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GC
2011
Springer
7 years 9 months ago
A Note on the Complexity of Real Algebraic Hypersurfaces
Given an algebraic hypersurface O in Êd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the...
Michael Kerber, Michael Sagraloff
COMPGEOM
2011
ACM
7 years 9 months ago
A generic algebraic kernel for non-linear geometric applications
We report on a generic uni- and bivariate algebraic kernel that is publicly available with Cgal 3.7. It comprises complete, correct, though efficient state-of-the-art implementati...
Eric Berberich, Michael Hemmer, Michael Kerber
CORR
2011
Springer
206views Education» more  CORR 2011»
8 years 1 months ago
Arrangement Computation for Planar Algebraic Curves
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decompos...
Eric Berberich, Pavel Emeliyanenko, Alexander Kobe...
COMPUTING
2004
108views more  COMPUTING 2004»
8 years 6 months ago
Fairness Criteria for Algebraic Curves
We develop methods for the variational design of algebraic curves. Our approach is based on truly geometric fairness criteria, such as the elastic bending energy. In addition, we ...
Pavel Chalmovianský, Bert Jüttler
SMA
2008
ACM
149views Solid Modeling» more  SMA 2008»
8 years 6 months ago
Exact arrangements on tori and Dupin cyclides
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 cyc...
Eric Berberich, Michael Kerber
IMAMS
2007
157views Mathematics» more  IMAMS 2007»
8 years 7 months ago
Regularity Criteria for the Topology of Algebraic Curves and Surfaces
In this paper, we consider the problem of analysing the shape of an object defined by polynomial equations in a domain. We describe regularity criteria which allow us to determine...
Lionel Alberti, Bernard Mourrain
NSF
1994
Springer
151views Computer Vision» more  NSF 1994»
8 years 10 months ago
Algebraic Geometry and Object Representation in Computer Vision
The goal of algebraic geometry is to gain an understanding of the behaviour of functions related by polynomial relationships. Algebraic curves and surfaces having considerable adva...
Sylvain Petitjean
ESA
2003
Springer
141views Algorithms» more  ESA 2003»
8 years 11 months ago
Jacobi Curves: Computing the Exact Topology of Arrangements of Non-singular Algebraic Curves
We present an approach that extends the BentleyOttmann sweep-line algorithm [3] to the exact computation of the topology of arrangements induced by non-singular algebraic curves o...
Nicola Wolpert
ISVC
2009
Springer
9 years 24 days ago
Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast
Given a Cylindrical Algebraic Decomposition of an implicit algebraic curve, visualizing distinct curve arcs is not as easy as it stands because, despite the absence of singularitie...
Pavel Emeliyanenko, Eric Berberich, Michael Sagral...
ECCV
2002
Springer
9 years 7 months ago
Using Robust Estimation Algorithms for Tracking Explicit Curves
The context of this work is lateral vehicle control using a camera as a sensor. A natural tool for controlling a vehicle is recursive filtering. The well-known Kalman fil...
Jean-Philippe Tarel, Sio-Song Ieng, Pierre Charbon...
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