Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein
Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413 We show how to compute and maintain the two-dimensional arrangement on a quadric that is induced by...
Eric Berberich, Elmar Schömer, Michael Hemmer, Nicola Wolpert, Lutz Kettner
We present the first exact, complete and efficient implementation that computes for a given set P = {p1,..., pn} of quadric surfaces the planar map induced by all intersection curves p1 ∩ pi, 2 ≤...
We discuss how to compute and implement three geometric problems dealing with nonlinear three-dimensional surfaces. As a main tool we rely on planar subdivisions induced by algebraic curves,...
Exact Arrangements on Tori and Dupin Cyclides (2008)
Berberich, Eric, Kerber, Michael
An algorithm and implementation is presented to compute the exact arrangement induced by arbitrary algebraic surfaces on a parametrized ring Dupin cyclide. The family of Dupin cyclides contains as a...
Arrangements on Surfaces of Genus One: Tori and Dupin Cyclides (2008)
Berberich, Eric, Kerber, Michael
An algorithm is presented to compute the exact arrangement induced by arbitrary algebraic surfaces on a parametrized ring Dupin cyclide, including the special case of the torus. The intersection of...
Geometric Analysis of Algebraic Surfaces Based on Planar Arrangements (2008)
Berberich, Eric, Kerber, Michael, Sagraloff, Michael
We present a method to compute the exact topology of a real algebraic surface $S$, implicitly given by a polynomial $f \in \mathbb{Q}[x,y,z]$ of arbitrary degree $N$. Additionally, our analysis...
Exact Geometric-Topological Analysis of Algebraic Surfaces (2008)
Berberich, Eric, Kerber, Michael, Sagraloff, Michael
We present a method to compute the exact topology of a real algebraic surface $S$, implicitly given by a polynomial $f \in \mathbb{Q}[x,y,z]$ of arbitrary degree $N$. Additionally, our analysis...
Berberich, Eric, Sagraloff, Michael
We present a generic framework on a set of surfaces $\calS$ in $\R^3$ that provides their geometric and topological analysis in order to support various algorithms and applications in computational...
Sweeping and maintaining two-dimensional arrangements on surfaces: A first step (2007)
Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein
We introduce a general framework for processing a set of curves defined on a continuous two-dimensional parametric surface, while sweeping the parameter space. We can handle planes, cylinders,...
Sweeping and maintaining two-dimensional arrangements on surfaces: A first step (2007)
Eric Berberich, Efi Fogel, Dan Halperin, Ron Wein
We introduce a general framework for processing a set of curves defined on a continuous two-dimensional parametric surface, while sweeping the parameter space. A major goal of our work is to maximize...
Sweeping and maintaining two-dimensional arrangements on surfaces: A first step (2007)
Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein
Abstract. We introduce a general framework for sweeping a set of curves embedded on a two-dimensional parametric surface. We can handle planes, cylinders, spheres, tori, and surfaces homeomorphic to...
The Bentley Ottmann sweep line algorithm is a standard tool to compute the arrangement of algebraic curves in the plane. If degenerate positions are not excluded from the input, variants of this...
Revision of interface specification of algebraic kernel (2007)
Berberich, Eric, Hemmer, Michael, Karavelas, Menelaos I., Teillaud, Monique
Sweeping and maintaining two-dimensional arrangements on surfaces: A first step (2007)
Berberich, Eric, Fogel, Efi, Halperin, Dan, Mehlhorn, Kurt, Wein, Ron
Sweeping and maintaining two-dimensional arrangements on quadrics (2007)
Berberich, Eric, Fogel, Efi, Halperin, Dan, Mehlhorn, Kurt, Wein, Ron
Exact Computation of Arrangements of Rotated Conics (2007)
Berberich, Eric, Caroli, Manuel, Wolpert, Nicola
Transformations of geometric objects, like translation and rotation, are fundamental operations in CAD-systems. Rotations trigger the need to deal with trigonometric functions, which is hard to...
Sweeping and maintaining two-dimensional arrangements on surfaces (2007)
Berberich, Eric, Fogel, Efi, Halperin, Dan, Wein, Ron
We introduce a general framework for processing a set of curves defined on a continuous two-dimensional parametric surface, while sweeping the parameter space. A major goal of our work is to maximize...
Computing Envelopes of Quadrics (2007)
Berberich, Eric, Meyerovitch, Michal
We present the computation of envelopes of a set of quadratic surfaces defined in ${\rm I\!\hspace{-0.025em} R}^3$. Our solution is based on the new {\sc Cgal} {\tt Envelope\_3} package that provides...
Eric Berberich, Elmar Schömer, Michael Hemmer, Lutz Kettner, Nicola Wolpert
Ú�ÖØ��×�ÒØ��×�Ö�Ô��Ö�Ø��×�Ò�ÙÐ�Ö�Ò�Ü�ÜØÖ�Ñ�ÔÓ�ÒØ ×...
Exacus: Efficient and exact algorithms for curves and surfaces (2005)
Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...
Abstract. We present the first release of the EXACUS C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness,...
Exacus: Efficient and exact algorithms for curves and surfaces (2005)
Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...
Abstract. We present the first release of the EXACUS C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness,...
EXACUS: Efficient and Exact Algorithms for Curves and Surfaces (2005)
Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...
We present the first release of the EXACUS C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are efficiency, correctness, completeness, clarity of...
Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Lutz Kettner, Kurt Mehlhorn, ...
Project funded by the European Community under the “Information Society Technologies” Programme (1998–2002)
Berberich, Eric, Hemmer, Michael, Kettner, Lutz, Schömer, Elmar, Wolpert, Nicola, Mitchell, Joe, ...
We present the first exact, complete and efficient implementation that computes for a given set $P=\{p_1,\dots,p_n\}$ of quadric surfaces the planar map induced by all intersection curves $p_1\cap...
EXACUS: Efficient and exact algorithms for curves and surfaces (2005)
Berberich, Eric, Eigenwillig, Arno, Hemmer, Michael, Hert, Susan, Kettner, Lutz, Mehlhorn, Kurt, ...
We present the first open-source release of the C\texttt{++} libraries of the \textsc{Exacus} project of the Max-Planck-Institut f{\"u}r Informatik. Our software computes arrangements of curves and...
An empirical comparison of software for constructing arrangements of curved arcs (2004)
Berberich,Eric, Eigenwillig,Arno, Emiris,Ioannis, Fogel,Efraim, Hemmer,Michael, Halperin,Dan, ...
EXACUS : Efficient and Exact Algorithms for Curves and Surfaces (2004)
Berberich,Eric, Eigenwillig,Arno, Hemmer,Michael, Hert,Susan, Kettner,Lutz, Mehlhorn,Kurt, ...
An empirical comparison of software for constructing arrangements of curved arcs (2004)
Berberich, Eric, Eigenwillig, Arno, Emiris, Ioannis, Fogel, Efraim, Hemmer, Michael, Halperin, Dan, ...
EXACUS : Efficient and Exact Algorithms for Curves and Surfaces (2004)
Berberich, Eric, Eigenwillig, Arno, Hemmer, Michael, Hert, Susan, Kettner, Lutz, Mehlhorn, Kurt, ...
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons (2002)
Berberich,Eric, Eigenwillig,Arno, Hemmer,Michael, Hert,Susan, Mehlhorn,Kurt, Schömer,Elmar
We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately...
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons (2002)
Berberich, Eric, Eigenwillig, Arno, Hemmer, Michael, Hert, Susan, Mehlhorn, Kurt, Schömer, Elmar, ...
We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately...
A computational basis for conic arcs and Boolean operations on conic polygons (2002)
Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Kurt Mehlhorn, Elmar Schömer
Abstract. We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that...
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons (2002)
Eric Berberich, Arno Eigenwillig, Michael Hemmer, Susan Hert, Kurt Mehlhorn, Elmar Schömer
We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately...
An Empirical Comparison of Software for Constructing Arrangements of Curved Arcs (2000)
Sylvain Pion, Monique Teillaud, Efraim Fogel, Dan Halperin, Ron Wein, Ioannis Emiris, ...
Arrangements of planar curves are fundamental structures in computational geometry.