Fractals and Bernstein polynomials

✍ Scribed by Ljubiša M. Kocić

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Weight: 582 KB
• Volume: 33
• Category: Article
• ISSN: 0031-5303
• DOI: 10.1007/bf00150833

✦ Synopsis

Self-similarity

of Bernstein polynomials, embodied in their subdivision property is used for construction of an Iterative (hyperbolic) Function System (IFS) whose attractor is the graph of a given algebraic polynomial of arbitrary degree. It is shown that such IFS is of just-touching type, and that it is peculiar to algebraic polynomials.

Such IFS is then applied to faster evaluation of Bezier curves and to introduce interactive free-form modeling component into fractal sets.