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.

De nos jours, la majorité des objets manufacturés sont conçus par des logiciels informatiques de CAO (Conception Assistée par Ordinateur). Cependant, lors de la visualisation, d'échange de données ou des processus de fabrication, le modèle géométrique doit être discrétisé en un maillage 3D composé d'un nombre fini de sommets et d'arêtes. Or, dans certaines situations le modèle initial peut être perdu ou indisponible. La représentation discrète 3D peut aussi être modifiée, par exemple après une simulation numérique, et ne plus correspondre au modèle initial. Une méthode de rétro-ingénierie est alors nécessaire afin de reconstruire une représentation continue 3D à partir de la représentation discrète.Dans ce manuscrit, nous présentons une procédure automatique et complète de rétro-ingénierie pour les maillages 3D issus principalement de la discrétisation d'objets mécaniques. Pour cela, nous proposons des améliorations sur la détection de primitives géométriques simples. Puis, nous introduisons un formalisme clair pour la définition de la topologie de l'objet et la construction des intersections entre les primitives. Enfin, nous décrivons une nouvelle méthode de construction de surfaces paramétriques 3D, fondée sur l'extraction automatique de grilles rectangulaires régulières supports. La méthode a été testée sur des maillages 3D issus d'applications industrielles et permet d'obtenir des modèles B-Rep cohérents. / Nowadays, most of the manufactured objects are designed using CAD (Computer-Aided Design) software. Nevertheless, for visualization, data exchange or manufacturing applications, the geometric model has to be discretized into a 3D mesh composed of a finite number of vertices and edges. But, in some cases, the initial model may be lost or unavailable. In other cases, the 3D discrete representation may be modified, for example after a numerical simulation, and does not correspond anymore to the initial model. A retro-engineering method is then required to reconstruct a 3D continuous representation from the discrete one.In this Ph.D. Thesis, we present an automatic and comprehensive reverse engineering process mainly dedicated to 3D meshes of mechanical items. We present first several improvements in automatically detecting geometric primitives from a 3D mesh. Then, we introduce a clear formalism to define the topology of the object and to construct the intersections between primitives. At the end, we describe a new method to fit 3D parametric surfaces which is based on extracting regular rectangular grids. The whole process is tested on 3D industrial meshes and results in reconstructing consistent B-Rep models.

This thesis treats how to generate collision information for multibody simulations in AgX Dynamicswhere the geometries are described with the data structure boundary representation, BREP. BREP is adata structure that contains the exact mathematical description of each individual surface. To describecomplex surfaces exact and efficient non uniform rational basis spline, NURBS, is used and for trivialsurfaces like planes or spheres simpler equations is used. Since all surfaces in a BREP is described veryaccurate, the accuracy for the collision information can be set high without affecting the amount of dataneeded to describe the geometries.To make AgX Dynamics able to calculate forces in a multibody simulation, collision informationabout were and how much two geometries are intersecting is required. The collision information containswere the overlap between two geometries is, how much the objects have penetrated each other and thedirection for which the objects have to separate. To find the penetration depth and the overlap theNewton Raphson method were used. The experiments conducted, showed that it is possible to useBREPs as a description of geometries to produce the collision information needed for the physics engineused by AgX Dynamics to handle collisions. A comparison between trimesh and BREP for producingthe collision information, shows that data usage is much lower for the representation of geometries withBREPs than trimesh. The results also shows that the accuracy can be significantly higher than fortrimesh as the data usage for trimesh becomes non practical to handle when the required accuracy ishigh. With the high accuracy and with the smooth surfaces used with the BREP the artificial friction isalmost negligible except for cases were intersection points could not be found all around the intersectioncurves due to limitations in the algorithm. / Detta examensarbete behandlar hur man skapar kollisionsinformation för flerkropps simuleringar i AgXDynamics där geometrier beskrivs med datastrukturen boundary representation, BREP. BREP är endatastruktur som innehåller den exakta matematiska beskrivningen för varje enskild yta. Att beskrivakomplexa ytor exakta och effektivt med non uniform rationell basis spline, NURBS, används och förtriviala ytor som plan eller sfärer kan enklare ekvationer används. Eftersom alla ytor i en BREP beskrivsexakt, kan noggrannheten för kollisions informationen sättas högt utan att påverka den mängd data sombehövs för att beskriva geometrier.För att göra AgX Dynamics kunna beräkna krafter i en flerkroppssimulering, krävs kollisions informationom var och hur mycket två geometrier kolliderar. Kollisions informationen innehåller varöverlappningen mellan två geometrier är, hur mycket objekten har penetrerat varandra och den riktningsom föremålen ska separeras. För att hitta penetrationsdjup och överlapp användes Newton Raphsonsmetod. De experiment som utförts, visade att det är möjligt att använda BREPs som en beskrivning avgeometrier för att producera kollisions information som behövs för att den fysikmotor som används avAGX Dynamics ska kunna hantera kollisioner. En jämförelse mellan trimesh och BREP för att producerakollisionen informationen, visar att dataanvändning är mycket lägre när geometrier representeras medBREPs än trimesh. Resultaten visar också att noggrannheten kan vara väsentligt högre för BREP änför trimesh eftersom dataanvändning för trimesh blir opraktiskt att hantera när noggrannheten är hög.Med hög noggrannhet och med de släta ytor som används med BREP blev den artificiella friction nästanförsumbar, utom i fallen där skärningspunkter inte kunde hittas runt hela skärningskurvor på grund avbegränsningar i algoritmen.

Inspections of bridges are today performed ocularly by an inspector at arm’s lengths distance to evaluate damages and to assess its current condition. Ocular inspections often require specialized equipment to aid the inspector to reach all parts of the bridge. The current state of practice for bridge inspection is therefore considered to be time-consuming, costly, and a safety hazard for the inspector. The purpose of this thesis has been to develop a method for automated modeling of bridges from point cloud data. Point clouds that have been created through photogrammetry from a collection of images acquired with an Unmanned Aerial Vehicle (UAV). This thesis has been an attempt to contribute to the long-term goal of making bridge inspections more efficient by using UAV technology. Several methods for the identification of structural components in point clouds have been evaluated. Based on this, a method has been developed to identify planar surfaces using the model-fitting method Random Sample Consensus (RANSAC). The developed method consists of a set of algorithms written in the programming language Python. The method utilizes intersection points between planes as well as the k-Nearest-Neighbor (k-NN) concept to identify the vertices of the structural elements. The method has been tested both for simulated point cloud data as well as for real bridges, where the images were acquired with a UAV. The results from the simulated point clouds showed that the vertices were modeled with a mean deviation of 0.13− 0.34 mm compared to the true vertex coordinates. For a point cloud of a rectangular column, the algorithms identified all relevant surfaces and were able to reconstruct it with a deviation of less than 2 % for the width and length. The method was also tested on two point clouds of real bridges. The algorithms were able to identify many of the relevant surfaces, but the complexity of the geometries resulted in inadequately reconstructed models. / Besiktning av broar utförs i dagsläget okulärt av en inspektör som på en armlängds avstånd bedömer skadetillståndet. Okulär besiktning kräver därmed ofta speciell utrustning för att inspektören ska kunna nå samtliga delar av bron. Detta resulterar i att det nuvarande tillvägagångssättet för brobesiktning beaktas som tidkrävande, kostsamt samt riskfyllt för inspektören. Syftet med denna uppsats var att utveckla en metod för att modellera broar på ett automatiserat sätt utifrån punktmolnsdata. Punktmolnen skapades genom fotogrammetri, utifrån en samling bilder tagna med en drönare. Uppsatsen har varit en insats för att bidra till det långsiktiga målet att effektivisera brobesiktning genom drönarteknik. Flera metoder för att identifiera konstruktionselement i punktmoln har undersökts. Baserat på detta har en metod utvecklats som identifierar plana ytor med regressionsmetoden Random Sample Consensus (RANSAC). Den utvecklade metoden består av en samling algoritmer skrivna i programmeringsspråket Python. Metoden grundar sig i att beräkna skärningspunkter mellan plan samt använder konceptet k-Nearest-Neighbor (k-NN) för att identifiera konstruktionselementens hörnpunkter. Metoden har testats på både simulerade punktmolnsdata och på punktmoln av fysiska broar, där bildinsamling har skett med hjälp av en drönare. Resultatet från de simulerade punktmolnen visade att hörnpunkterna kunde identifieras med en medelavvikelse på 0,13 − 0,34 mm jämfört med de faktiska hörnpunkterna. För ett punktmoln av en rektangulär pelare lyckades algoritmerna identifiera alla relevanta ytor och skapa en rekonstruerad modell med en avvikelse på mindre än 2 % med avseende på dess bredd och längd. Metoden testades även på två punktmoln av riktiga broar. Algoritmerna lyckades identifiera många av de relevanta ytorna, men geometriernas komplexitet resulterade i bristfälligt rekonstruerade modeller.

No description available.

- ABSTRACT - Noncommutative Choquet theory Let S be a linear subspace of a commutative C∗ -algebra C(X) that se- parates points of C(X) and contains identity. Then the closure of the Choquet boundary of the function system S is the Šilov boundary relati- ve to S. In the case of a noncommutative unital C∗ -algebra A, consider S a self-adjoint linear subspace of A that contains identity and generates A. Let us call S operator system. Then the noncommutative formulation of the stated assertion is that the intersection of all boundary representa- tions for S is the Šilov ideal for S. To that end it is sufficient to show that S has sufficiently many boundary representations. In the present work we make for the proof of that this holds for separable operator system.

[pt] Num modelador de sólidos, uma das ferramentas mais poderosas para a criação de objetos tridimensionais de qualquer nível de complexidade geométrica é a aplicação das operações booleanas. Elas são formas intuitivas e populares de combinar sólidos, baseadas nas operações aplicadas a conjuntos. Os tipos principais de operações booleanas comumente aplicadas a sólidos são: união, interseção e diferença. Havendo interesse prático, para garantir que os objetos resultantes possuam a mesma dimensão dos objetos originais, sem partes soltas ou pendentes, o processo de regularização é aplicado. Regularizar significa restringir o resultado de tal forma que apenas volumes preenchíveis possam existir. Na prática, a regularização é realizada classificando-se os elementos topológicos e eliminando-se estruturas de dimensão inferior. A proposta deste trabalho é o desenvolvimento de um algoritmo genérico que permita a aplicação do conjunto de operações booleanas em um ambiente de modelagem geométrica aplicada à análise por elementos finitos e que agregue as seguintes funcionalidades: trabalhar com um número indefinido de entidades topológicas (conceito de Grupo), trabalhar com objetos de dimensões diferentes, trabalhar com objetos non-manifold, trabalhar com objetos não necessariamente poliedrais ou planos e garantir a eficiência, robustez e aplicabilidade em qualquer ambiente de modelagem baseado em representação B-Rep. Neste contexto, apresenta-se a implementação do algoritmo num modelador geométrico pré- existente, denominado MG, seguindo o conceito de programação orientada a objetos e mantendo a interface com o usuário simples e eficiente. / [en] In a solid modeler, one of the most powerful tools to create threedimensional objects with any level of geometric complexity is the application of the Boolean set operations. They are intuitive and popular ways to combine solids, based on the operations applied to sets. The main types of Boolean operations commonly applied to solids are: union, intersection and difference. If there is practical interest, in order to assure that the resulting objects have the same dimension of the original objects, without loose or dangling parts, the regularization process is applied. To regularize means to restrict the result in a way that only filling volumes are allowed. In practice, the regularization is performed classifying the topological elements and removing the lower dimensional structures. The objective of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite element analysis, which aggregates the following functionalities: working with an undefined number of topological entities (Group concept), working with objects of different dimensions, working with nonmanifold objects, working with objects not necessarily plane or polyhedrical and assuring the efficiency, robustness and applicability in any modeling environment based on B-Rep representation. In this context, the implementation of the algorithm in a pre-existing geometric modeler named MG is presented, using the concept of object oriented programming and keeping the user interface simple and efficient.

Cette thèse traite de la construction de quelques représentations par les frontières, ou BREP (pour "Boundary REPresentation"), et des difficultés rencontrées. Aussi cette introduction rappelle-t-elle très brièvement ce que sont les BREP; on se reportera à [PERO 87] pour un exposé plus détaillé et pour d'autres références. La synthèse d'images et la CAO utilisent diverses modélisations des solides pour les visualiser et calculer leurs propriétés géométriques et mécaniques : masse, aire de l'enveloppe, centre de gravité, axes principaux d'inertie, etc. Plusieurs modèles informatiques des solides ont été proposés :

In the field of mechanical engineering, particularly in managing 3D CAD model databases, there's a pressing challenge in efficiently identifying and reusing duplicate models instead of the costly process of creating new ones from scratch. Shape-based similarity retrieval stands out as a crucial solution for industry players like Epiroc, offering a strategy for duplicate detection and overcoming the constraints of text-based searches. In this thesis, we explore an innovative Machine Learning-based framework for shape retrieval, leveraging UV-Net to encode 3D models for effective shape description and incorporating Self-Supervised Learning to improve the identification of model similarities without relying heavily on labeled data. To assess the effectiveness of our approach and understand its performance, we tested it using three foundational ML models for a quantitative evaluation of the shape embeddings. The findings highlight the framework's ability to accurately identify similar models within extensive datasets. Moreover, we applied this methodology to retrieve similar models of ’Epirocs product 3D models within ’Epirocs Standard Part Dataset, demonstrating the successful integration of ML in mechanical design for efficient shape retrieval and presenting a viable industrial application for Epiroc. Despite its achievements, the study acknowledges limitations in system integration and computational efficiency, suggesting future research directions such as improving access to various file formats, enhancing the user interface, and optimizing computational resources. / Inom området maskinteknik, särskilt när det gäller hantering av 3D CAD-modelldatabaser, finns det en akut utmaning i att effektivt identifiera och återanvända dubbletter av modeller istället för den kostsamma processen att skapa nya från grunden. Formbaserad likhetshämtning framstår som en avgörande lösning för branschaktörer som Epiroc, och erbjuder en strategi för dubblettdetektering och att övervinna begränsningarna med textbaserade sökningar. I det här examensarbetet utforskar vi ett innovativt Maskininlärning-baserat ramverk för formåtervinning, utnyttjar UV-Net för att koda 3D-modeller för effektiv formbeskrivning och införlivar Självledd Inlärning för att förbättra identifieringen av modelllikheter utan att förlita oss mycket på märkta data. För att bedöma effektiviteten av vårt tillvägagångssätt och förstå dess prestanda, testade vi det med tre grundläggande ML-modeller för en kvantitativ utvärdering av forminbäddningarna. Resultaten belyser ramverkets förmåga att exakt identifiera liknande modeller inom omfattande datauppsättningar. Dessutom tillämpade vi denna metod för att hämta liknande modeller av Epirocs produkt-3D-modeller inom Epirocs standarddeldataset, vilket visar den framgångsrika integrationen av ML i mekanisk design för effektiv formhämtning och presenterar en hållbar industriell applikation för Epiroc. Trots sina framgångar erkänner studien begränsningar i systemintegration och beräkningseffektivitet, och föreslår framtida forskningsriktningar som att förbättra tillgången till olika filformat, förbättra användargränssnittet och optimera beräkningsresurser.

Dans cette thèse, nous identifions et exploitons des similarités partielles dans des objets 3D pour répondre à des besoins courants du domaine de la Conception Assistée par Ordinateur (CAO). De nouvelles méthodes sont introduites, d'une part pour détecter les similarités partielles, d'autre part pour utiliser ces similarités dans des applications spécifiques telles que l'édition de forme, la compression et l'indexation d'objets 3D. Grâce au développement des applications de la modélisation géométrique, ces modèles sont de plus en plus nombreux et sont disponibles à travers plusieurs modalités. Pour augmenter la productivité dans la création de tels objets virtuels, la réutilisation et l'adaptation des modèles existants est un choix prioritaire. Cela exige donc des méthodes facilitant le stockage, la recherche et l'exploitation de ces modèles. Heureusement, les similarités dans des objets 3D est un phénomène fréquent. De nombreux objets sont composés de parties similaires à une rotation, à une translation ou à une symétrie près. De ce fait, la détection des similarités partielles dans ces modèles est capable de répondre aux problématiques courantes : la taille du stockage est réduite en conservant seulement une partie au lieu de toutes les parties répétées d'un modèle; l'indexation des modèles 3D requiert a priori l'orientation canonique des modèles. Or, la symétrie dans un objet 3D est toujours une référence d'orientation cohérente avec la perception humaine. Nous utilisons donc la symétrie partielle pour aligner ces modèles et ainsi renforcer la robustesse des méthodes d'indexation. Dans un premier temps, nous introduisons une approche similaire à la Transformée de Hough pour détecter des similarités partielles dans des modèles BRep-NURBS. Cette approche identifie non seulement les parties similaires mais aussi les transformations qui les lient. À travers la classification des isométries dans l'analyse des transformations, notre approche peut distinguer la nature de transformation liant des parties similaires d'un modèle, c'est-à-dire, les parties similaires à une rotation, à une translation ou à une symétrie près. Dans le deuxième temps, nous proposons deux applications héritées directement des résultats obtenus par la détection. Tout d'abord, pour la compression, un modèle se transforme en un graphe de similarités d'où les faces principales à conserver sont sélectionnées dans la structure compressée. Ensuite, pour l'orientation, le plan de la symétrie dominante et la projection orthographique d'un modèle autour de ce plan permettent de définir un repère canonique pour aligner ce modèle. / In this thesis, we identify and exploit the partial similarities within 3D objects to answer the current needs of the Computer Aided Design field (CAD). Novel methods are introduced, on the one hand to detect the partial similarities, on the other hand to use these similarities for specific applications such as shape editing, compression and indexation of 3D objects. Because of the development of geometric modeling applications, 3D models are getting more numerous and available through many channels. To increase the productivity in creating such 3D virtual objects, the reuse and the adaptation of existing models becomes a prior choice. Thus, it requires methods easing the storage, the searching and the exploitation of these models. Fortunately, similarities within the 3D objects is a popular phenomenon. Many objects are composed of similar patches up to an approximated rotation, translation or symmetry. Hence, detecting the partial similarities within NURBSBRep models is able to solve the current issues : the storage size is reduced by coding a single patch instead of repeated patches of a model ; 3D model indexation requires a canonical orientation of these models. Furthermore, the symmetry within a 3D object is a good orientation reference, coherent with the human perception. Accordingly, we use the partial symmetries to align 3D models and so reinforce the robustness of indexation methods. In a first phase, we introduce an orginal approach similar to the Hough Transform to detect partial similarities within NURBS-BRep models. This approach identifies not only similar patches but also identifies the corresponding transformations that connect them. Additionally, through the classification of isometries in transformations analysis, our approach can distinguish the nature of transformations of similar patches of a model, that is, the patches similar up to an approximated rotation, translation or symmetry. This classification is advantageous for further applications : the similar patches of other transformation natures are considered in compressing ; the symmetric patches are used to normalize 3D models aim at a robust indexation. In the second phase, we propose two applications inherited directly from the obtained results of the detection. Firstly, for the compression, a model is transformed into a similarity graph where the principal faces to be coded are selected to form the compressed structure. Secondly, for the orientation, the plane of the dominant symmetry and the orthographic projection of a model around this plane generate a canonical frame to align this model.