Sylvain Petitjean

Ciprian Borcea, Xavier Goaoc, Sylvain Petitjean

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying...

Line (2009)

transversals to disjoint balls

Common tangents to spheres in R 3 (2009)

Ciprian Borcea, Xavier Goaoc, Sylvain Lazard, Sylvain Petitjean, Loria Inria Lorraine

Abstract. We prove that four spheres in R 3 have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent. 1

INVARIANT-BASED CHARACTERIZATION OF THE RELATIVE POSITION OF TWO PROJECTIVE CONICS (2009)

Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics ⋆ (2009)

Abstract. In this paper, we give predicates of bidegree at most (6, 6) in the input for characterizing the relative position of two projective conics. By relative position we mean the morphology of...

Laurent Dupont, Michael Hemmer, Sylvain Petitjean, Elmar Schömer

Abstract. We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the...

Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangment of Quadrics ∗ (2008)

Arrangment Of Quadrics, Michel Hemmer, Laurent Dupont, Elmar Schoemer, Sylvain Petitjean, Laurent Dupont, ...

We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, surfaces of algebraic degree 2. This is a major step towards the computation of...

Algebraic Geometry and Object Representation in Computer Vision (2008)

Sylvain Petitjean, Crin /inria Lorraine, Bâtiment Loria

Abstract. 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 advantages as...

Chapter 1 TOWARDS THE ROBUST INTERSECTION OF IMPLICIT QUADRICS (2008)

Laurent Dupont, Sylvain Lazard, Sylvain Petitjean, Daniel Lazard

Abstract We are interested in efficiently and robustly computing a parametric form of the intersection of two implicit quadrics with rational coefficients. Our method is similar in spirit to the...

On the Enumerative Geometry of Aspect Graphs (2008)

Sylvain Petitjean, Bâtiment Loria Bp

Abstract. Most of the work achieved thus far on aspect graphs has concentrated on the design of algorithms for computing the representation. After reviewing how the space of viewpoints can be...

Helly-Type Theorems for Line Transversals to Disjoint Unit Balls (2008)

Cheong, Otfried, Goaoc, Xavier, Holmsen, Andreas, Petitjean, Sylvain

We prove Helly-type theorems for line transversals to disjoint unit balls in Rd . In particular, we show that a family of n ≥ 2d disjoint unit balls in Rd has a line transversal if, for some...

Algebraic Geometry and Object Representation in Computer Vision (2008)

Sylvain Petitjean, Crin Inria Lorraine

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 advantages as objects...

Hadwiger and Helly-type theorems for disjoint unit spheres (2008)

Cheong, Otfried, Goaoc, Xavier, Holmsen, Andreas, Petitjean, Sylvain

We prove Helly-type theorems for line transversals to disjoint unit balls in $\R^{d}$. In particular, we show that a family of $n \geq 2d$ disjoint unit balls in $\R^d$ has a line transversal if, for...

Hadwiger and Helly-type theorems for disjoint unit spheres (2008)

Cheong, Otfried, Goaoc, Xavier, Holmsen, Andreas, Petitjean, Sylvain

We prove Helly-type theorems for line transversals to disjoint unit balls in $\R^{d}$. In particular, we show that a family of $n \geq 2d$ disjoint unit balls in $\R^d$ has a line transversal if, for...

Line transversals to disjoint balls (2008)

Line transversals to disjoint balls (2008)

We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$...

Near-Optimal Parameterization of the Intersection of Quadrics: I.~The Generic Algorithm (2008)

We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$...

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present an exact and efficient algorithm for computing a proper parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with...

Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils (2008)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present here the first classification of pencils of quadrics based on the type of their intersection in real projective space and we show how this classification can be used to compute efficiently...

Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections (2008)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We conclude, in this third part, the presentation of an algorithm for computing an exact and proper parameterization of the intersection of two quadrics. The coordinate functions of the...

Near-Optimal Parameterization of the Intersection of Quadrics: I.~The Generic Algorithm (2008)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present an exact and efficient algorithm for computing a proper parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with...

Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils (2008)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present here the first classification of pencils of quadrics based on the type of their intersection in real projective space and we show how this classification can be used to compute efficiently...

Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections (2008)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We conclude, in this third part, the presentation of an algorithm for computing an exact and proper parameterization of the intersection of two quadrics. The coordinate functions of the...

x (2007)

Olivier Devillers, Vida Dujmovi C, Hazel Everett, Xavier Goaoc, Sylvain Lazard, Hyeon-suk Na, ...

A linear bound on the expected

Abstract Least Squares Conformal Maps for Automatic Texture Atlas Generation (2007)

Bruno Lévy, Sylvain Petitjean, Nicolas Ray, Jérome Maillot

A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded...

On the Enumerative Geometry of Aspect Graphs (2007)

Contributions au calcul géométrique effectif avec des objets courbes de faible degré (2007)

Most of the work achieved thus far on aspect graphs has concentrated on the design of algorithms for computing the representation. After reviewing how the space of viewpoints can be partitioned in...

Hadwiger and Helly-type theorems for disjoint unit spheres (2007)

Le monde physique dans lequel nous vivons est essentiellement géométrique. Le calcul géométrique est une brique centrale de nombreux domaines, comme la conception assistée par ordinateur, le...

Cheong, Otfried, Goaoc, Xavier, Holmsen, Andreas, Petitjean, Sylvain

We prove Helly-type theorems for line transversals to disjoint unit balls in $\R^{d}$. In particular, we show that a family of $n \geq 2d$ disjoint unit balls in $\R^d$ has a line transversal if, for...

Line transversals to disjoint balls (2007)

Line transversals to disjoint balls (2007)

We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$...

Contributions au calcul géométrique effectif avec des objets courbes de faible degré (2007)

We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$...

Contributions au calcul géométrique effectif avec des objets courbes de faible degré (2007)

Le monde physique dans lequel nous vivons est essentiellement géométrique. Le calcul géométrique est une brique centrale de nombreux domaines, comme la conception assistée par ordinateur, le...

Contributions au calcul géométrique effectif avec des objets courbes de faible degré (2007)

Le monde physique dans lequel nous vivons est essentiellement géométrique. Le calcul géométrique est une brique centrale de nombreux domaines, comme la conception assistée par ordinateur, le...

On the Expected Size of the 2D Visibility Complex (2007)

Le monde physique dans lequel nous vivons est essentiellement géométrique. Le calcul géométrique est une brique centrale de nombreux domaines, comme la conception assistée par ordinateur, le...

Everett, Hazel, Lazard, Sylvain, Petitjean, Sylvain, Zhang, Linqiao

We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the asymptotic expected number of free bitangents (which correspond to 0-faces of...

On the Expected Size of the 2D Visibility Complex (2007)

Everett, Hazel, Lazard, Sylvain, Petitjean, Sylvain, Zhang, Linqiao

We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the asymptotic expected number of free bitangents (which correspond to 0-faces of...

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...

Line transversals to disjoint balls (2006)

On the Expected Size of the 2D Visibility Complex (2006)

We prove that the set of directions of lines intersecting three disjoint balls in $R^3$ in a given order is a strictly convex subset of $S^2$. We then generalize this result to $n$ disjoint balls in...

Everett, Hazel, Lazard, Sylvain, Petitjean, Sylvain, Zhang, Linqiao

We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the expected asymptotic number of free bitangents (which correspond to the 0-faces...

Intersecting Quadrics: An Efficient and Exact Implementation (2006)

Lazard, Sylvain, Mariano Penaranda, Luis, Petitjean, Sylvain

We present the first complete, exact, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the...

On the Expected Size of the 2D Visibility Complex (2006)

Everett, Hazel, Lazard, Sylvain, Petitjean, Sylvain, Zhang, Linqiao

We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the expected asymptotic number of free bitangents (which correspond to the 0-faces...

On the Expected Size of the 2D Visibility Complex (2006)

Everett, Hazel, Lazard, Sylvain, Petitjean, Sylvain, Zhang, Linqiao

We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the expected asymptotic number of free bitangents (which correspond to the 0-faces...

Intersecting Quadrics: An Efficient and Exact Implementation (2006)

Lazard, Sylvain, Mariano Penaranda, Luis, Petitjean, Sylvain

We present the first complete, exact, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the...

Common Tangents to Spheres in $R3$ (2006)

Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain

We prove that four spheres in $R3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.

Common Tangents to Spheres in $R3$ (2006)

Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain

We prove that four spheres in $R3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.

Helly-type Theorems for Line transversals to Disjoint Unit Balls (2006)

Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Sylvain Petitjean

We prove Helly-type theorems for line transversals to disjoint unit balls in R d. In particular, we show that a family of n � 2d disjoint unit balls in R d has a line transversal if, for some...

Helly-type Theorems for Line transversals to Disjoint Unit Balls (2006)

Otfried Cheong, Xavier Goaoc, Andreas Holmsen, Sylvain Petitjean

We prove Helly-type theorems for line transversals to disjoint unit balls in R d. In particular, we show that a family of n � 2d disjoint unit balls in R d has a line transversal if, for some...

Helly-type Theorems for Line transversals to Disjoint Unit Balls (Extended abstract) (2006)

Cheong, Otfried, Goaoc, Xavier, Holmsen, Andreas, Petitjean, Sylvain

We prove Helly-type theorems for line transversals to disjoint unit balls in R^d. In particular, we show that a family of n >= 2d disjoint unit balls in Rd has a line transversal if, for some...

Helly-type Theorems for Line transversals to Disjoint Unit Balls (Extended abstract) (2006)

Cheong, Otfried, Goaoc, Xavier, Holmsen, Andreas, Petitjean, Sylvain

We prove Helly-type theorems for line transversals to disjoint unit balls in R^d. In particular, we show that a family of n >= 2d disjoint unit balls in Rd has a line transversal if, for some...

Near-Optimal Parameterization of the Intersection of Quadrics: IV. An Efficient and Exact Implementation (2005)

Lazard, Sylvain, Mariano Penaranda, Luis, Petitjean, Sylvain

We present the first complete, robust, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the...

Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...

Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...

Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...

Near-Optimal Parameterization of the Intersection of Quadrics: IV. An Efficient and Exact Implementation (2005)

Lazard, Sylvain, Mariano Penaranda, Luis, Petitjean, Sylvain

We present the first complete, robust, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the...

Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...

Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...

Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...

Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...

Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...

Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...

Near-Optimal Parameterization of the Intersection of Quadrics: IV. An Efficient and Exact Implementation (2005)

Lazard, Sylvain, Peñaranda, Luis Mariano, Petitjean, Sylvain

We present the first complete, robust, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the...

An Experimental Assessment of the 2D Visibility Complex (2005)

Everett, Hazel, Lazard, Sylvain, Petitjean, Sylvain, Zhang, Linqiao

We make an experimental assessment of the size of the 2D visibility complex of disjoint unit discs randomly distributed in the plane with density $\mu$. We observe that the number of free bitangents...

Intersecting Quadrics: An Efficient and Exact Implementation (2005)

Lazard, Sylvain, Mariano Penaranda, Luis, Petitjean, Sylvain

We present the first complete, exact, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the...

An Experimental Assessment of the 2D Visibility Complex (2005)

Everett, Hazel, Lazard, Sylvain, Petitjean, Sylvain, Zhang, Linqiao

We make an experimental assessment of the size of the 2D visibility complex of disjoint unit discs randomly distributed in the plane with density $\mu$. We observe that the number of free bitangents...

Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...

Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...

Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...

Near-Optimal Parameterization of the Intersection of Quadrics: IV. An Efficient and Exact Implementation (2005)

Lazard, Sylvain, Peñaranda, Luis Mariano, Petitjean, Sylvain

We present the first complete, robust, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the...

Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

We present the first efficient algorithm for computing an exact parametric representation of the intersection of two quadrics in three-dimensional real space given by implicit equations with rational...

Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all...

Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections (2005)

Dupont, Laurent, Lazard, Daniel, Lazard, Sylvain, Petitjean, Sylvain

In Part II [3] of this paper, we have shown, using a classification of pencils of quadrics over the reals, how to determine quickly and efficiently the real type of the intersection of two given...

Near-Optimal Parameterization of the Intersection of Quadrics: IV. An Efficient and Exact Implementation (2005)

Lazard, Sylvain, Peñaranda, Luis Mariano, Petitjean, Sylvain

We present the first complete, robust, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the...

An Experimental Assessment of the 2D Visibility Complex (2005)

Everett, Hazel, Lazard, Sylvain, Petitjean, Sylvain, Zhang, Linqiao

We make an experimental assessment of the size of the 2D visibility complex of disjoint unit discs randomly distributed in the plane with density $\mu$. We observe that the number of free bitangents...

On the expected size of the 2d visibility complex (2005)

Hazel Everett, Sylvain Lazard, Sylvain Petitjean, Linqiao Zhang

We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the asymptotic expected number of free bitangents (which correspond to 0-faces of...

An experimental assessment of the 2d visibility complex (2005)

Hazel Everett, Sylvain Lazard, Sylvain Petitjean, Linqiao Zhang

We make an experimental assessment of the size of the 2D visibility complex of disjoint unit discs randomly distributed in the plane with density µ. We observe that the number of free bitangents is...

Near-optimal parameterization of the intersection of quadrics: III. Parameterizing singular intersections. Research Report n o 5669 (2005)

Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean, Thème Sym, Laurent Dupont, ...

apport de recherche

Near-optimal parameterization of the intersection of quadrics: III. Parameterizing singular intersections. Research Report n o 5669 (2005)

Laurent Dupont, Sylvain Lazard, Daniel Lazard, Sylvain Petitjean

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Near-optimal parameterization of the intersection of quadrics: IV. An efficient and exact implementation. Research Report no 5670 (2005)

Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean, Thème Sym, Laurent Dupont, ...

apport de recherche

Near-optimal parameterization of the intersection of quadrics: IV. An efficient and exact implementation. Research Report n o 5670 (2005)

Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean, Thème Sym, Laurent Dupont, ...

apport de recherche

Common Tangents to Spheres in R^3 (2004)

Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain

We prove that four spheres in $\R^3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.

On tangents to quadric surfaces (2004)

Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain

We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to configurations of four quadrics admitting a continuum of common tangents....

Common Tangents to Spheres in R^3 (2004)

Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain

We prove that four spheres in $\R^3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.

Common Tangents to Spheres in R^3 (2004)

Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain

We prove that four spheres in $\R^3$ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.

Intersecting Quadrics: An Efficient and Exact Implementation (2004)

Lazard, Sylvain, Mariano Penaranda, Luis, Petitjean, Sylvain

We present the first complete, exact and efficient C++ implementation of a method for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based...

Intersecting Quadrics: An Efficient and Exact Implementation (2004)

Lazard, Sylvain, Mariano Penaranda, Luis, Petitjean, Sylvain

We present the first complete, exact and efficient C++ implementation of a method for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based...

Intersecting Quadrics: An Efficient and Exact Implementation (2004)

Sylvain Lazard, Loria-inria Lorraine, Luis Mariano Penaranda, Sylvain Petitjean

We present the first complete, exact and e#cient C++ implementation of a method for parameterizing the intersection of two implicit quadrics with integer coe#cients of arbitrary size. It is based on...

On Tangents to Quadric Surfaces (2004)

Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain

We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to congurations of four quadrics admitting a continuum of common tangents. We...

On Tangents to Quadric Surfaces (2004)

Borcea, Ciprian, Goaoc, Xavier, Lazard, Sylvain, Petitjean, Sylvain

We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to congurations of four quadrics admitting a continuum of common tangents. We...

Near-Optimal Parameterization of the Intersection of Quadrics (2003)

Laurent Dupont, Daniel Lazard, Sylvain Lazard, Sylvain Petitjean

In this paper, we present the rst exact, robust and practical method for computing an explicit representation of the intersection of two arbitrary quadrics whose coecients are rational. Combining...

The expected number of 3D visibility events is linear (2002)

Devillers, Olivier, Dujmovic, Vida, Everett, Hazel, Goaoc, Xavier, Lazard, Sylvain, Na, Hyeon-Suk, ...

In this paper, we show that, amongst n uniformly distributed unit balls in R^3, the expected number of maximal non-occluded line segments tangent to four balls is linear, considerably improving the...

The expected number of 3D visibility events is linear (2002)

Devillers, Olivier, Dujmovic, Vida, Everett, Hazel, Goaoc, Xavier, Lazard, Sylvain, Na, Hyeon-Suk, ...

In this paper, we show that, amongst n uniformly distributed unit balls in R^3, the expected number of maximal non-occluded line segments tangent to four balls is linear, considerably improving the...

The expected number of 3D visibility events is linear (2002)

Devillers, Olivier, Dujmovic, Vida, Everett, Hazel, Goaoc, Xavier, Lazard, Sylvain, Na, Hyeon-Suk, ...

In this paper, we show that, amongst n uniformly distributed unit balls in R^3, the expected number of maximal non-occluded line segments tangent to four balls is linear, considerably improving the...

Least Squares Conformal Maps for Automatic Texture Atlas Generation (2002)

Bruno Lévy, Sylvain Petitjean, Nicolas Ray, Jérôme Maillot

A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded...

Curve and surface reconstruction from regular and non regular point sets. Computational Geometry (2001)

Edmond Boyer, Sylvain Petitjean

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants which are polygonal approximations of planar curves and surfaces...

Towards The Robust Intersection Of Implicit Quadrics (2001)

Laurent Dupont, Sylvain Lazard, Sylvain Petitjean, Daniel Lazard

We are interested in eciently and robustly computing a parametric form of the intersection of two implicit quadrics with rational coe- cients. Our method is similar in spirit to the general method...

Regular and Non-Regular Point Sets: (2001)

Properties And Reconstruction, Sylvain Petitjean, Edmond Boyer

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying...

Curve and surface reconstruction from regular and non regular point sets. Computational Geometry (2001)

Edmond Boyer, Sylvain Petitjean

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants which are polygonal approximations of planar curves and surfaces...

A Computational Geometric Approach To Visual Hulls (1997)

Sylvain Petitjean, Communicated Ming, C. Lin, Dinesh Manocha

Recognizing 3D objects from their 2D silhouettes is a popular topic in computer vision. Object reconstruction can be performed using the volume intersection approach. The visual hull of an object is...

The Enumerative Geometry of Projective Algebraic Surfaces and The Complexity of Aspect Graphs (1996)

The Enumerative Geometry of Projective Algebraic Surfaces and The Complexity of Aspect Graphs (1996)

The aspect graph is a popular viewer-centered representation that enumerates all the topologically distinct views of an object. Building the aspect graph requires partitioning viewpoint space in...

The number of views of piecewise-smooth algebraic objects. Proc. Sympos. Theoret (1995)

The aspect graph is a popular viewer-centered representation that enumerates all the topologically distinct views of an object. Building the aspect graph requires partitioning viewpoint space in...

The Number of Views of Piecewise-Smooth Algebraic Objects (1995)

Abstract. A solid object in 3-dimensional space may be described by a collection of all its topologically distinct 2-dimensional appearances, its aspect graph. In this paper, we study the complexity...

The Number of Views of Piecewise-Smooth Algebraic Objects (1995)

A solid object in 3-dimensional space may be described by a collection of all its topologically distinct 2-dimensional appearances, its aspect graph. In this paper, we study the complexity of aspect...