Papers by Jean-Pascal Pavone
Software - Synaps, a module for symbolic and numeric computations
A sampling algorithm computing self-intersections of parametric surfaces
Summary. In this paper we present a sampling algorithm which detects and describes the self-inter... more Summary. In this paper we present a sampling algorithm which detects and describes the self-intersection locus of a parametric surface. We provide several criteria of injectivity, they serve to decompose the domain of the parametrization to get a family of smaller patches. The organization of our algorithm relies on a segmentation of the surface based on simple informations such as
Géométrie, Algèbre, Algorithmes
SYNAPS: A library for symbolic-numeric computation
An elastic stocking has an upper thigh panel which is adjustable both at the top and bottom of th... more An elastic stocking has an upper thigh panel which is adjustable both at the top and bottom of the panel and is fastened in adjustable overlapping relation according to the location of printed indicia that appears along both the top and bottom edges of the panel for indicating where the fastening means should hold the overlapping part of the panel according to the known upper and lower circumferential thigh dimensions of the wearer.
Selfintersections of a bézier bicubic surface
Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, 2005
We present the computation of selfintersections as a major problem in Computer Aided Geometric De... more We present the computation of selfintersections as a major problem in Computer Aided Geometric Design (CAD) and Geometric Modeling, and particularly for patches of parametrized bicubic surfaces. Then we expose two complementary contributions on that subject with Computer Algebra tools: First, a specific sparse bivariate resultant adapted to the corresponding elimination problem, second a semi-numeric polynomial solver able to deal
Selfintersections of a bézier bicubic surface
Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05, 2005
We present the computation of selfintersections as a major problem in Computer Aided Geometric De... more We present the computation of selfintersections as a major problem in Computer Aided Geometric Design (CAD) and Geometric Modeling, and particularly for patches of parametrized bicubic surfaces. Then we expose two complementary contributions on that subject with Computer Algebra tools: First, a specific sparse bivariate resultant adapted to the corresponding elimination problem, second a semi-numeric polynomial solver able to deal
Geometric Modeling and Algebraic Geometry, 2008
In this paper, we describe a subdivision method for handling algebraic implicit curves in 2d and ... more In this paper, we describe a subdivision method for handling algebraic implicit curves in 2d and 3d. We use the representation of polynomials in the Bernstein basis associated with a given box, to check if the topology of the curve is determined inside this box, from its points on the border of the box. Subdivision solvers are used for computing these points on the faces of the box, and segments joining these points are deduced to get a graph isotopic to the curve. Using envelop of polynomials, we show how this method allow to handle efficiently and accurately implicit curves with large coefficients. We report on implementation aspects and experimentations on 2d curves such as ridge curves or self intersection curves of parameterized surfaces, and on silhouette curves of implicit surfaces, showing the interesting practical behavior of this approach.
The IMA Volumes in Mathematics and its Applications, 2008
Journal of Symbolic Computation, 2009
This paper presents a new algorithm for solving a system of polynomials, in a domain of R n . It ... more This paper presents a new algorithm for solving a system of polynomials, in a domain of R n . It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed by Sherbrooke and Patrikalakis [Sherbrooke, E.C., Patrikalakis, N.M., 1993. Computation of the solutions of nonlinear polynomial systems. Comput. Aided Geom. Design 10 (5), 379-405]. It uses a powerful reduction strategy based on univariate root finder using Bernstein basis representation and Descarte's rule. We analyse the behavior of the method, from a theoretical point of view, shows that for simple roots, it has a local quadratic convergence speed and gives new bounds for the complexity of approximating real roots in a box of R n . The improvement of our approach, compared with classical subdivision methods, is illustrated on geometric modeling applications such as computing intersection points of implicit curves, selfintersection points of rational curves, and on the classical parallel robot benchmark problem.
Selfintersections of a bézier bicubic surface
Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05, 2005
We present the computation of selfintersections as a major problem in Computer Aided Geometric De... more We present the computation of selfintersections as a major problem in Computer Aided Geometric Design (CAD) and Geometric Modeling, and particularly for patches of parametrized bicubic surfaces. Then we expose two complementary contributions on that subject with Computer Algebra tools: First, a specific sparse bivariate resultant adapted to the corresponding elimination problem, second a semi-numeric polynomial solver able to deal
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Papers by Jean-Pascal Pavone