期刊
DISCRETE & COMPUTATIONAL GEOMETRY
卷 63, 期 3, 页码 624-655出版社
SPRINGER
DOI: 10.1007/s00454-019-00101-1
关键词
Discrete differential geometry; Projective geometry; Discrete conjugate nets (Q-nets); Circular nets; Conical nets; Interpolatory subdivision
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.
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