=ADD=
=reftype=
14
=number=
97-30
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1997/97-30.ps.gz
=sponsor=
Supported by the Austrian Science Foundation (FWF) project HySaX, 
Proj. No. P11160-TEC and Partially supported by the CGAL Project, 
ESPRIT IV, No. 21957
=year=
1997
=author=
Quoc-Nam; Tran + Van Geem; Carl
=title=
{NURBS} Interpolation of Surface-to-Surface Intersections
=month=
10
=keywords=
Symbolic-Numerical Method, CAGD, NURBS
=abstract=
We present a hybrid symbolic-numerical algorithm for piecewise 
interpolation and representation of surface-to-surface intersections -- 
a fundamental and difficult problem in Computer Aided Geometric Design 
(CAGD) and solid modeling.
Our method helps to get a fast and accurate insight of the intersections --
This is the main contribution of the paper.
The method overcomes the main difficulties of numerical tracing, namely 
finding a sample point for every real branch and marching through 
singularities by using techniques for real root isolation of polynomials 
with real algebraic number coefficients. 
On the other hand, the method does not require the expensive 
computation of birational mapping, projections, re-constructions, etc.\ as
in a pure symbolic method.
Further it utilizes non-uniform rational B-spline (NURBS) to piecewise 
interpolate the
intersection in order to improve the efficiency of the algorithms and
the smoothness of the plots.
Experiments from surface-to-surface intersection examples found in the
literature show a dramatic speed up of the method.
=location=
2
=owner=
2
=source=
3