Propriétés différentielles du raccord entre deux courbes fractales

International audience

Study and Comparison of Surface Roughness Measurements

Journées du Groupe de Travail en Modélisation Géométrique (GTMG'14), Lyon; This survey paper focus on recent researches whose goal is to optimize treatments on 3D meshes, thanks to a study of their surface features, and more precisely their roughness and saliency. Applications like watermarking or lossy compression can benefit from a precise roughness detection, to better hide the watermarks or quantize coarsely these areas, without altering visually the shape. Despite investigations on scale dependence leading to multi-scale approaches, an accurate roughness or pattern characterization is still lacking, but challenging for those treatments. We think there is still room for investigations t…

NURBS and Iterated Functions Systems

Méthodes de contrôle de la rugosité à partir des propriétés différentiels de courbes autosimilaires.

La rugosité a de nombreuses applications, l’industrie l’utilise comme outil pour avoir des propriétés de surface recherchés ou pour le contrôle qualité, le domaine de l’informatique graphique s’intéresse à la synthétiser pour la génération de terrains ou la génération de textures et aussi à simuler ses effets sur la lumière avec les BRDF. . . Dans cette présentation, nous proposeronsun rappel sur la rugosité, notamment sa définition plus précise que "surface ou courbe non lisse" et ses outils de quantification suivi d’une comparaison de certaines de ses méthodes de génération, illustrant l’intérêt d’une approche fractale pour l’étudier. Nous commencerons par des méthodes simples mais offran…

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…

Modeling of Human Posturokinetic Movements by a Linear Feedback System: Relations among Feedback Coefficients

This study describes a method of modeling human trunk and whole body backward bending and suggests a possible neural control strategy. The hypothesis was that the control system can be modeled as a linear feedback system, in which the torque acting at a given joint is a function of the state variables (angular positions and angular velocities). The linear system enabled representation of the feedback system by a gain matrix. The matrix was computed from the kinematics recorded by a movement analysis system and from the joint torques calculated by inverse dynamics. To validate the control model, a comparison was made between the angular kinematics yielded by the model and the experimental d…

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…

Tangents to fractal curves and surfaces

International audience; The aim of our work is to specify and develop a geometric modeler, based on the formalism of iterated function systems with the following objectives: access to a new universe of original, various, aesthetic shapes, modeling of conventional shapes (smooth surfaces, solids) and unconventional shapes (rough surfaces, porous solids) by defining and controlling the relief (surface state) and lacunarity (size and distribution of holes). In this context we intend to develop differential calculus tools for fractal curves and surfaces defined by IFS. Using local fractional derivatives, we show that, even if most fractal curves are nowhere differentiable, they admit a left and…

Differential constraints for iteratively generated curves

Roughness is a complex concept, that is multiscale, and based on the study of the local behavior of a curve or a surface in a given neighborhood. A large number of conventional statistical parameters are currently available to attempt to appreciate this concept in the different application areas that make use of it. But it is often difficult, for a given application domain or a special need, to know precisely which parameter(s) connect(s) the topography of a surface to the physical phenomena that it undergoes. We believe that a geometric characterization should be more suitable. We suggest to control roughness by exploiting the differential behavior of curves and surfaces. We are interested…

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.

Nycthemeral variations in core temperature and heart rate: continuous cycling exercise versus continuous rest.

Circadian rhythms have formed the subject of many researches in man during bed rest or usual routine, but have been little studied during continuous and sustained physical exercise. This study deals with the influence of time of day on biological markers in competitive cyclists during continuous physical exercise versus continuous rest. Ultra-distance cyclists were studied over a 24 h period (13:00 to 13:00 h the next day) in the laboratory. The subjects were requested to maintain a constant speed (set at 65% - 70% of their maximal aerobic speed obtained during a preliminary test) on their own bicycles which were equipped with home trainers. Workload, core temperature and heart rate were mo…

Modélisation géométrique de formes fractales pour la CAO

International audience

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

International audience

Uniformisation de NURBS par blossoming

Représentation, analyse et caractérisation de surfaces rugueuses

Nous présentons un projet de recherche dans lequel, nous proposons d’aborder la problématique de la représentation numérique, de l’analyse et de la caractérisation de surfaces rugueuses. La rugosité est un concept complexe, par nature multi-échelle et reposant sur l’étude du comportement local d’une surface dans un voisinage donné. Son évaluation sur les surfaces est essentielle pour de nombreux problèmes expérimentaux. Cela explique les nombreuses études réalisées dans les domaines applicatifs liés à la physique et la mécanique, là où le contrôle et la maîtrise de l’état des surfaces constituent un besoin majeur pour les industriels. Un grand nombre de paramètres conventionnels normalisés …

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

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.

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.

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…

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…

Iterative geometric modelling and new world of shapes

Mes recherches ont pour cadre la modélisation géométrique pour la Conception Assistée par Ordinateur et la Synthèse d'images. Plus précisément, j'étudie les possibilités qu'offrent les procédés de construction itératifs basés sur le principe de la géométrie fractale. Partant du modèle IFS (Iterated Function System), nous avons montré qu'il est possible de modéliser des formes non conventionnelles et ainsi de donner accès à un nouvel univers de formes aux concepteurs, artistes et designers. Cette approche est notamment utilisée pour modéliser des surfaces plissées (comme pour la réalisation de coques en architecture) ou des surfaces rugueuses. Nous avons orienté nos travaux sur la notion de …

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…

Simulating mechanical consequences of voluntary movement upon whole-body equilibrium: the arm-raising paradigm revisited.

Voluntary arm-raising movement performed during the upright human stance position imposes a perturbation to an already unstable bipedal posture characterised by a high body centre of mass (CoM). Inertial forces due to arm acceleration and displacement of the CoM of the arm which alters the CoM position of the whole body represent the two sources of disequilibrium. A current model of postural control explains equilibrium maintenance through the action of anticipatory postural adjustments (APAs) that would offset any destabilising effect of the voluntary movement. The purpose of this paper was to quantify, using computer simulation, the postural perturbation due to arm raising movement. The m…