 

Chand T. John
All Bézier curves are attractors of iterated function systems


Published: 
April 18, 2007 
Keywords: 
Bézier, subdivision, IFS, selfaffine, selfsimilar, polynomial, curve 
Subject: 
53A 


Abstract
The fields of computer aided geometric design and fractal geometry have
evolved independently of each other over the past several decades. However,
the existence of socalled smooth fractals, i.e., smooth curves or surfaces
that have a selfsimilar nature, is now wellknown. Here
we describe the selfaffine nature of quadratic Bézier curves in detail and
discuss how these selfaffine properties can be extended to other types of
polynomial and rational curves. We also show how these properties can be used
to control shape changes in complex fractal shapes by performing simple
perturbations to smooth curves. 

Author information
Computer Science Department, Stanford University, Stanford, CA 94305
ctj@stanford.edu
http://www.stanford.edu/~ctj

