Спираль страницӑн кодне пӑхни

{{Пĕлтерĕшсем|Спираль (пĕлтерĕшсем)}}
'''Спираль''' — хăшпĕр йышши йĕрсем тĕлĕшпе историлле майпа çирĕпленне ят. 

Çав вăхăтрах спираль пирки [[математика]] енчен [[тĕллĕх]]лĕ [[палăртав]]сем те майлаштараççĕ. 
== Лаптак спиральсем ==
<gallery>
Image:Archimedean spiral.svg|Архимед спиралĕ
Image:Cornu Spiral.svg|Корню спиралĕ
Image:Fermat's spiral.svg|Ферма спиралĕ
Image:Hyperspiral.svg|Гиперболăлла спираль
Image:Lituus.svg| lituus
Image:Logarithmic Spiral Pylab.svg|Логарифмла спираль
Image:Spiral of Theodorus.svg|Феодор спиралĕ
Image:Fibonacci_spiral.svg|Фибоначчи спиралĕ (Ылттăн спираль)
Image:Archimedean-involute-circle-spirals-comparison.svg|[[Çавракăш эвольвенти|Çаврашка инволюти]] (хури) Архимед спиралĕпе (хĕрли) пĕр мар
</gallery>
== Уçлăхри спиральсем ==
=== Сферăлла спираль ===
== Çавăн пекех ==
* [[Геликоид]]
* [[Синусоидăлла спираль]]

== Асăрхавсем ==
{{Асăрхавсем}}

== Литература ==
* Cook, T., 1903. ''Spirals in nature and art''. Nature 68 (1761), 296.
* Cook, T., 1979. ''The curves of life''. Dover, New York.
* Habib, Z., Sakai, M., 2005. ''Spiral transition curves and their applications''. Scientiae Mathematicae Japonicae 61 (2), 195—206.
* Dimulyo, S., Habib, Z., Sakai, M., 2009. ''Fair cubic transition between two circles with one circle inside or tangent to the other''. Numerical Algorithms 51, 461—476 [http://www.springerlink.com/content/113644325114041q/] {{Webarchive|url=https://web.archive.org/web/20181127024818/https://link.springer.com/article/10.1007/s11075-008-9252-1 |date=2018-11-27 }}{{Недоступная ссылка|date=Февраль 2020 |bot=InternetArchiveBot }}.
* Harary, G., Tal, A., 2011. ''The natural 3D spiral''. Computer Graphics Forum 30 (2), 237—246 [http://webee.technion.ac.il/~ayellet/Ps/11-HararyTal.pdf] {{Webarchive|url=https://web.archive.org/web/20151122013249/http://webee.technion.ac.il/~ayellet/Ps/11-HararyTal.pdf |date=2015-11-22 }}.
* Xu, L., Mould, D., 2009. ''Magnetic curves: curvature-controlled aesthetic curves using magnetic ﬁelds''. In: Deussen, O., Hall, P. (Eds.), Computational Aesthetics in Graphics, Visualization, and Imaging. The Eurographics Association [http://gigl.scs.carleton.ca/sites/default/files/ling_xu/artn-cae.pdf].
* Wang, Y., Zhao, B., Zhang, L., Xu, J., Wang, K., Wang, S., 2004. ''Designing fair curves using monotone curvature pieces''. Computer Aided Geometric Design 21 (5), 515—527 [http://www.sciencedirect.com/science/article/pii/S0167839604000470].
* A. Kurnosenko. ''Applying inversion to construct planar, rational spirals that satisfy two-point G2 Hermite data''. Computer Aided Geometric Design, 27(3), 262—280, 2010 [http://www.sciencedirect.com/science/article/pii/S0167839609001423].
* A. Kurnosenko. ''Two-point G2 Hermite interpolation with spirals by inversion of hyperbola''. Computer Aided Geometric Design, 27(6), 474—481, 2010.
* Miura, K.T., 2006. ''A general equation of aesthetic curves and its self-affinity''. Computer-Aided Design and Applications 3 (1-4), 457—464 [https://web.archive.org/web/20130628000547/http://ktm11.eng.shizuoka.ac.jp/profile/ktmiura/pdf/KTMiura-CAD06Final.pdf].
* Miura, K., Sone, J., Yamashita, A., Kaneko, T., 2005. ''Derivation of a general formula of aesthetic curves''. In: 8th International Conference on Humans and Computers (HC2005). Aizu-Wakamutsu, Japan, pp. 166—171 [https://web.archive.org/web/20130628051506/http://ktm11.eng.shizuoka.ac.jp/profile/ktmiura/pdf/acurveHC0.pdf].
* Meek, D., Walton, D., 1989. ''The use of Cornu spirals in drawing planar curves of controlled curvature''. Journal of Computational and Applied Mathematics 25 (1), 69-78 [http://www.sciencedirect.com/science/article/pii/0377042789900769].
* Farin, G., 2006. ''Class A Bézier curves''. Computer Aided Geometric Design 23 (7), 573—581 [http://www.sciencedirect.com/science/article/pii/S016783960600032X].
* Farouki, R.T., 1997. ''Pythagorean-hodograph quintic transition curves of monotone curvature''. Computer-Aided Design 29 (9), 601—606.
* Yoshida, N., Saito, T., 2006. ''Interactive aesthetic curve segments''. The Visual Computer 22 (9), 896—905 [http://www.yoshida-lab.net/aesthetic/ias2006pg.pdf] {{Webarchive|url=https://web.archive.org/web/20160304064701/http://www.yoshida-lab.net/aesthetic/ias2006pg.pdf |date=2016-03-04 }}.
* Yoshida, N., Saito, T., 2007. ''Quasi-aesthetic curves in rational cubic Bézier forms''. Computer-Aided Design and Applications 4 (9-10), 477—486 [http://www.yoshida-lab.net/aesthetic/cad07yoshida.pdf] {{Webarchive|url=https://web.archive.org/web/20160303205632/http://www.yoshida-lab.net/aesthetic/cad07yoshida.pdf |date=2016-03-03 }}.
* Ziatdinov, R., Yoshida, N., Kim, T., 2012. ''Analytic parametric equations of log-aesthetic curves in terms of incomplete gamma functions''. Computer Aided Geometric Design 29 (2), 129—140 [https://www.dropbox.com/s/mlvpvsta33ii00s/Analytic_equations_of_LACs.pdf].
* Ziatdinov, R., Yoshida, N., Kim, T., 2012. ''Fitting G2 multispiral transition curve joining two straight lines'', Computer-Aided Design 44(6), 591—596 [https://www.dropbox.com/s/29qdj82l868246d/transition_multisiral.pdf].
* Ziatdinov, R., 2012. ''Family of superspirals with completely monotonic curvature given in terms of Gauss hypergeometric function''. Computer Aided Geometric Design 29(7): 510—518, 2012 [https://www.dropbox.com/s/evqdncl18yngviy/Superspiral.pdf].
* Ziatdinov, R., Miura K.T., 2012. ''On the Variety of Planar Spirals and Their Applications in Computer Aided Design''. European Researcher 27(8-2), 1227—1232 [http://www.erjournal.ru/pdf.html?n=1345307278.pdf] {{Webarchive|url=https://web.archive.org/web/20200723082739/http://www.erjournal.ru/pdf.html?n=1345307278.pdf |date=2020-07-23 }}.

{{Кукрашкасем}}

[[Категори:Спиральсем|*]]