=ADD=
=reftype=
14
=number=
04-10
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2004/04-10.ps.gz
=year=
2004
=month=
04
=author=
Shalaby; Mohamed + Juettler; Bert + Schicho; Josef
=title=
$C^1$ Spline Implicitization of Planar Curves
=abstract=
We present a new method for constructing a low degree $C^1$ 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 spline segments are implicitized. After
multiplying the implicit spline segments by suitable polynomial
factors the resulting bivariate functions are joined along suitable
transversal lines. This yields  a globally $C^1$ bivariate
function.          
=note=
conference paper
=howpublished=
Proceedings of ADG2002, Springer LNAI 2930
=sponsor=
FWF project SFB01315
=keywords=
implicitization, B-spline, approximation, $C^1$ continuity