=ADD=
=reftype=
14
=number=
04-11
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2004/04-11.ps.gz
=year=
2004
=month=
04
=author=
Juettler; Bert + Schicho; Josef + Shalaby; Mohamed
=title=
Spline Implicitization of Planar Curves
=abstract=
 We present a new method for constructing a low degree
implicit spline representation of a given parametric planar curve.  To
ensure the low degree condition, quadratic B-splines are used to
approximate the given curve via orthogonal projection in Sobolev
spaces. Adaptive knot removal, which is based on spline wavelets, is
used
to reduce the number of segments. The B-spline segments are
implicitized, and the resulting bivariate functions are joined along
suitable transversal lines, yielding a globally continuous bivariate
function. As shown by analyzing the asymptotic behavior of these
transversal lines for step size $h\to0$, the given curve can be
implicitized with any desired accuracy.        
=note=
conference paper
=howpublished=
In T. Lyche, M.L. Mazure, L. Schumaker (eds.), Curve and Surface Design: St. Malo 2002 , Nashboro Press, Brentwood 2003, 225-234
=sponsor=
FWF project SFB01315
=keywords=
implicitization, B-spline, approximation, knot removal