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#### Asymptotic Analysis of Discrete Normals and Curvatures of Polylines

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##### Citation

Langer, T., Belyaev, A., & Seidel, H.-P. (2005). Asymptotic Analysis of Discrete
Normals and Curvatures of Polylines. In *21st Spring Conference on Computer Graphics (SCCG 2005)*
(pp. 221-224). Bratislava, Slovakia: Comenius University.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-25C9-F

##### Abstract

Accurate estimations of geometric properties of a smooth curve from
its discrete approximation are important for many computer graphics and
computer vision applications.
To assess and improve the quality of such an approximation, we assume that the
curve is known in general form. Then we can represent the
curve by a Taylor series expansion
and compare its geometric properties with the corresponding discrete
approximations. In turn
we can either prove convergence of these approximations towards the true
properties
as the edge lengths tend to zero, or we can get hints on how
to eliminate the error.
In this paper, we propose and study discrete schemes for estimating tangent and
normal vectors as well as
for estimating curvature and torsion of a smooth 3D curve approximated by a
polyline.
Thereby we make some interesting findings about connections between (smooth)
classical curves
and certain estimation schemes for polylines.