A Multiscale Spline Representation for Implicit Objects

Luiz Velho
Jonas de Miranda Gomes
IMPA -- Instituto de Matematica Pura e Aplicada 
22460, Rio de Janeiro, Brazil
 
This paper introduces a new representation for implicitly
defined objects. The effective description of geometry is a
fundamental problem in modeling and rendering of complex shapes.
We propose as a solution to this problem
an implicit piecewise description adapted to local features
of the object geometry. This representation is obtained by
decomposing the implicit function
into a multiscale spline basis.
This B-spline pyramid is constructed through an
adaptation process based on the wavelet transform.