Title :
The fractal nature of Bezier curves
Author_Institution :
Dept. of Comput. Sci., Rice Univ., Houston, TX, USA
Abstract :
Fractals are attractors - fixed points of iterated function systems. Bezier curves are polynomials - linear combinations of Bernstein basis functions. The de Casteljau subdivision algorithm is used here to show that Bezier curves are also attractors. Thus, somewhat surprisingly, Bezier curves are fractals. This fractal nature of Bezier curves is exploited to derive a new rendering algorithm for Bezier curves.
Keywords :
computational geometry; curve fitting; fractals; iterative methods; polynomials; rendering (computer graphics); Bernstein basis functions; Bezier curves; de Casteljau subdivision algorithm; fixed points; fractal nature; iterated function systems; linear combinations; polynomials; Computer science; Convergence; Fractals; Gaskets; Polynomials; Solid modeling;
Conference_Titel :
Geometric Modeling and Processing, 2004. Proceedings
Print_ISBN :
0-7695-2078-2
DOI :
10.1109/GMAP.2004.1290020
