螺线

螺线（英語：spiral）是指一些围着某些定点或轴旋转且不断收缩或扩展的曲线。 费马螺线 等角螺线 双曲螺线 圆内螺线 阿基米德螺线 连锁螺线 柯奴螺线 欧拉螺線 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 [1] （页面存档备份，存于互联网档案馆）. Harary, G., Tal, A., 2011. The natural 3D spiral. Computer Graphics Forum 30 (2), 237 – 246 [2] （页面存档备份，存于互联网档案馆）. 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 [3] （页面存档备份，存于互联网档案馆）. 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 [4] （页面存档备份，存于互联网档案馆）. 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 [5] （页面存档备份，存于互联网档案馆）. 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 [6]. 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 [7]. 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 [8] （页面存档备份，存于互联网档案馆）. Farin, G., 2006. Class A Bézier curves. Computer Aided Geometric Design 23 (7), 573–581 [9] （页面存档备份，存于互联网档案馆）. 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 [10] （页面存档备份，存于互联网档案馆）. Yoshida, N., Saito, T., 2007. Quasi-aesthetic curves in rational cubic Bézier forms. Computer-Aided Design and Applications 4 (9–10), 477–486 [11] （页面存档备份，存于互联网档案馆）. 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 [12] （页面存档备份，存于互联网档案馆）. Ziatdinov, R., Yoshida, N., Kim, T., 2012. Fitting G2 multispiral transition curve joining two straight lines, Computer-Aided Design 44(6), 591–596 [13] （页面存档备份，存于互联网档案馆）. 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 [14] （页面存档备份，存于互联网档案馆）. 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 [15] （页面存档备份，存于互联网档案馆）.