Solid shape
ACM Transactions on Mathematical Software (TOMS)
Numerically Invariant Signature Curves
International Journal of Computer Vision
Exact and interpolatory quadratures for curvature tensor estimation
Computer Aided Geometric Design
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
An accurate vertex normal computation scheme
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Proceedings of the International Symposium on Sketch-Based Interfaces and Modeling
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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.