No / Parameterisation of facial expressions on PDE surface representations of human faces are presented in this work. Taking advantage of the boundary-value approach inherent to Bloor-Wilson PDE method, facial expressions are achieved by manipulating the original boundary curves. Such curves are responsible for generating a surface representation of a human face in its neutral configuration, so that regions on these curves represent a given facial expression in a fast and realistic manner. Additionally, the parameterisation proposed here is carried out by applying different mathematical transformations to the affected curves according to the corresponding facial expression. Full analytic expressions parameterising some of the most common facial expressions such as smiling and eyebrow raising are in this work. Some graphical examples of these facial expressions are used to illustrate the results obtained using Bloor-Wilson PDE method as the foundations of the parameterisation scheme proposed here. Thus, it is shown that an efficient, intuitive and realistic parameterisation of facial expressions is attainable using Bloor-Wilson PDE method in along with a suitable mathematical expression.

Pharmaceutical tablets have been the most dominant form for drug delivery and they need to be strong enough to withstand external stresses due to packaging and loading conditions before use. The strength of the produced tablets, which is characterised by their compressibility and compactibility, is usually deter-mined through a physical prototype. This process is sometimes quite expensive and time consuming. Therefore, simulating this process before hand can over-come this problem. A technique for shape modelling of pharmaceutical tablets based on the use of Partial Differential Equations is presented in this thesis. The volume and the sur-face area of the generated parametric tablet in various shapes have been es-timated numerically. This work also presents an extended formulation of the PDE method to a higher dimensional space by increasing the number of pa-rameters responsible for describing the surface in order to generate a solid tab-let. The shape and size of the generated solid tablets can be changed by ex-ploiting the analytic expressions relating the coefficients associated with the PDE method. The solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load has been utilised in order to model a displace-ment component of a compressed PDE-based representation of a flat-faced round tablet. The simulation results, which are analysed using the Heckel model, show that the developed model is capable of predicting the compressibility of pharmaceutical powders since it fits the experimental data accurately. The opti-mal design of pharmaceutical tablets with particular volume and maximum strength has been obtained using an automatic design optimisation which is performed by combining the PDE method and a standard method for numerical optimisation.

Computing surface and/or object intersections is a cornerstone of many algorithms in Geometric Modeling and Computer Graphics, for example Set Operations between solids, or surface Ray Casting display. We present an object centered, information preserving, hierarchical representation for polyhedra called Prism Tree. We use the representation to decompose the intersection algorithms into two steps: the localization of intersections, and their processing. When dealing with polyhedra with many faces (typically more than one thousand), the first step is by far the most expensive. The Prism Tree structure is used to compute efficiently this localization step. A preliminary implementation of the Set Operations and Ray casting algorithms has been constructed.

This thesis discusses a novel method for modelling facial action units. It presents facial action units model based on boundary value problems for accurate representation of human facial expression in three-dimensions. In particular, a solution to a fourth order elliptic Partial Differential Equation (PDE) subject to suitable boundary conditions is utilized, where the chosen boundary curves are based on muscles movement defined by Facial Action Coding System (FACS). This study involved three stages: modelling faces, manipulating faces and application to simple facial animation. In the first stage, PDE method is used in modelling and generating a smooth 3D face. The PDE formulation using small sets of parameters contributes to the efficiency of human face representation. In the manipulation stage, a generic PDE face of neutral expression is manipulated to a face with expression using PDE descriptors that uniquely represents an action unit. A combination of the PDE descriptor results in a generic PDE face having an expression, which successfully modelled four basic expressions: happy, sad, fear and disgust. An example of application is given using simple animation technique called blendshapes. This technique uses generic PDE face in animating basic expressions.

Les propriétés de symétrie d'un objet représenté sous la forme d'un modèle B-Rep CAO sont analysées localement et globalement à travers une approche de type diviser pour conquérir. La surface frontière de l'objet est décrite à partir de surfaces canoniques fréquemment utilisées dans les formes de composants mécaniques. La première phase de l'analyse consiste en la génération de faces et d'arêtes maximales indépendantes du processus de modélisation de l'objet mais préservant ses propriétés de symétrie. Ces faces et arêtes constituent des ensembles infinis de points traités globalement. La seconde phase est l'étape de division consistant en la création de plan et axes de symétrie de candidats pour les faces et arêtes maximales générées précédemment. Enfin, suit l'étape de propagation de ces plans et axes de symétrie représentant la phase de conquête et déterminant les propriétés de symétrie locales et globales de l'objet et caractérisant ses zones non-symétriques. / Symmetry properties of objects described as B-Rep CAD models are analyzed locally as well as globally through an approach of type divide-and-conquer. The boundary of the object is defined using canonical surfaces frequently used when shaping mechanical components. Then, the first phase consists in generating maximal faces and edges that are independent from the object modelling process but that preserve its symmetry properties. These faces and edges form infinite sets of points that are processed globally. The second phase is the division one that creates candidate symmetry planes and axes attached to the previous maximal edges and faces. Finally, comes the propagation step of these candidate symmetry planes and axes forming the conquer phase that determines the local as well as the global symmetries of the object while characterizing its asymmetric areas.

This thesis discusses a novel method for modelling facial action units. It presents facial action units model based on boundary value problems for accurate representation of human facial expression in three-dimensions. In particular, a solution to a fourth order elliptic Partial Differential Equation (PDE) subject to suitable boundary conditions is utilized, where the chosen boundary curves are based on muscles movement defined by Facial Action Coding System (FACS). This study involved three stages: modelling faces, manipulating faces and application to simple facial animation. In the first stage, PDE method is used in modelling and generating a smooth 3D face. The PDE formulation using small sets of parameters contributes to the efficiency of human face representation. In the manipulation stage, a generic PDE face of neutral expression is manipulated to a face with expression using PDE descriptors that uniquely represents an action unit. A combination of the PDE descriptor results in a generic PDE face having an expression, which successfully modelled four basic expressions: happy, sad, fear and disgust. An example of application is given using simple animation technique called blendshapes. This technique uses generic PDE face in animating basic expressions. / Ministry of Higher Education, Malaysia and Universiti Malaysia Terengganu

An alternative technique for shape morphing using a surface generating method using partial differential equations is outlined throughout this work. The boundaryvalue nature that is inherent to this surface generation technique together with its mathematical properties are hereby exploited for creating intermediate shapes between an initial shape and a final one. Four alternative shape morphing techniques are proposed here. The first one is based on the use of a linear combination of the boundary conditions associated with the initial and final surfaces, the second one consists of varying the Fourier mode for which the PDE is solved whilst the third results from a combination of the first two. The fourth of these alternatives is based on the manipulation of the spine of the surfaces, which is computed as a by-product of the solution. Results of morphing sequences between two topologically nonequivalent surfaces are presented. Thus, it is shown that the PDE based approach for morphing is capable of obtaining smooth intermediate surfaces automatically in most of the methodologies presented in this work and the spine has been revealed as a powerful tool for morphing surfaces arising from the method proposed here.

Le contexte économique actuel montre que la représentation et l'analyse des données dans l'espace 3D croît de plus en plus dans les Systèmes d'Information Géographique (SIG). Le nombre d'applications SIG est en constante augmentation dans de nombreux secteurs d'activités comme par exemple la Défense, l'Aménagement du Territoire ou  la Sécurité Civile. Cependant, nous voyons l'émergence d'une forte demande pour l'analyse 3D dans les SIG. Ces développements nécessitent une standardisation des structures de données et d'échanges. Cette démarche est réalisée par l'Open Geospatial Consortium (OGC) et l'organisation internationale de normalisation (ISO). Une norme récente (ISO 19107:2003) décrit les objets complexes à prendre en compte et les traitements qu’il est possible de leur appliquer. Elle cherche à mettre en place l’interopérabilité des échanges et des analyses de données géométriques et topologiques dans les SIG. Actuellement aucune implémentation informatique complète de cette norme n’a été encore réalisée, compte tenu de son niveau d'abstraction. Une version simplifiée a toutefois été développée pour des objets uniquement 2D (ISO 19137:2007). Ce travail de thèse propose la modélisation et l’analyse d'objets complexes dans un espace tridimensionnel, et les traitements associés pour réaliser une première bibliothèque de fonctionnalités conforme à la norme ISO 19107. De plus, cette norme est actuellement portée en révision au sein du consortium OGC (Open Geospatial Consortium, www.opengeospatial.org) avec une nécessité de correction et d’évolution. Les travaux menés jusqu'à présent ont permis d’apporter une contribution pertinente avec l'ajout de nouvelles primitives géométriques, l'harmonisation de primitives par l'usage de courbes et surfaces paramétriques rationnelles. Les travaux sur cette norme ont permis également l’élaboration d'une application au sein de la société GEOMATYS, rendant possible la modélisation et l'analyse 3D d'un trafic aérien reposant sur des données SIG. / In the current economic context, the representation and the analysis of 3D data is growing more and more in the field of Geographic Information Systems (GIS). The number of GIS applications is constantly increasing in many industries, such as Defense, Regional Development and Civil Security. However, we can point out the emergence of an important request for 3D analysis in GIS. These developments require a standardization of data and exchange structures. This is carried out by Open Geospatial Consortium (OGC) and International Organization for Standardization (ISO). A recent standard (ISO 19107:2003) describes the complex objects to be taken into consideration and the associated treatments that can be used. It aims to develop interoperable exchange and analysis of geometric and topological data in GIS. Currently, no complete implementation on a computer of this standard has been done yet, regarding the level of abstraction sought. However, a simplified version was exclusively developed for 2D objects (ISO 19137:2007). This thesis proposes the modeling and the analysis of complex objects in three dimensional space, with their associated treatments. The objective is to create a first library whose the features are conform to ISO19107. Moreover, this standard is currently under review within the OGC Consortium (Open Geospatial Consortium) with a need for correction and evolution. The work done until now have enabled us to make a meaningful contribution with the addition of new geometrical primitives, the harmonization of primitives through the use of rational parametric curves and surfaces. The works on this standard also allowed the development of an application within the GEOMATYS company, making possible the 3D modeling and analysis for traffic simulation based on GIS data.

Actuellement, la restauration des oeuvres d’art, notamment des statues fracturées, repose sur des techniqueséprouvées, mais empiriques. Les statues endommagées comportent souvent des parties brisées. Leur restaurationconsiste la plupart du temps à les rassembler. Ainsi apparait la nécessité de prendre en compte lespropriétés mécaniques des interfaces entre les différentes parties brisées, ce qui permet de limiter l’ampleur desréparations et ainsi, de mieux conserver l’intégrité de l’oeuvre. Par ailleurs, les techniques numériques d’acquisition3D font leur entrée au service de la conservation du patrimoine. Cette thèse propose une méthodologiecapable d’utiliser des données issues d’une acquisition 3D pour simuler les opérations de restauration et leurseffets sur la structure de l’oeuvre. Les processus de restauration peuvent ainsi être testés et optimisés.Un scanner laser est utilisé pour l’acquisition de la géométrie des oeuvres, ce qui nous permet de reconstruireun modèle 3D pour la simulation numérique. Les calculs sont menés dans le cadre de la mécanique des milieuxcontinus déformables avec FLAC3D. Pour vérifier tous les points clés garantissant la stabilité mécanique, lecomportement des éléments de renforts et celui des interfaces entre les blocs ont été considérés. À partirdes résultats de ces études, une critique des stratégies de restauration mises en oeuvre ou envisageables estproposée.De plus, plusieurs méthodes de caractérisation visant à retrouver la provenance du matériau et/ou estimerles propriétés mécaniques de l’oeuvre sont proposées : caractérisations physico-chimiques et minéralogiques,essais non destructifs et destructifs. Une campagne expérimentale visant à caractériser le comportement desfractures en contact frottant avec acquisition de l’état de surface a été réalisée. Une analyse des corrélationsentre les propriétés mécaniques et morphologique des interfaces est ensuite élaborée. Enfin nous proposonsdes modèles prédictifs construits par régressions linéaires multiples et multivariées. Cette étude permet desimuler le comportement d’une oeuvre fracturée. / Currently, the artworks restoration, including broken statues, are based on proven but empirical techniques. Damaged statues often have broken parts. Restoration mainly consists in joining these parts. Thus appears the necessity of taking into account the interfaces mechanical properties between the different broken parts, reducing thereby the extent of repairs and thus better maintain the integrity of the work. Beside this, digital 3D acquisition techniques become more and more popular among the cultural heritage community. This thesis proposes a methodology able to use 3D acquisition datas to simulate the restoration operations and their effects on the structure. The restoration strategy can thus be tested and optimized. A laser scanner is used to acquire the statue geometry, allowing to reconstruct a 3D model for numerical simulation. Computations are carried out within the framework of deformable continuum mechanics using the FLAC3D software. In order to check all the key points ensuring mechanical stability, the behavior of reinforcing elements and those of the interfaces between blocks were considered. From the results of the present studies, a critical analysis of implemented or possible restoration strategy is proposed. In addition, several characterization methods to find the material origin and/or estimate the mechanical properties of the work are proposed : physico-chemical and mineralogical characterizations, non-destructive and destructive tests. An experimental campaign to characterize the behavior of fractures in contact with surface acquisition was performed. An analysis of correlations between mechanical and morphological interfaces properties is then developed. Finally, we propose a predictive modelling based on multiple linear and multivariate regressions. This study allow the simulation of fractured artworks behaviour.

The main objective of this thesis was to develop appropriate strategies and find factors that affect the usability of parameterized designs. This was accomplished by investigate the user-interface and how it is designed to meet the user's information needs. The thesis also embraces the basic theories in terms of investigation, cognitive design principles and human behavior patterns in the interaction with the machine. The approach has led to an explorative investigation in this subject area. The thesis also had the purpose to achieve more efficient ways for development of motor chainsaws at Husqvarna AB's department Global Cutting Equipment. That can be achieved through reduce costs of development per sold unit. To reduce cost depends to what extend the program is helping the user to achieve goals during the design execution. The thesis also includes an investigation of the factors that affect the design of such a program. To explore appropriate strategies was a theoretical design process implemented in the study. From the perspective of technology has the author utilized knowledge in engineering design and programming. The program approach utilized was Visual Basic languish in Visual Studio enviroment for the user-interface and a Catia V5 CAD-platform for the chainsaw design. The result is a program which could use reconfigured parameters as needed to create customized designs correctly and effectively. This thesis has also resulted in appropriate principles for the design of a user-friendly interface that were up for the task to be a supporting tool through the execution. It has also been established appropriate tools and methods for analysis and optimization of the program. The author feels that the results of methods and principles in this study were of high reliability and can therefore be applied to other projects, even if the results only are valid for this specific case. / Huvudsyftet med detta examensarbete har varit att utveckla lämpliga strategier och finna faktorer vilka påverkar användarvänligheten för en parametriserad design. Detta åstadkomms genom att undersöka hur användarformulärets gränssnitt ska utformas för att möta användarens informationsbehov. Examensarbetet omfattar även grundteorier vad gäller undersökningsmetoder, kognitiva designprinciper och människans beteendemönster i interaktion med maskin. Tillvägagångsättet har inneburit en explorativ undersökning i detta ämnesområdet. Examensarbetet har även haft syftet att åstadkomma effektivare utvecklingsprocess av motorsågskedjor för Husqvarna AB’s avdelning Global Cutting Equipment. Detta kan åstadkommas genom minskade kostnader i utveckling per såld enhet. Att reducera kostnader påverkas av vilken omfattning programmet hjälper användaren att uppnå mål under exekveringen. Examensarbetet inkluderar även en undersökning av faktorer vilka påverkar designen i ett sådant program. För att undersöka lämpliga strategier i genomförandet har en teoretisk designprocess använts. Ur tekniskt perspektiv har författaren även använt kunskaper inom konstruktionsdesign och programmering. De använda programmen i genomförandet har varit Visual Basic språk i Visual Studio miljö för användarformuläret och en CAD-plattform i Catia V5 för kedjekonstruktionen. Resultat är ett program vilken skulle kunna omkonstruera designen korrekt och effektivt med parametrar efter behov. Arbetet har även resulterat i lämpliga principer för designen av ett användarvänligt gränssnitt vilken kan klara uppgiften att vara ett hjälpande verktyg under exekveringen. Det har även fastställts en del lämpliga verktyg eller metoder för analys och optimering av programmet. Författaren upplever även att resultaten av metoder och principer i denna studie, var av hög reliabilitet och kan därför appliceras på andra projekt, även om resultaten bara är giltiga för denna specifika studie.