Propriétés différentielles du raccord entre deux courbes fractales

International audience

Constrained free form deformation on subdivision surfaces

International audience

NURBS and Iterated Functions Systems

A Reverse Scheme For Quadrilateral Meshes

International audience

Un nouveau principe de Loop non uniforme.

International audience

Geometry control of the junction between two fractal curves

International audience; The general objective of our work is to create a geometric modeller based on iterative processes. With this objective in mind, we have to provide tools that work with fractal objects in the same manner as with objects of classical topology. In this article we focus on the constructing of an intermediate curve between two other curves defined by different iterative construction processes. A similar problem often arises with subdivision surfaces, when the goal is to connect two surfaces with different subdivision masks. We start by dealing with curves, willing to later generalise our approach to surfaces. We formalise the problem with the Boundary Controlled Iterated F…

Curvilinear constraints for free form deformations on subdivision surfaces

This paper presents a method to deform a subdivision surface with curvilinear constraints. It combines an intuitive free form deformation with a Loop subdivision algorithm. The main advantage of this method of deformation is that it uses only vertices of an object and satisfies the geometrical constraints provided by the user. It permits us to control the final shape of the deformed object, defining the range (i.e. the impact) of the deformation before applying it. The deformation takes into account the Loop properties to follow the subdivision scheme, allowing the user to fix some curvilinear constraints at the subdivision level he works on and to render the final object at the level he wa…

Algorithme d'intersection entre un rayon et un carreau de Bézierpar quasi-interpolant bilinéaire.

International audience

Méthodes d’approximation d’opérations géométriques sur des objets fractals

National audience

Representation of NURBS surfaces by Controlled Iterated Functions System automata

Iterated Function Systems (IFS) are a standard tool to generate fractal shapes. In a more general way, they can represent most of standard surfaces like Bézier or B-Spline surfaces known as self-similar surfaces. Controlled Iterated Function Systems (CIFS) are an extension of IFS based on automata. CIFS are basically multi-states IFS, they can handle all IFS shapes but can also manage multi self-similar shapes. For example CIFS can describe subdivision surfaces around extraordinary vertices whereas IFS cannot. Having a common CIFS formalism facilitates the development of generic methods to manage interactions (junctions, differences...) between objects of different natures.This work focuses…

Précision des surfaces de Loop et applications

International audience

Reverse Catmull-Clark Subdivision

Reverse subdivision consists in constructing a coarse mesh of a model from a finer mesh of this same model. In this paper, we give formulas for reverse Catmull-Clark subdivision. These formulas allow the constructing of a coarse mesh for almost all meshes. The condition for being able to apply these formulas is that the mesh to be reversed must be generated by the subdivision of a coarse mesh. Except for this condition, the mesh can be arbitrary. Vertices can be regular or extraordinary and the mesh itself can be arbitrary (triangular, quadrilateral…).

A priori Computation of a mesh size for Adaptive Loop Subdivision

International audience

A new non-uniform subdivision scheme.

International audience

Reverse Triangle/Quad Subdivision

International audience

Reverse Catmull-Clark Subdivison

International audience

Approximation de l'enveloppe convexe de l'attracteur d'un IFS affine

International audience

Uniformisation de NURBS par blossoming

Un schéma de Subdivision approximant/interpolant sur un maillage quad/triangle

International audience; Récemment, l’étude et la construction des schémas de subdivision mixte (quad/triangle) ont attiré l’attention de la communauté de la modélisation géométrique. À partir d’un maillage mixte composé de quadrangles etde triangles, le schéma de subdivision quad/triangle produit un maillage mixte de plus en plus fin (figure 1). L’utilisation de la structure quad/triangle pour la conception des surfaces est motivée par le fait que dans lamodélisation CAO, les concepteurs veulent souvent travailler sur des modèles avec des maillages quadrilatéraux dans certaines régions et triangulaires dans d’autres afin d’obtenir des surfaces de subdivision avec une meilleure qualité visue…

A priori computation of the number of surface subdivision levels

International audience

Discrétisation directe de la surface limite de Catmull-Clark par Systèmes de Fonctions Itérés

Free form deformation on subdivision surfaces.

International audience

Vers un modeleur géométrique déclaratif

International audience; no abstract

La rugosité des surfaces et ses applications

Dans cet article, nous présentons un état de l'art sur les applications liées à la notion de rugosité des surfaces. Ce travail ne prétend pas être exhaustif. Nous nous sommes attachés à référencer les travaux dans les domaines qui nous ont paru les plus pertinents. Le monde industriel s'intéresse depuis longtemps à caractériser et à contrôler la rugosité pour la conception, la fabrication et le contrôle qualité. En informatique graphique, la rugosité est modélisée pour produire des géométries de surfaces ou pour simuler son impact sur la lumière lors du processus de rendu.

Generalized SCODEF Deformations on Subdivision Surfaces

This paper proposes to define a generalized SCODEF deformation method on a subdivision surface. It combines an “easy-to-use” free-form deformation with a Loop subdivision algorithm. The deformation method processes only on vertices of an object and permits the satisfaction of geometrical constraints given by the user. The method controls the resulting shape, defining the range (i.e. the impact) of the deformation on an object before applying it. The deformation takes into account the Loop properties to follow the subdivision scheme, allowing the user to fix some constraints at the subdivision-level he works on and to render the final object at the level he wants to. We also propose an adapt…

An Approximating-Interpolatory Subdivision Scheme.

International audience; In the last decade, study and construction of quad/triangle subdivision schemes have attracted attention. The quad/triangle subdivision starts with a control mesh consisting of both quads and triangles and produces ner and ner meshes with quads and triangles (Fig. 1). Design- ers often want to model certain regions with quad meshes and others with triangle meshes to get better visual qual- ity of subdivision surfaces. Smoothness analysis tools exist for regular quad/triangle vertices. Moreover C1 and C2 quad/triangle schemes (for regular vertices) have been con- structed. But to our knowledge, there are no quad/triangle schemes that uni es approximating and interpola…

Détection de surfaces de subdivision de Loop dans des maillages

International audience

A Graph Based Algorithm For Intersection Of Subdivision Surfaces

Computing surface intersections is a fundamental problem in geometric modeling. Any boolean operation can be seen as an intersection calculation followed by a selection of the parts necessary for building the surface of the resulting object. A robust and efficient algorithm to compute intersection on subdivision surfaces (surfaces generated by the Loop scheme) is proposed here. This algorithm relies on the concept of a bipartite graph which allows the reduction of the number of faces intersection tests. Intersection computations are accelerated by the use of the bipartite graph and the neighborhood of intersecting faces at a given level of subdivision to deduce intersecting faces at the fol…

Joining primal/dual subdivision surfaces

International audience; In this article we study the problem of constructing an intermediate surface between two other surfaces defined by different iterative construction processes. This problem is formalised with Boundary Controlled Iterated Function System model. The formalism allows us to distinguish between subdivision of the topology and subdivision of the mesh. Although our method can be applied to surfaces with quadrangular topology subdivision, it can be used with any mesh subdivision (primal scheme, dual scheme or other.) Conditions that guarantee continuity of the intermediate surface determine the structure of subdivision matrices. Depending on the nature of the initial surfaces…

A Geometric Algorithm for Ray/Bezier Surfaces Intersectionusing Quasi-interpolating Control Net

International audience

Représentation des NURBS par Systèmes Itérés de Fonctions

International audience; Les Systèmes Itérés de Fonctions (IFS) sont un outil standard pour la génération de formes fractales. Les IFS controlés (CIFS) en sont une extension pour la création de formes fractales à dessein industriel. Un des avantages de cette approche est la possibilité de représenter des surfaces standards comme les surfaces de Bézier, Splines, et de subdivision. La représentation des surfaces par un unique formalisme facilite leur manipulation et la gestion des interactions comme par exemple la construction de raccords entre deux surfaces de natures différentes. Dans cet article, la formulation des B-Splines Rationnelles Non-Uniformes (NURBS) dans le formalisme des CIFS est…

Calcul direct d'une tesselation de la surface limite pour les schémas de subdivision uniformes

International audience; Le peu d'utilisation des surfaces de subdivision dans les systèmes CAO est principalement lié au fait que la surface est le plus souvent seulement approchée par des niveaux de raffinement successifs, ce qui induit un manque de pré-cision. De plus, il est difficile d'intégrer la représentation des surfaces de subdivision dans le noyau géométrique (ensemble de primitives et d'outils) des applications CAO. C'est dans ce but que nous décrirons un formalisme général de construction de surfaces de subdivision basé sur les Systèmes Itérés de Fonctions. Le principal apport est que toutes les surfaces de subdivision classiques sont gérées de la même manière quel que soit le s…

Approximate convex hull of affine iterated function system attractors

International audience; In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In additio…

A Geometric Algorithm for Ray/Bézier Surfaces Intersection Using Quasi-Interpolating Control Net

In this paper, we present a new geometric algorithm to compute the intersection between a ray and a rectangular Bezier patch. The novelty of our approach resides in the use of bounds of the difference between a Bezier patch and its quasi-interpolating control net. The quasi-interpolating polygon of a Bezier surface of arbitrary degree approximates the limit surface within a precision that is function of the second order difference of the control points, which allows for very simple projections and 2D intersection tests to determine sub-patches containing a potential intersection. Our algorithm is simple, because it only determines a 2D parametric interval containing the solution, and effici…

Déformations libres de surfaces de subdivision.

International audience