More-or-less-uniform sampling and lengths of curves
Authors:
Lyle Noakes and Ryszard Kozera
Journal:
Quart. Appl. Math. 61 (2003), 475-484
MSC:
Primary 65D05; Secondary 41A05, 51M25
DOI:
https://doi.org/10.1090/qam/1999832
MathSciNet review:
MR1999832
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Abstract: More-or-less-uniform samples are introduced and used to estimate lengths of smooth regular strictly convex curves in ${\mathbb {R}^{2}}$. Quartic convergence is proved and illustrated by examples.
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R. Klette, A. Rosenfeld, and F. Sloboda (eds.), Advances of Digital and Computational Geometry, Springer-Verlag, 1998
J. Milnor, Morse Theory, Annals. of Math. Studies, Vol. 51, Princeton University Press, Princeton, NJ, 1963
P. A. P. Moran, Measuring the length of a curve, Biometrika 53, 359–364 (1966)
L. Noakes, R. Kozera, and R. Klette, Length estimation for curves with different samplings, In: G. Bertrand, A. Imiya, and R. Klette (eds.), Digital and Image Geometry, Lecture Notes in Computer Science, Vol. 2243, Springer-Verlag, Berlin Heidelberg, 2001 pp. 339–351
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F. Sloboda, B. Zaťko, and J. Stoer, On approximation of planar one-dimensional continua, In: R. Klette, A. Rosenfeld, and F. Sloboda (eds.), Advances in Digital and Computational Geometry, Springer, Singapore, 1998, pp. 113–160
H. Steinhaus, Praxis der Rektifikation und zum Längenbegriff, Akad. Wiss. Leipzig. Berlin 82, 120–130 (1930)
B. L. van der Waerden, Geometry and Algebra in Ancient Civilizations, Springer-Verlag, Berlin, 1983
A. G. Werschulz and H. Woźniakowski, What is the complexity of surface integration?, J. Complexity 17, 442–466 (2001)
K. Mørken and K. Scherer, A general framework for high-accuracy parametric interpolation, Math. of Comp. 66, No. 217, 237–260 (1997)
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© Copyright 2003
American Mathematical Society
