On the Topology of Planar Algebraic Curves (2009)
Jinsan Cheng, Sylvain Lazard, Luis Peñar, Marc Pouget, Fabrice Rouillier, Elias Tsigaridas
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
The Voronoi diagram of three arbitrary lines in R 3 (2009)
Hazel Everett, Christian Gillot, Daniel Lazard, Sylvain Lazard, Marc Pouget
In this paper we study the Voronoi diagram of lines in R 3. The Voronoi diagram of three lines in general position was studied in [14]. In this paper we complete this work by presenting a complete...
The Voronoi diagram of three arbitrary lines in R3 (2009)
Everett, Hazel, Gillot, Christian, Lazard, Daniel, Lazard, Sylvain, Pouget, Marc
In this paper we study the Voronoi diagram of lines in R3 . The Voronoi diagram of three lines in general position was studied in [8]. In this paper we complete this work by presenting a complete...
The Voronoi diagram of three arbitrary lines in R3 (2009)
Everett, Hazel, Gillot, Christian, Lazard, Daniel, Lazard, Sylvain, Pouget, Marc
In this paper we study the Voronoi diagram of lines in R3 . The Voronoi diagram of three lines in general position was studied in [8]. In this paper we complete this work by presenting a complete...
On the topology of planar algebraic curves (2009)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...
On the topology of planar algebraic curves (2009)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...
Ridges and Umbilics of Polynomial Parametric Surfaces (2008)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
On The Topology of Planar Algebraic Curves (2008)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
Ridges and Umbilics of Polynomial Parametric Surfaces (2008)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
On The Topology of Planar Algebraic Curves (2008)
Cheng, Jinsan, Lazard, Sylvain, Peñaranda, Luis Mariano, Pouget, Marc, Rouillier, Fabrice, Tsigaridas, Elias P.
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
On the topology of planar algebraic curves (2008)
Jinsan Cheng, Sylvain Lazard, Luis Peñar, Marc Pouget, Fabrice Rouillier, Elias Tsigaridas
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...
Cazals, Frédéric, Pouget, Marc
Surfaces of R^3 are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in...
Cazals, Frédéric, Pouget, Marc
Surfaces of R^3 are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in...
Cazals, Frédéric, Pouget, Marc
Surfaces of R^3 are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in...
Cazals, Frédéric, Pouget, Marc
Surfaces of R^3 are ubiquitous in science and engineering, and estimating the local differential properties of a surface discretized as a point cloud or a triangle mesh is a central building block in...
Ce travail de recherche porte sur les aspects géométriques desmathématiques et de l'informatique. Il est fortement motivé par des applications telles que la conception assistée par ordinateur,...
The implicit structure of ridges of a smooth parametric surface (2006)
Cazals, Frederic, Jean-Charles, Faugere, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of {\em...
The implicit structure of ridges of a smooth parametric surface (2006)
Cazals, Frédéric, Jean-Charles, Faugere, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of {\em...
The implicit structure of ridges of a smooth parametric surface (2006)
Cazals, Frédéric, Jean-Charles, Faugere, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of {\em...
Ce travail de recherche porte sur les aspects géométriques desmathématiques et de l'informatique.Il est fortement motivé par des applications telles que la conception assistée par...
Topologically certified approximation of umbilics and ridges on polynomial parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
The implicit structure of ridges of a smooth parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
Topology driven algorithms for ridge extraction on meshes (2005)
Cazals, Frédéric, Pouget, Marc
Given a smooth surface, a ridge is a curve along which one of the principal curvatures has an extremum along its curvature line. Ridges are curves of extremal curvature and therefore encode important...
Topologically certified approximation of umbilics and ridges on polynomial parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
The implicit structure of ridges of a smooth parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
Topology driven algorithms for ridge extraction on meshes (2005)
Cazals, Frédéric, Pouget, Marc
Given a smooth surface, a ridge is a curve along which one of the principal curvatures has an extremum along its curvature line. Ridges are curves of extremal curvature and therefore encode important...
Estimating Differential Quantities using Polynomial fitting of Osculating Jets (2005)
Cazals, Frederic, Pouget, Marc
This paper addresses the point-wise estimation of differential properties of a smooth manifold $S$ ---a curve in the plane or a surface in $3D$--- assuming a point cloud sampled over $S$ is provided....
Estimating Differential Quantities using Polynomial fitting of Osculating Jets (2005)
Cazals, Frederic, Pouget, Marc
This paper addresses the point-wise estimation of differential properties of a smooth manifold $S$ ---a curve in the plane or a surface in $3D$--- assuming a point cloud sampled over $S$ is provided....
Differential topology and geometry of smooth embedded surfaces: selected topics (2005)
Cazals, Frédéric, Pouget, Marc
The understanding of surfaces embedded in E3 requires local and global concepts, which are respectively evocative of differential geometry and differential topology. While the local theory has been...
Ce travail de recherche porte sur les aspects géométriques desmathématiques et de l'informatique. Il est fortement motivé par des applications telles que la conception assistée par ordinateur,...
Topologically certified approximation of umbilics and ridges on polynomial parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
The implicit structure of ridges of a smooth parametric surface (2005)
Cazals, Frédéric, Faugère, Jean-Charles, Pouget, Marc, Rouillier, Fabrice
Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and...
Topology driven algorithms for ridge extraction on meshes (2005)
Cazals, Frédéric, Pouget, Marc
Given a smooth surface, a ridge is a curve along which one of the principal curvatures has an extremum along its curvature line. Ridges are curves of extremal curvature and therefore encode important...
Differential topology and geometry of smooth embedded surfaces: selected topics (2005)
Cazals, Frédéric, Pouget, Marc
The understanding of surfaces embedded in E3 requires local and global concepts, which are respectively evocative of differential geometry and differential topology. While the local theory has been...
Estimating Differential Quantities using Polynomial fitting of Osculating Jets (2005)
Cazals, Frederic, Pouget, Marc
This paper addresses the point-wise estimation of differential properties of a smooth manifold $S$ ---a curve in the plane or a surface in $3D$--- assuming a point cloud sampled over $S$ is provided....
Differential topology and geometry of smooth embedded surfaces: selected topics (2005)
Cazals, Frédéric, Pouget, Marc
The understanding of surfaces embedded in E3 requires local and global concepts, which are respectively evocative of differential geometry and differential topology. While the local theory has been...
Ce travail de recherche porte sur les aspects géométriques desmathématiques et de l'informatique. Il est fortement motivé par des applications telles que la conception assistée par ordinateur,...
Ce travail de recherche porte sur les aspects géométriques desmathématiques et de l'informatique. Il est fortement motivé par des applications telles que la conception assistée par ordinateur,...
Differential topology and geometry of smooth embedded surfaces: selected topics (2005)
Cazals, Frédéric, Pouget, Marc
The understanding of surfaces embedded in E3 requires local and global concepts, which are respectively evocative of differential geometry and differential topology. While the local theory has been...
The implicit structure of ridges of a smooth parametric surface (2005)
Frédéric Cazals, Jean-charles Faugère, Marc Pouget, Fabrice Rouillier
Given a smooth surface, a blue (red) ridge is a curve such that at each of its points, the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of...
Cazals, Frédéric, Pouget, Marc
Consider a smooth surface, and at each point which is not an umbilic, respectively paint in blue (red) anything related to the maximum (minimum) principal curvature. Given such a surface, a blue...
Cazals, Frédéric, Pouget, Marc
The understanding of surfaces embedded in R^3 requires local and global concepts, which are respectively evocative of differential geometry and differential topology. While the local theory has been...
Cazals, Frédéric, Pouget, Marc
Consider a smooth surface, and at each point which is not an umbilic, respectively paint in blue (red) anything related to the maximum (minimum) principal curvature. Given such a surface, a blue...
Cazals, Frédéric, Pouget, Marc
The understanding of surfaces embedded in R^3 requires local and global concepts, which are respectively evocative of differential geometry and differential topology. While the local theory has been...
Cazals, Frédéric, Pouget, Marc
Consider a smooth surface, and at each point which is not an umbilic, respectively paint in blue (red) anything related to the maximum (minimum) principal curvature. Given such a surface, a blue...
Cazals, Frédéric, Pouget, Marc
The understanding of surfaces embedded in R^3 requires local and global concepts, which are respectively evocative of differential geometry and differential topology. While the local theory has been...
Estimating Differential Quantities using Polynomial fitting of Osculating Jets (2003)
Cazals, Frédéric, Pouget, Marc
This paper addresses the pointwise estimation of differential properties of a smooth manifold S ---a curve in the plane or a surface in 3D--- assuming a point cloud sampled over S is provided. The...
Estimating Differential Quantities using Polynomial fitting of Osculating Jets (2003)
Cazals, Frédéric, Pouget, Marc
This paper addresses the pointwise estimation of differential properties of a smooth manifold S ---a curve in the plane or a surface in 3D--- assuming a point cloud sampled over S is provided. The...
Estimating Differential Quantities using Polynomial fitting of Osculating Jets (2003)
Cazals, Frédéric, Pouget, Marc
This paper addresses the pointwise estimation of differential properties of a smooth manifold S ---a curve in the plane or a surface in 3D--- assuming a point cloud sampled over S is provided. The...
Estimating Differential Quantities Using Polynomial Fitting of Osculating Jets (2003)
principal frames, umbilics and ridges.