=ADD=
=reftype=
14
=number=
99-27
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1999/99-27.ps.gz
=year=
1999
=month=
09
=author=
Hillgarter; Erik + Landsmann; G\"unter + Schicho; Josef + Winkler; Franz
=title=
Generalized Offsets as Envelopes of a One-parameter Set of Spheres
=abstract=
A generalized offset of a parametrized curve $m(t)$ in ${\R}^n$ is the
set of all points
having a normal distance $r(t)$ from $m(t).$ Thus the concept covers
the classical offsets (for $r(t)=const$) of plane curves as well as
pipes and canal surfaces. In this paper we develop methods for
generating a rational parametrization of
generalized offsets of rational curves $m(t)$ with rational radius
variation $r(t),$ in case such a parametrization exists. In addition
we try to select those methods, which allow an
implementation, that provides solutions in reasonable time.
=sponsor=
Austrian Science Fund (FWF), Proj.Nr. P11160-TEC (HySax), Proj.Nr.
P12662-TEC (Adjoints), and the special research
area SFB F013, subprojects 03 and 04.
=keywords=
canal surface, sum of two squares
=end=