# Refereed Conference Paper

An Exact, Complete and Efficient
Implementation for Computing Planar Maps of Quadric Intersection
Curves. Eric Berberich, Michael Hemmer, Lutz Kettner, Elmar
Schömer, and Nicola Wolpert. In: Proc. of the
21st ACM Symp. on Computational Geometry,
Pisa Italy, pp. ..., June 2005.

## Abstract

We present the first exact, complete and efficient
implementation that computes for a given set
*P={p*_{1},...,p_{n}} of quadric surfaces the
planar map induced by all intersection curves
*p*_{1} p_{i}, *2 <= i <= n*,
running on the surface of *p*_{1}. The vertices in this
graph are the singular and *x*-extreme points of the curves as well
as all intersection points of pairs of curves. Two vertices are connected
by an edge if the underlying points are connected by a branch of one of the
curves. Our work is based on and extends ideas developed in
[Schömer&Wolpert 2004] and [Eigenwillig et.al. 2004].

Our implementation is *complete* in the sense
that it can handle all kind of inputs including all degenerate ones
where intersection curves have singularities or pairs of curves intersect
with high multiplicity. It is *exact* in that it always computes the
mathematical correct result. It is *efficient measured in running
times.*

*
*[PDF]
© ACM 2005.

[PostScript]
© ACM 2005.

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Lutz Kettner
(

*<surname>*@mpi-inf.mpg.de).
Last modified on Friday, 15-Jul-2005 18:55:31 MEST.