Smooth Self-Similar Curves
Inhaltsverzeichnis
Reference
Craig S. Kaplan: Smooth Self-Similar Curves. In: Bridges 2011. Pages 209–216
DOI
Abstract
I present a technique for constructing self-similar curves from smooth base curves. The technique is similar to that used in Iterated Function Systems like the Koch curve, except that it does not require a piecewise linear path in order to induce a set of similarities. I explain the mathematical machinery behind the technique, describe a practical numerical approximation that can be implemented in software, and show some results.
Extended Abstract
Bibtex
Used References
[1] Michael F. Barnsley. Fractals Everywhere. Morgan Kauffman, second edition, 2000.
[2] Adam Finkelstein and David H. Salesin. Multiresolution curves. In Proceedings of the 21st annual confer- ence on Computer graphics and interactive techniques, SIGGRAPH ’94, pages 261–268. ACM, 1994.
[3] Aaron Hertzmann, Nuria Oliver, Brian Curless, and Steven M. Seitz. Curve analogies. In Proceedings of the 13th Eurographics workshop on Rendering, EGRW ’02, pages 233–246. Eurographics Association, 2002.
[4] Benoît B. Mandelbrot. The Fractal Geometry of Nature. Times Books, 1983.
[5] Peter Shirley. Fundamentals of Computer Graphics. A K Peters, second edition, 2005.
Links
Full Text
http://archive.bridgesmathart.org/2011/bridges2011-209.pdf
