%0 Journal Article
%A Amat Plata, Sergio
%A Moncayo Hormigo, María José
%T Error bounds for a class of subdivision schemes based on the two-scale refinement equation
%D 2008
%@ 1088-6842(e)
%U http://hdl.handle.net/10317/555
%X Subdivision schemes are iterative procedures to construct curves and constitute fundamental tools in Computer Aided Design. Starting with an initial control polygon, a subdivision scheme refines the
computed values at the previous step according to some basic rules.
The scheme is said to be convergent if there exists a limit curve. The computed values define a control polygon in each step. This paper is devoted to estimate error bounds between the “ideal” limit curve and
the control polygon defined after k subdivision stages. In particular,
a stop criteria of convergence is obtained. The considered refinement rules in the paper are widely used in practice and are associated to the well known two-scale refinement equation including as particular
examples Daubechies’ schemes. Companies such as Pixar have made subdivision schemes the basic tool for much of their computer graphicsmodelling software.
%K Curvas
%K Equaciones
%K Software informático de modelado de gráficos
%K Matemática Aplicada
%~ GOEDOC, SUB GOETTINGEN