Cette thèse s'inscrit dans le cadre d'un projet pluridisciplinaire, le projet DRAMA, qui consiste à générer des scènes virtuelles 3D à partir des descriptions contenues dans les textes théâtraux. L'un des objectifs de ce projet consiste à simplifier au maximum la tâche des utilisateurs finaux en leur offrant un outil simple, rapide, et efficace. Ainsi, la technique adoptée dans cette étude est axée sur la modélisation déclarative d'environnements virtuels qui s'appuie sur trois phases (description, génération et prise de connaissances). La phase de description permet au concepteur de décrire l'environnement à partir d'un ensemble de propriétés, interprétées en un ensemble de contraintes destinées à un système de génération qui produit un ou plusieurs environnements virtuels solutions.Dans le cadre de ce projet DRAMA, des nouvelles méthodes de balisage ont été proposées afin de détecter les éléments essentiels pour la création d'une pièce théâtrale, notamment les informations sur les placements d'objets. Par ailleurs, les utilisateurs peuvent, aussi, lancer des requêtes au niveau du texte à partir de ces balises. Les propriétés sur les placements seront traduites en contraintes spatiales grâce aux données initialement stockées dans une base de connaissance qui utilise le langage XML. Une technique adoptant la méthode des métaheuristiques est ensuite utilisée pour la résolution des contraintes de placements obtenues précédemment. La gestion des propriétés physiques des objets (collision, gravité, friction) a été aussi gérée à partir d'un moteur physique. À la fin, les scènes solutions finales seront proposées à l'utilisateur, en utilisant un moteur de rendu 3D. / This thesis is part of a multidisciplinary project, the DRAMA project, which attempts to generate 3D virtual scenes from the descriptions which are obtained from theatrical text. This project aims to simplify, as soon as possible, the tasks of the end-users by providing simple, fast, and effective tools. Thus, the technique used in this study is focused on the declarative modeling of virtual environments that is based on three phases (description, generation and management of knowledge). The description phase allows the designer to describe the environment from a set of properties, interpreted as a set of constraints for a generation system which produces one or several virtual environments solutions. This project, new tagging methods have been proposed to detect essential for the creation of scene, including information on the placement of objects. In addition, users can also run queries in the text from these tags. Placement properties are translated into spatial constraints with the data originally stored in a knowledge base that uses XML. A technique adopting the method of metaheuristics is then used for solving constraints. The object physical properties (collision, gravity, friction) were also managed from a physics engine. At the end, the finals scenes solutions were be proposed to the user, using a 3D rendering engine.

This thesis describes work on a new high-level mathematical modeling language and framework called PDEModelica for modeling with partial differential equations. It is an extension to the current Modelica modeling language for object-oriented, equation-based modeling based on differential and algebraic equations. The language extensions and the framework presented in this thesis are consistent with the concepts of Modelica while adding support for partial differential equations and space-distributed variables called fields. The specification of a partial differential equation problem consists of three parts: 1) the description of the definition domain, i.e., the geometric region where the equations are defined, 2) the initial and boundary conditions, and 3) the actual equations. The known and unknown distributed variables in the equation are represented by field variables in PDEModelica. Domains are defined by a geometric description of their boundaries. Equations may use the Modelica derivative operator extended with support for partial derivatives, or vector differential operators such as divergence and gradient, which can be defined for general curvilinear coordinates based on coordinate system definitions. The PDEModelica system also allows the partial differential equation models to be defined using a coefficient-based approach, where PDE models from a library are instantiated with different parameter values. Such a library contains both continuous and discrete representations of the PDE model. The user can instantiate the continuous parts and define the parameters, and the discrete parts containing the equations are automatically instantiated and used to solve the PDE problem numerically. Compared to most earlier work in the area of mathematical modeling languages supporting PDEs, this work provides a modern object-oriented component-based approach to modeling with PDEs, including general support for hierarchical modeling, and for general, complex geometries. It is possible to separate the geometry definition from the model definition, which allows geometries to be defined separately, collected into libraries, and reused in new models. It is also possible to separate the analytical continuous model description from the chosen discretization and numerical solution methods. This allows the model description to be reused, independent of different numerical solution approaches. The PDEModelica field concept allows general declaration of spatially distributed variables. Compared to most other approaches, the field concept described in this work affords a clearer abstraction and defines a new type of variable. Arrays of such field variables can be defined in the same way as arrays of regular, scalar variables. The PDEModelica language supports a clear, mathematical syntax that can be used both for equations referring to fields and explicit domain specifications, used for example to specify boundary conditions. Hierarchical modeling and decomposition is integrated with a general connection concept, which allows connections between ODE/DAE and PDE based models. The implementation of a Modelica library needed for PDEModelica and a prototype implementation of field variables are also described in the thesis. The PDEModelica library contains internal and external solver implementations, and uses external software for mesh generation, requisite for numerical solution of the PDEs. Finally, some examples modeled with PDEModelica and solved using these implementations are presented.