Curvature line parametrization from circle patterns

Details Curvature line parametrization from circle patterns Curvature line parametrization from circle patterns

2007-06-21

arxiv.org/abs/0706.3221v1

Mathematics

Differential Geometry

LaTeX, 22 p., 7 EPS figures

Scientific paper

We study local and global approximations of smooth nets of curvature lines and smooth conjugate nets by respective discrete nets (circular nets and planar quadrilateral nets) with infinitesimal quads. It is shown that choosing the points of discrete nets on the smooth surface one can obtain second-order approximation globally. Also a simple geometric construction for approximate determination of principal directions of smooth surfaces is given.

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