Spirála

Technology

12 hours ago

Author

Spirála je křivka, která obíhá pevně daný ústřední bod (pól spirály) a přitom se od tohoto bodu soustavně vzdaluje. Formální matematická definice, která by zahrnovala všechny spirály, neexistuje (na rozdíl např. od kuželoseček).

Mezi důležité spirály patří: * Archimédova spirála * Fermatova spirála * hyperbolická spirála * hyperbolická platformická spirála * lituus * logaritmická spirála * klotoida (též Eulerova nebo Cornuova spirála)

Literatura

Miroslava Jarešová - Ivo Volf: Matematika křivek, studijní text pro řešitele FO a ostatní zájemce o fyziku. [http://fyzikalniolympiada. +morecz/texty/matematika/mkrivek. pdf] * 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/]. * 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]. * 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].