螺線

螺線（英語：spiral）是指一些圍着某些定點或軸旋轉且不斷收縮或擴展的曲線。

阿基米德螺線

等角螺線

費馬螺線

雙曲螺線

二維螺線

參考文獻

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] （頁面存檔備份，存於網際網路檔案館）.
Harary, G., Tal, A., 2011. The natural 3D spiral. Computer Graphics Forum 30 (2), 237 – 246 [2] （頁面存檔備份，存於網際網路檔案館）.
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] （頁面存檔備份，存於網際網路檔案館）.
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] （頁面存檔備份，存於網際網路檔案館）.
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] （頁面存檔備份，存於網際網路檔案館）.
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] （頁面存檔備份，存於網際網路檔案館）.
Farin, G., 2006. Class A Bézier curves. Computer Aided Geometric Design 23 (7), 573–581 [9] （頁面存檔備份，存於網際網路檔案館）.
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] （頁面存檔備份，存於網際網路檔案館）.
Yoshida, N., Saito, T., 2007. Quasi-aesthetic curves in rational cubic Bézier forms. Computer-Aided Design and Applications 4 (9–10), 477–486 [11] （頁面存檔備份，存於網際網路檔案館）.
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] （頁面存檔備份，存於網際網路檔案館）.
Ziatdinov, R., Yoshida, N., Kim, T., 2012. Fitting G2 multispiral transition curve joining two straight lines, Computer-Aided Design 44(6), 591–596 [13] （頁面存檔備份，存於網際網路檔案館）.
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] （頁面存檔備份，存於網際網路檔案館）.
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] （頁面存檔備份，存於網際網路檔案館）.

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