[[GeoGebra]]
* 曲率函数から曲線を生成3 [#md7cf93f]
** Reconstruction of curve from its curvature with composite Simpson's rule. [#ua69f942]
#ref(curve_from_curvature3.png)
#ref(curve_from_curvature3.ggb)
- 曲率函数が k(x) で与えられたとき、そのような曲率を持つ曲線を (simpson_g, simpson_h) で表しました．
- Integral[]で積分できる函数が限定されているので合同シンプソンの公式で数値積分しています。
- I added ZoomIn[1] to the "On Update" script for k(x), thank you, @mike_geogebra.
- [[Dynamic Worksheet:http://www.knoppix-math.org/geogebra/curve_from_curvature3.html]]（Java Applet）
** Reference [#x8015062]
- Gray, A. "Modern Differential Geometry of Curves and Surfaces with Mathematica", 3rd ed., 2006.
- [[Plane and Space Curves. Curvature. Curvature-based Features:http://www.mpi-inf.mpg.de/~ag4-gm/handouts/06gm_curves.pdf]] by Alexander Belyaev
- Weisstein, Eric W. "Cornu Spiral." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CornuSpiral.html
- [[F. Dillen, The classification of hypersurfaces of a Euclidean space with parallel higher order fundamental form:http://www.springerlink.com/content/xn17187417p4pg78/]]
- http://en.wikipedia.org/wiki/Simpson's_rule
![[PukiWiki]](image/knxmpen.png "[PukiWiki]")
