Effective Computational Geometry for Curves and Surfaces (2009)
Meshing is the process of computing, for a given surface, a representation consisting of piecesof simple surface patches, like triangles. This survey discusses all currently known surface (and curve)...
Abstract Isotopic Approximation of Implicit Curves and Surfaces (2008)
Implicit surfaces are defined as the zero set of a function F: R 3 → R. Although several algorithms exist for generating piecewise linear approximations, most of them are based on a userdefined...
Henk W. Broer, Martin Golubitsky, Gert Vegter
Resonance tongues arise in bifurcations of discrete or continuous dynamical systems undergoing bifurcations of a fixed point or an equilibrium satisfying certain resonance conditions. They occur in...
Effective Computational Geometry for Curves and Surfaces Chapter 7 (2008)
We give an introduction to combinatorial topology, with an emphasis on subjects that are of interest for computational geometry in two and three dimensions. We cover the notions of homotopy and...
Abstract. Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree,...
Kevin Buchin, Simon Plantinga, Günter Rote, Astrid Sturm, Gert Vegter
Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413 Given points in convex position in three dimensions, we want to find an approximating convex...
Abstract Isotopic Approximation of Implicit Curves and Surfaces (Extended Abstract) (2008)
Implicit surfaces are defined as the zero set of a function F: R 3 → R. Although several algorithms exist for generating piecewise linear approximations, most of them are based on a user-defined...
Effective Computational Geometry for Curves and Surfaces (2008)
Meshing is the process of computing, for a given surface, a representation consisting of piecesof simple surface patches, like triangles. This survey discusses all currently known surface (and curve)...
Extented Abstract, M. Pocchiola, G. Vegter, Michel Pocchiola, Gert Vegter
Order types and visibility types of configurations of disjoint convex plane sets
Computing a Canonical Polygonal Schema of an Orientable (2007)
Triangulated Surface, Francis Lazarus, Michel Pocchiola, Gert Vegter, Anne Verroust
A closed orientable surface of genus g can be obtained by appropriate identication of pairs of edges of a 4g-gon (the polygonal schema). The identied edges form 2g loops on the surface, that are...
Computing a Canonical Polygonal Schema of an (2007)
Orientable Triangulated Surface, Francis Lazarus, Michel Pocchiola, Gert Vegter, Anne Verroust
A closed orientable surface of genus g can be obtained by appropriate identication of pairs of edges of a 4ggon (the polygonal schema). The identied edges form 2g loops on the surface, that are...
MULTIPLE PURPOSE ALGORITHMS FOR INVARIANT MANIFOLDS (2007)
Henk Broer, Aaron Hagen, Gert Vegter
This paper deals with the numerical continuation of invariant manifolds, regardless of the restricted dynamics. Typically, invariant manifolds make up the skeleton of the dynamics of phase space....
Effective Computational Geometry for Curves and Surfaces (2007)
Jean-daniel Boissonnat, David Cohen-steiner, Bernard Mourrain, Günter Rote, Gert Vegter
Meshing is the process of computing, for a given surface, a representation consisting of pieces of simple surface patches, like triangles. This survey discusses all currently known surface (and...
Effective Computational Geometry for Curves and Surfaces (2007)
Jean-daniel Boissonnat, David Cohen-steiner, Bernard Mourrain, Günter Rote, Gert Vegter
Meshing is the process of computing, for a given surface, a representation consisting of pieces of simple surface patches, like triangles. This survey discusses all currently known surface (and...
Approximation by conic splines (2007)
Sunayana Ghosh, Sylvain Petitjean, Gert Vegter
Abstract. We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε −1/4 + O(1), if...
Convex Approximation by Spherical Patches (2006)
Kevin Buchin, Simon Plantinga, Günter Rote, Astrid Sturm, Gert Vegter
3 Partially supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-006413 (ACS – Algorithms for Complex Shapes) Given points in convex position in...
Isotopic implicit surface meshing (2004)
Jean-daniel Boissonnat, David Cohen-steiner, Gert Vegter
This paper addresses the problem of piecewise linear approximation of implicit surfaces. We first give a criterion ensuring that the zero-set of a smooth function and the one of a piecewise linear...
Meshing skin surfaces with certified topology (2004)
We present an algorithm that approximates a skin surface with a topologically correct mesh. The number of vertices of the mesh is quadratic in the number of input balls defining the skin surface. We...
Isotopic approximation of implicit curves and surfaces (2004)
Implicit surfaces are defined as the zero set of a function F: R 3 → R. Although several algorithms exist for generating piecewise linear approximations, most of them are based on a user-defined...
Meshing implicit surfaces with certified topology title (2003)
Boissonnat, Jean-Daniel, Cohen-Steiner, David, Vegter, Gert
We describe a new algorithm for building piecewise linear approximations of an implicit surface. This algorithm is the first one guaranteeing that the implicit surface and its approximation are...
Meshing implicit surfaces with certified topology title (2003)
Boissonnat, Jean-Daniel, Cohen-Steiner, David, Vegter, Gert
We describe a new algorithm for building piecewise linear approximations of an implicit surface. This algorithm is the first one guaranteeing that the implicit surface and its approximation are...
Meshing implicit surfaces with certified topology title (2003)
Boissonnat, Jean-Daniel, Cohen-Steiner, David, Vegter, Gert
We describe a new algorithm for building piecewise linear approximations of an implicit surface. This algorithm is the first one guaranteeing that the implicit surface and its approximation are...
Approximation by skin surfaces (2003)
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The geometry of resonance tongues: a singularity theory approach (2003)
Henk W. Broer, Gert Vegter, Martin Golubitsky
Resonance tongues and their boundaries are studied for nondegenerate and (certain) degenerate Hopf bifurcations of maps using singularity theory meth-ods of equivariant contact equivalence and...
Contour generators of evolving implicit surfaces (2003)
Simon Plantinga, Simon Plantinga, Gert Vegter, Gert Vegter
The contour generator is an important visibility feature of a smooth object seen under parallel projection. It is the curve on the surface which seperates front-facing regions from back-facing...
Meshing Implicit Surfaces with Certified Topology (2003)
Jean-daniel Boissonnat, David Cohen-Steiner, Gert Vegter
We address the problem of isosurface meshing with topological guaranties. Assuming the critical points of the considered function are given, we give a certified algorithm for this problem. This seems...
Pocchiola, Michel, Vegter, Gert
Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known...
Tutte’s barycenter method applied to isotopies (2001)
This paper is concerned with applications of Tutte’s barycentric embedding theorem (Proc. London Math. Soc. 13 (1963), 743–768). It presents a method for building isotopies of triangulations in...
Tutte’s barycenter method applied to isotopies (2001)
This paper provides a short and intuitive proof of Tutte's barycentric embedding theorem [14], compared to the original one which involved a lot of graph theory and complicated terminology. We...
Tutte’s barycenter method applied to isotopies (2001)
This paper provides a simple proof of Tutte's barycentric embedding theorem [38]; a counterexample showing that Tutte's theorem does not hold in dimensions higher than 3; and the...
The apolar bilinear form in CAGD: new applications (2000)
. Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a xed degree, already known...
The Apolar Bilinear Form in Geometric Modeling (1998)
Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known...
A polygonal cover of a finite collection of pairwise disjoint convex compact sets in the plane is a finite collection of non-overlapping bounded convex polygons such that each polygon covers exactly...
Pseudo-triangulations: Theory and applications (1996)
Pseudotriangles and pseudo-triangulations have played a key role in the recent design of two optimal visibility graph algorithms; see [1, 2]. The purpose
Uperieure S Ormale, N Ecole, Michel Pocchiola, Michel Pocchiola, Michel Pocchiola, Gert Vegter, ...
A polygonal cover of a finite collection of pairwise disjoint convex compact sets in the plane is a finite collection of non-overlapping convex polygons such that each polygon covers exactly one...
Computing the Visibility Graph via Pseudo-triangulations (1995)
We show that the k free bitangents of a collection of n pairwise disjoint convex plane sets can be computed in time O(k+n log n) and O(n) working space. The algorithm uses only one advanced data...
Minimal Tangent Visibility Graphs (1995)
Uperieure S Ormale, N Ecole, Michel Pocchiola, Michel Pocchiola, Michel Pocchiola, Gert Vegter, ...
We prove the tight lower bound 4n \Gamma 4 on the size of tangent visibility graphs on n pairwise disjoint bounded obstacles in the euclidean plane, and we give a simple description of the...
Computing Visibility Graphs via Pseudo-triangulations (1995)
Michel Pocchiola, Michel Pocchiola, Michel Pocchiola, Gert Vegter, Gert Vegter, Gert Vegter
We show that the k free bitangents of a collection of n pairwise disjoint convex plane sets can be computed in time O(k + n log n) and O(n) working space. The algorithm uses only one advanced data...
Finding minimal circumscribing simplices - Part 1: Classifying local minima (1993)
The contents of this paper are: 1. Introduction; definition of barycentric coordinates 2. Characterization of critical tetrahedra 3. Constrained volume minimization 4. The quadratic part of the...
Grapevine: An exemise in distributed computing (1982)
Implicit surfaces are given as the zero set of a function F: R 3 → R. Although several algorithms exist for generating piecewise linear approximations, most of these are based on a user-defined...