On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
On the angular defect of triangulations and the pointwise approximation of curvatures
Computer Aided Geometric Design
Inequalities for the curvature of curves and surfaces
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
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Let P be a polygonal line approximating a planar curve @C, the discrete curvature k"d(P) at a vertex P@?P is (usually) defined to be the quotient of the angle between the normals of the two segments with vertex P by the average length of these segments. In this article we give an explicit upper bound of the difference |k(P)-k"d(P)| between the curvature k(P) at P of the curve and the discrete curvature in terms of the polygonal line's data, the supremums over @C of the curvature function k and its derivative k^', and a new geometrical invariant, the return factor@W"@C. One consequence of this upper bound is that it is not needed to know precisely which curve is passing through the vertices of the polygonal line P to have a pointwise information on its curvature.