Geodesic
High-precision invariant on rotation parameterization of curves
Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 16-28.

Voir la notice de l'article provenant de la source Math-Net.Ru

A problem of invariant on rotation curves, specified by the points, was investigated. Arc length was chosen as curve parameter. The algorithm for evaluation of arch length with 4th order of accuracy is proposed. Methods for calculating of others curve characteristics as tangent slope, curvature and derivative of curvature, were also offered. The common requirements for approximation supplying invariant on rotation approximation were investigated. 
@article{MM_2008_20_1_a1,
     author = {E. A. Alshina and E. S. Ivanchenko and N. N. Kalitkin and V. F. Tishkin},
     title = {High-precision invariant on rotation parameterization of curves},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {16--28},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_1_a1/}
}
TY  - JOUR
AU  - E. A. Alshina
AU  - E. S. Ivanchenko
AU  - N. N. Kalitkin
AU  - V. F. Tishkin
TI  - High-precision invariant on rotation parameterization of curves
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 16
EP  - 28
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_1_a1/
LA  - ru
ID  - MM_2008_20_1_a1
ER  - 
%0 Journal Article
%A E. A. Alshina
%A E. S. Ivanchenko
%A N. N. Kalitkin
%A V. F. Tishkin
%T High-precision invariant on rotation parameterization of curves
%J Matematičeskoe modelirovanie
%D 2008
%P 16-28
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2008_20_1_a1/
%G ru
%F MM_2008_20_1_a1
E. A. Alshina; E. S. Ivanchenko; N. N. Kalitkin; V. F. Tishkin. High-precision invariant on rotation parameterization of curves. Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 16-28. http://geodesic.mathdoc.fr/item/MM_2008_20_1_a1/

[1] N. N. Kalitkin, A. N. Rubtsov, “Rotatsionno-invariantnyi metod interpolyatsii”, Matematicheskoe modelirovanie, 4:7 (1992), 107–120 | MR | Zbl

[2] N. N. Kalitkin, L. V. Kuzmina, E. V. Maevskii, V. F. Tishkin, “Rotatsionnaya invariantnost parametricheskoi splain interpolyatsii”, Matematicheskoe modelirovanie, 10:4 (1998), 83–90 | MR

[3] N. N. Kalitkin, L. V. Kuzmina, “Ob estestvennykh interpolyatsionnykh splainakh”, Matematicheskoe modelirovanie, 6:4 (1994), 77–114 | MR | Zbl

[4] N. N. Kalitkin, Chislennye metody, Nauka, M., 1978 | MR