螺線

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

## 二維螺線

* 費馬螺線
* 等角螺線
* 雙曲螺線
* 圓內螺線
* 阿基米德螺線
* 連鎖螺線
* 柯奴螺線
* 歐拉螺線

## 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.
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* 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）.