Geodesic
On the length preserving approximation of plane curves by circular arcs
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 588-604 
A. I. Kurnosenko. On the length preserving approximation of plane curves by circular arcs. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 588-604. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a1/
@article{ZVMMF_2017_57_4_a1,
     author = {A. I. Kurnosenko},
     title = {On the length preserving approximation of plane curves by circular arcs},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {588--604},
     year = {2017},
     volume = {57},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a1/}
}
TY  - JOUR
AU  - A. I. Kurnosenko
TI  - On the length preserving approximation of plane curves by circular arcs
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 588
EP  - 604
VL  - 57
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a1/
LA  - ru
ID  - ZVMMF_2017_57_4_a1
ER  - 
%0 Journal Article
%A A. I. Kurnosenko
%T On the length preserving approximation of plane curves by circular arcs
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 588-604
%V 57
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a1/
%G ru
%F ZVMMF_2017_57_4_a1

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

A technique for the length preserving approximation of plane curves by two circular arcs is analyzed. The conditions under which this technique can be applied are extended, and certain consequences of the proved results unrelated to the approximation problem are discussed. More precisely, inequalities for the length of a convex spiral arc subject to the given boundary conditions are obtained. Conjectures on curve closeness conditions obtained using computer simulation are discussed.

[1] Sabitov I. X., Slovesnov A. V., “Priblizhenie ploskikh krivykh krugovymi dugami”, Zh. vychisl. matem. i matem. fiz., 50:8 (2010), 1347–1356 | Zbl

[2] Kurnosenko A. I., “Obschie svoistva ploskikh spiralnykh krivykh”, Zapiski nauch. sem. POMI, 353, 2009, 93–115 | Zbl

[3] Bolton K. M., “Biarc curves”, Comp.-Aided Design, 7:2 (1975), 89–92 | DOI

[4] Kurnosenko A., “Inversnyi invariant pary okruzhnostei”, Zapiski nauch. sem. POMI, 261, 1999, 167–186 | Zbl

[5] Kurnosenko A. I., “Korotkie spirali”, Zapiski nauch. sem. POMI, 372, 2009, 34–43

[6] Kurnosenko A. I., “Biarcs and bilens”, Comp. Aided Geom. Design, 30 (2013), 310–330 | DOI | MR | Zbl

[7] Aleksandrov A. D., Vnutrennyaya geometriya vypuklykh poverkhnostei, OGIZ, M.–L., 1948

[8] Savelov A. A., Ploskie krivye. Sistematika, svoistva, primenenie, Spravochnoe rukovodstvo, Fizmatgiz, M., 1960