Curvature line parametrization from circle patterns
A.I. Bobenko, S.P. Tsarev
TL;DR
This paper explores how discrete circle and planar quadrilateral nets can effectively approximate smooth curvature and conjugate nets on surfaces, providing methods for global approximation and principal direction estimation.
Contribution
It introduces a new approach for second-order global approximation of smooth nets using discrete nets with infinitesimal quads and offers a geometric method for estimating principal directions.
Findings
Discrete nets can achieve second-order approximation of smooth nets.
A simple geometric construction for principal directions is proposed.
Global approximation is feasible with appropriate point selection.
Abstract
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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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · 3D Shape Modeling and Analysis · Computer Graphics and Visualization Techniques