Engineering · #51A05 #51B10 #51B15 (Secondary) #53A20 #65D17 (Primary) #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics #Manufacturing Process and Optimization
paper · pdf · doi:10.48550/arxiv.1802.05063
openalex publication_date 2018/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the common underlying discrete structures for various smooth\nand discrete nets. The main idea is to impose the characteristic properties of\nthe nets not only on elementary quadrilaterals but also on larger parameter\nrectangles. For discrete planar quadrilateral nets, circular nets, Q^*-nets\nand conical nets we obtain a characterization of the corresponding discrete\nmulti-nets. In the limit these discrete nets lead to some classical classes of\nsmooth surfaces. Furthermore, we propose to use the characterized discrete nets\nas discrete extensions for the nets to obtain structure preserving subdivision\nschemes.\n