Spirála

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:

Literatura
  • Miroslava Jarešová – Ivo Volf: Matematika křivek, studijní text pro řešitele FO a ostatní zájemce o fyziku.
  • (anglicky) Cook, T., 1903. Spirals in nature and art. Nature 68 (1761), 296.
  • (anglicky) Cook, T., 1979. The curves of life. Dover, New York.
  • (anglicky) Habib, Z., Sakai, M., 2005. Spiral transition curves and their applications. Scientiae Mathematicae Japonicae 61 (2), 195 – 206.
  • (anglicky) 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 [nedostupný zdroj].
  • (anglicky) Harary, G., Tal, A., 2011. The natural 3D spiral. Computer Graphics Forum 30 (2), 237 – 246 .
  • (anglicky) 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 .
  • (anglicky) 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 .
  • (anglicky) 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 .
  • (anglicky) A. Kurnosenko. Two-point G2 Hermite interpolation with spirals by inversion of hyperbola. Computer Aided Geometric Design, 27(6), 474-481, 2010.
  • (anglicky) Miura, K.T., 2006. A general equation of aesthetic curves and its self-affinity. Computer-Aided Design and Applications 3 (1–4), 457–464 .
  • (anglicky) 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 .
  • (anglicky) 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 .
  • (anglicky) Farin, G., 2006. Class A Bézier curves. Computer Aided Geometric Design 23 (7), 573–581 .
  • (anglicky) Farouki, R.T., 1997. Pythagorean-hodograph quintic transition curves of monotone curvature. Computer-Aided Design 29 (9), 601–606.
  • (anglicky) Yoshida, N., Saito, T., 2006. Interactive aesthetic curve segments. The Visual Computer 22 (9), 896–905 .
  • (anglicky) Yoshida, N., Saito, T., 2007. Quasi-aesthetic curves in rational cubic Bézier forms. Computer-Aided Design and Applications 4 (9–10), 477–486 .
  • (anglicky) 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 .
  • (anglicky) Ziatdinov, R., Yoshida, N., Kim, T., 2012. Fitting G2 multispiral transition curve joining two straight lines, Computer-Aided Design 44(6), 591–596 .
  • (anglicky) 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 .
  • (anglicky) 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 .

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