Modélisation géométrique

Résumé

La modélisation géométrique est l’ensemble des outils mathématiques, numériques et informatiques qui combinés permettent de construire un modèle virtuel (ou modèle informatique) d’un objet réel. Cet objet peut être plus ou moins complexe, plus ou moins schématisé. Il peut être le fruit de l’imagination, d’une tendance ou plutôt une solution plus ou moins exacte d’un problème physique donné, voire un compromis entre les deux. La modélisation géométrique sous-entend d’être en mesure de réaliser la construction et l’assemblage de formes élémentaires pour créer des objets de plus en plus complexes en respectant des contraintes topologiques. Des manipulations géométriques pour représenter, modifier, analyser:

processus " élémentaires " (transformations géométriques, calcul, ...)
processus complexes (intersection)
processus spécifiques (objets décalés (fabrication), raccordements et congés)

La modélisation géométrique implique aussi de savoir reconstruire des objets à partir de nu

Source officielle

https://fr.wikipedia.org/wiki/Mod%C3%A9lisation_g%C3%A9om%C3%A9trique

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Unique decomposition of homogeneous languages and application to isothetic regions

Nicolas René Jean Ninin

A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group G(n) on the collection of homogeneous languages of length n is an element of N. One recovers the isothetic regions from (Haucourt 2017, to appear (online since October 2017)) by considering the alphabet of connected subsets of the space vertical bar G vertical bar, viz the geometric realization of a finite graph G. Factoring the geometric model of a conservative program amounts to parallelize it, and there exists an efficient factoring algorithm for isothetic regions. Yet, from the theoretical point of view, one wishes to go beyond the class of conservative programs, which implies relaxing the finiteness hypothesis on the graph G. Provided that the collections of n-dimensional isothetic regions over G (denoted by R-n vertical bar G vertical bar) are co -unital distributive lattices, the prime decomposition of isothetic regions is given by an algorithm which is, unfortunately, very inefficient. Nevertheless, if the collections R-n vertical bar G vertical bar satisfy the stronger property of being Boolean algebras, then the efficient factoring algorithm is available again. We relate the algebraic properties of the collections R-n vertical bar G vertical bar to the geometric properties of the space I GI. On the way, the algebraic structure R-n vertical bar G vertical bar is proven to be the universal tensor product, in the category of semilattices with zero, of n copies of the algebraic structure R-1 vertical bar G vertical bar.

2019

Chargement

In our everyday life we interact with the surrounding environment using our hands. A main focus of recent research has been to bring such interaction to virtual objects, such as the ones projected in virtual reality devices, or super-imposed as holograms in AR/MR headsets. For these applications, it is desirable for the tracking technology to be robust, accurate, and have a seamless deployment. In this thesis we address these requirements by proposing an efficient and robust hand tracking algorithm, introducing a hand model representation that strikes a balance between accuracy and performance, and presenting the online algorithm for precise hand calibration. In the first part we present a robust method for capturing articulated hand motions in real time using a single depth camera. Our system is based on a realtime registration process that accurately reconstructs hand poses by fitting a 3D articulated hand model to depth images. We register the hand model using depth, silhouette, and temporal information. To effectively map low-quality depth maps to realistic hand poses, we regularize the registration with kinematic and temporal priors, as well as a data-driven prior built from a database of realistic hand poses. We present a principled way of integrating such priors into our registration optimization to enable robust tracking without severely restricting the freedom of motion. In the second part we propose the use of sphere-meshes as a novel geometric representation for real-time generative hand tracking. We derive an optimization to non-rigidly deform a template model to fit the user data in a number of poses. This optimization jointly captures the user's static and dynamic hand geometry, thus facilitating high-precision registration. At the same time, the limited number of primitives in the tracking template allows us to retain excellent computational performance. We confirm this by embedding our models in an open source real-time registration algorithm to obtain a tracker steadily running at 60Hz. In the third part we introduce an online hand calibration method that learns the geometry as the user performs live in front of the camera, thus enabling seamless virtual interaction at the consumer level. The key novelty in our approach is an online optimization algorithm that jointly estimates pose and shape in each frame, and determines the uncertainty in such estimates. This knowledge allows the algorithm to integrate per-frame estimates over time, and build a personalized geometric model of the captured user. Our approach can easily be integrated in state-of-the-art continuous generative motion tracking software. We provide a detailed evaluation that shows how our approach achieves accurate motion tracking for real-time applications, while significantly simplifying the workflow of accurate hand performance capture.

EPFL2018

Chargement

Méthode d'étalonnage d'une machine-outil à cinématique parallèle à cinq axes à grands angles d'inclinaison

Hélène Frayssinet Mazerolle

A machine-tool is able to manufacture precisely only when it is calibrated. Calibration consists in correcting the model of the machine so that it represents the real kinematics. On no account calibrating a structure consists in changing some parts of the machine. The industrial machining prototype of the Hita-STT (Stiffness Tracking Technology) machine-tool has a four-axis parallel kinematics associated to a turning table as left hand. The spindle is fixed to the parallel kinematics; the workpiece is fixed to the turning table. This new machine-tool was developed by the Laboratoire de Systèmes Robotiques from EPFL and Willemin-Macodel S.A. For its industrialization, it needs an absolute accuracy of 10 microns after calibration considering a repeatability of 5 microns. These specifications should be obtained in the entire workspace between the spindle and the turning device. This doctoral thesis deals with the calibration of the Hita-STT machine-tool. Several methods can be developed. They differ in: the geometrical model that is used. For each kinematics, three geometrical models exist: the implicit model, the forward geometrical model and the inverse geometrical model; the way the corrections are applied. Pose errors are compensated correcting the commands sent to the controller; or the parameters of the structure are identified and updated on the controller. This last solution allows to use a model for the control of the machine that is closer to the real kinematics. These different methods are presented and compared. An optimal calibration method is proposed. Whatever calibration methodology is chosen, it is divided into four steps: modeling the kinematics. An unique distribution of the parameters of the Hita-STT parallel kinematics is proposed; measurement of the pose errors. The choice and the design of the measuring device are presented. A set-up and characterization procedure is explained. It is compatible with the industrial environment. The pose errors measurements are automatic thanks to special ISO functions added to the controller. Data processing is automatic; calculation of the corrections of the model. Several methods are compared in terms of accuracy that can be obtained. An "ideal" method is proposed for the parallel kinematics calibration. It combines the two families of calibration methods, it means an identification method followed by a direct calibration method; implementation. The "ideal" method is tested on the industrial machining prototype Hita-STT. The structure of the programs used to automate the calibration process are given. Tests used to verify the calibration quality are presented. They can also be used to make sure that the parallel kinematics is accurate enough to satisfy the required quality of the manufactured parts.

EPFL2007

Chargement

Méthode d'étalonnage d'une machine-outil à cinématique parallèle à cinq axes à grands angles d'inclinaison

Hélène Frayssinet Mazerolle

EPFL2007

EPFL2018