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

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

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…

Using Semantics to Manage 3D Scenes in Web Platforms

Computer graphics has widely spread out into various computer applications. After the early wire-frame computer generated images of the 60s, spatial representation of objects improved in the 70s with Boundary Representation (B-Rep) modeling, Constructive Solid Geometry (CSG) objects, and free-form surfaces. Realistic rendering in the 90s, taking into account sophisticated dynamic interactions (between objects or between objects and human actors, physical interactions with light, etc.) now make 3D-scenes much better than simple 3D representations of the real world. Indeed, they are a way to conceive products (industrial products, art products, etc.) and to modify them over time, either inter…

Tangentes à une courbe fractale

http://www.irit.fr/REFIG/index.php/refig/article/view/10; National audience; Nous nous intéressons au calcul des tangentes à une courbe fractale définie à l'aide d'un IFS. Généralement, les courbes fractales sont nulle part dérivables, mais sous certaines conditions on peut montrer qu'elles admettent, en un ensemble de points, des demi-tangentes à droite et à gauche. Nous proposons une méthode permettant de déterminer ces demi-tangentes.

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…).

Toward a real-time tracking of dense point-sampled geometry

4 pages; International audience; In this paper, we address the problem of tracking temporal deformations between two arbitrary densely sampled point-based surfaces. We propose an intuitive and efficient resolution to the point matching problem within two frames of a sequence. The proposed method utilizes two distinct space partition trees, one for each point cloud, which both are defined on a unique discrete space. Our method takes advantage of multi-resolution concerns, voxel adjacency relations, and a specific distance function. Experimental results obtained from both simulated and real reconstructed data sets demonstrate that the proposed method can handle efficiently the tracking proces…

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

Conversion d'un carreau de Bézier rationnel biquadratique en un carreau de cyclide de Dupin quartique

Dupin cyclides were introduced in 1822 by the French mathematician C-P. Dupin. They are algebraic surfaces of degree 3 or 4. The set of geometric properties of these surfaces has encouraged an increasing interest in using them for geometric modeling. A couple of algorithmes is already developed to convert a Dupin cyclide patch into a rational biquadratic Bezier patch. In this paper, we consider the inverse problem: we investigate the conditions of convertibility of a Bezier patch into a Dupin cyclide one, and we present a conversion algorithm to compute the parameters of a Dupin cyclide with the boundary of the patch that corresponds to the given Bezier patch.

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

The Local Fractional Derivative of Fractal Curves

Fractal curves described by iterated function system (IFS) are generally non-integer derivative. For that we use fractional derivative to investigate differentiability of this curves. We propose a method to calculate local fractional derivative of a curve from IFS property. Also we give some examples of IFS representing the slopes of the right and left half-tangent of the fractal curves.

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…

Mixed-aspect fractal surfaces

In order to provide accurate tools to model original surfaces in a Computer Aided Geometric Design context, we develop a formalism based on iterated function systems. This model enables us to represent both smooth and fractal free-form curves and surfaces. But, because of the self-similarity property underlying the iterated function systems, curves and surfaces can only have homogeneous roughness. The aim of our work was to elaborate a method to build parametric shapes (curves, surfaces, ...) with a non-uniform local aspect: every point is assigned a ''geometric texture'' that evolves continuously from a smooth to a rough aspect. The principle is to blend shapes with uniform aspects to defi…

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

Facial animation by reverse morphing on a sequence of real images: application to film and video production

Research on facial animation is as vast as the many interests and needs that can be found in the general public, television or film production. For Mac Guff Ligne, a company specialized in the fabrication of special effects and computer generated images, the needs and the constraints on such a topic are very big. Morphing is often used in facial animation, and consists in mixing several expression models. As we will discover, the advantages in using morphing are numerous, but the animation workload remains long and time-consuming. Our goal is to propose a fast and reliable animation tool that is based on the same morphing technique with which the graphic artists are familiar. Our method is …

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…

Extended constrained deformations: a new sculpturing tool

Modelling tools tend to virtual sculpturing, in which a basic object is deformed by user supplied actions. The model we present aims to be generic: whatever the geometric description of the object, we can deform it to satisfy location constraints. Our model deforms the whole space, the image of a point is a blend of deformation functions with a projection matrix which allows the satisfaction of the constraints. The user can define the extent of the deformation (i.e. the part of the object to be deformed), the shape of the deformation function to create profiles and the displacement of the constraint points to be satisfied.

From Dupin cyclides to scaled cyclides

Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. They have a low algebraic degree and have been proposed as a solution to a variety of geometric modeling problems. The circular curvature line’s property facilitates the construction of the cyclide (or the portion of a cyclide) that blends two circular quadric primitives. In this context of blending, the only drawback of cyclides is that they are not suitable for the blending of elliptic quadric primitives. This problem requires the use of non circular curvature blending surfaces. In this paper, we present another formulation of cyclides: Scaled cyclides. A scaled cy…

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

International audience

B-Deformable Superquadrics for 3D Reconstruction

We propose a new model for 3D representation and reconstruction. It is based on deformable superquadrics and parametric B-Splines. The 3D object deformation method uses B-Splines, instead of a Finite Element Method (FEM). This new model exhibits advantages of B-Splines It is significantly faster than deformable superquadrics without loss of generality (no assumption is made on object shapes,).

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…

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…