Higher-order spectral analysis of acoustical waveforms can provide phase information that is not retained in calculations of power spectral density. In the propagation of high intensity sound, nonlinearity can cause substantial changes in the waveform as frequency components interact with one another. The bispectrum, which is one order higher than power spectral density, may provide a useful measure of nonlinearity in propagation by highlighting spectral regions of interaction. This thesis provides a review of the bispectrum, places it in the context of nonlinear acoustic propagation, and presents spectra calculated as a function of distance for numerically propagated acoustic waveforms. The calculated spectra include power spectral density, quad-spectral density, bispectrum, spatial derivative of the bispectrum, bicoherence, and skewness function. / text

Após o ajustamento de observações pelo método dos mínimos quadrados (MMQ) ter sido realizado, é possível a detecção e a identificação de erros não aleatórios nas observações, por meio de testes estatísticos. A teoria da confiabilidade faz uso de medidas adequadas para quantificar o menor erro detectável em uma observação, e a sua influência sobre os parâmetros ajustados, quando não detectado. A teoria de confiabilidade convencional foi desenvolvida para os procedimentos de teste convencionais, como o data snooping, que pressupõem que apenas uma observação está contaminada por erros grosseiros por vez. Recentemente foram desenvolvidas medidas de confiabilidade generalizadas, relativas a testes estatísticos que pressupõem a existência, simultânea, de múltiplas observações com erros (outliers). Outras abordagens para o controle de qualidade do ajustamento, alternativas a estes testes estatísticos, também foram propostas recentemente, como por exemplo, o método QUAD (Quasi-Accurate Detection of outliers method). Esta pesquisa tem por objetivo fazer um estudo sobre o controle de qualidade do ajustamento de observações geodésicas, por meio de experimentos em uma rede GPS (Global Positioning System), utilizando tanto os métodos convencionais quanto o atual estado da arte. Desta forma, foram feitos estudos comparativos entre medidas de confiabilidade convencionais e medidas de confiabilidade generalizadas para dois outliers simultâneos, bem como estudos comparativos entre o procedimento data snooping e testes estatísticos para a identificação de múltiplos outliers. Também se investigou como a questão das variâncias e covariâncias das observações, bem como a geometria/configuração da rede GPS em estudo, podem influenciar nas medidas de confiabilidade, tanto na abordagem convencional, quanto na abordagem generalizada. Por fim, foi feito um estudo comparativo entre o método QUAD e os testes estatísticos para a identificação de erros. / After the adjustment of observations has been carried out by Least Squares Method (LSM), it is possible to detect and identify non-random errors in the observations using statistical tests. The reliability theory makes use of appropriate measures to quantify the minimal detectable bias (error) in an observation, and its influence on the adjusted parameters, if not detected. The conventional reliability theory has been developed for conventional testing procedures such as data snooping, which assumes that only one observation is contaminated by errors at a time. Recently, generalized measures of reliability has been developed, relating to statistical tests that assumes the existence, simultaneous, of multiple observations with errors (outliers). Other approaches to the quality control of the adjustment, alternatives to these statistical tests, were also proposed recently, such as the QUAD method (Quasi-Accurate Detection of outliers method). The goal of this research is to make a study about the quality control of the adjustment of geodetic observations, by means of experiments in a GPS (Global Positioning System) network, using both conventional methods and the current state of the art. In this way, comparisons were made between conventional reliability measures and generalized measures of reliability for two outliers, as well as comparisons between the data snooping procedure and statistical tests to identify multiple outliers. It was also investigated how the variances and covariances of the observations, as well as the geometry/configuration of the GPS network in study, can influence the measures of reliability, both in the conventional approach and in the generalized approach. Finally, a comparison was made between the QUAD method and the statistical tests to identify outliers (errors).

Após o ajustamento de observações pelo método dos mínimos quadrados (MMQ) ter sido realizado, é possível a detecção e a identificação de erros não aleatórios nas observações, por meio de testes estatísticos. A teoria da confiabilidade faz uso de medidas adequadas para quantificar o menor erro detectável em uma observação, e a sua influência sobre os parâmetros ajustados, quando não detectado. A teoria de confiabilidade convencional foi desenvolvida para os procedimentos de teste convencionais, como o data snooping, que pressupõem que apenas uma observação está contaminada por erros grosseiros por vez. Recentemente foram desenvolvidas medidas de confiabilidade generalizadas, relativas a testes estatísticos que pressupõem a existência, simultânea, de múltiplas observações com erros (outliers). Outras abordagens para o controle de qualidade do ajustamento, alternativas a estes testes estatísticos, também foram propostas recentemente, como por exemplo, o método QUAD (Quasi-Accurate Detection of outliers method). Esta pesquisa tem por objetivo fazer um estudo sobre o controle de qualidade do ajustamento de observações geodésicas, por meio de experimentos em uma rede GPS (Global Positioning System), utilizando tanto os métodos convencionais quanto o atual estado da arte. Desta forma, foram feitos estudos comparativos entre medidas de confiabilidade convencionais e medidas de confiabilidade generalizadas para dois outliers simultâneos, bem como estudos comparativos entre o procedimento data snooping e testes estatísticos para a identificação de múltiplos outliers. Também se investigou como a questão das variâncias e covariâncias das observações, bem como a geometria/configuração da rede GPS em estudo, podem influenciar nas medidas de confiabilidade, tanto na abordagem convencional, quanto na abordagem generalizada. Por fim, foi feito um estudo comparativo entre o método QUAD e os testes estatísticos para a identificação de erros. / After the adjustment of observations has been carried out by Least Squares Method (LSM), it is possible to detect and identify non-random errors in the observations using statistical tests. The reliability theory makes use of appropriate measures to quantify the minimal detectable bias (error) in an observation, and its influence on the adjusted parameters, if not detected. The conventional reliability theory has been developed for conventional testing procedures such as data snooping, which assumes that only one observation is contaminated by errors at a time. Recently, generalized measures of reliability has been developed, relating to statistical tests that assumes the existence, simultaneous, of multiple observations with errors (outliers). Other approaches to the quality control of the adjustment, alternatives to these statistical tests, were also proposed recently, such as the QUAD method (Quasi-Accurate Detection of outliers method). The goal of this research is to make a study about the quality control of the adjustment of geodetic observations, by means of experiments in a GPS (Global Positioning System) network, using both conventional methods and the current state of the art. In this way, comparisons were made between conventional reliability measures and generalized measures of reliability for two outliers, as well as comparisons between the data snooping procedure and statistical tests to identify multiple outliers. It was also investigated how the variances and covariances of the observations, as well as the geometry/configuration of the GPS network in study, can influence the measures of reliability, both in the conventional approach and in the generalized approach. Finally, a comparison was made between the QUAD method and the statistical tests to identify outliers (errors).

This diploma thesis defines the term indexing and in preamble are discussed known indexing algorithms and difference between indexing static and moving objects. The practical part of this diploma thesis is aimed to designing and implementing of indexing algorithm for open source application MaNGOS with respect to generic design pattern and effectiveness of spatial search queries for selection of the objects given properties in the specified area. At the end I present and discuss reached results.

The goal of the master ́s thesis is to study index methods, spatial data type objects in PostgreSQL database systems and to create SP-GiST index by quadtree in the PostGIS. The PostGIS is spatial database, which extends of PostgreSQL. PostGIS adds support for geographic and spatial objects. It is a big benefit. PostGIS has its own data types, methods and GiST index too, but there is SP-GiST index missing, therefore master's thesis was created.

A lightweight, powerful, yet efficient quad-rotor platform was designed and constructed to obtain experimental results of completely autonomous control of a hovering micro-UAV using a complete on-board vision system. The on-board vision and control system is composed of a Helios FPGA board, an Autonomous Vehicle Toolkit daughterboard, and a Kestrel Autopilot. The resulting platform is referred to as the Helio-copter. An efficient algorithm to detect, correlate, and track features in a scene and estimate attitude information was implemented with a combination of hardware and software on the FPGA, and real-time performance was obtained. The algorithms implemented include a Harris feature detector, template matching feature correlator, RANSAC similarity-constrained homography, color segmentation, radial distortion correction, and an extended Kalman filter with a standard-deviation outlier rejection technique (SORT). This implementation was designed specifically for use as an on-board vision solution in determining movement of small unmanned air vehicles that have size, weight, and power limitations. Experimental results show the Helio-copter capable of maintaining level, stable flight within a 6 foot by 6 foot area for over 40 seconds without human intervention.

La problématique de cette thèse réside dans la caractérisation et le maintien de la stabilité des Véhicules Légers Tout Terrain (VLTT). Elle se concentre plus particulièrement sur le développement de systèmes de sécurité actifs capables à la fois de prévenir le conducteur des risques encourus mais aussi de les limiter afin d'assurer l'évolution du véhicule dans une zone de stabilité prédéfinie. Comme le cadre expérimental privilégié est l'application à la stabilité des quadricycles légers à moteurs, plus connus sous le terme anglophone "quad", une des contraintes du projet a été de se limiter à un système sensoriel bas-coût afin d'être en mesure d'industrialiser un tel système. En premier lieu, les métriques de stabilité (Transfert de Charge Latéral et Longitudinal : TCLa et TCLo) ont été choisies grâce à une étude préliminaire sur la stabilité des VLTT. Par la suite, une modélisation 2D en roulis et en tangage avec la prise en compte des déplacements du pilote sur le véhicule sont présentées, ce qui permet d'estimer respectivement le TCLa et le TCLo uniquement à partir de la mesure de l'accélération latérale et longitudinale. Étant donné que pour la suite des travaux, l'anticipation du risque de renversement latéral est nécessaire, un modèle 2D en lacet du véhicule est proposé afin d'obtenir un modèle analytique décrivant la dynamique latérale du véhicule. La suite du mémoire présente les différentes techniques d'observation proposées pour l'estimation des variables et paramètres non-directement mesurables du modèle en lacet du véhicule et qui influencent sa stabilité latérale : les glissements, les conditions d'adhérence et les inclinaisons du véhicule. Plusieurs observateurs ont été proposés, dont le dernier permet de considérer des conditions d'adhérence différentes entre les essieux avant et arrière en utilisant plus largement les accélérations mesurées. Cela permet d'intégrer les passages de sous- à sur-vireur qu'il est essentiel de considérer quand on étudie la stabilité de ce type de véhicule. Ainsi, l'estimation des glissements est toujours pertinente, ce qui permet d'obtenir par la suite une meilleure prédiction de la métrique de stabilité latérale (TCLa) quel que soit le comportement du véhicule. Puis en s'appuyant sur les estimations des observateurs couplées aux modèles dynamiques du véhicule et sur l'extrapolation des commandes du conducteur sur un horizon de prédiction, il est possible de prédire les évolutions du TCLa. Cette valeur prédite ainsi que les estimations en ligne des métriques de stabilité constituent alors le point d'entrée pour la synthétisation d'un système de sécurité actif dédié aux VLTT. Celui-ci est basé sur la génération d'un retour d'effort au niveau de la gâchette des gaz permettant soit d'informer le pilote du risque encouru par la création d'une sensation de dureté, soit d'imposer le retour complet de la gâchette des gaz, ce qui implique une diminution de la vitesse et donc la réduction du risque. Finalement, dans le cas où il est possible de maîtriser la vitesse du véhicule par l'installation d'un système de rétroaction sur les freins (Quad haut de gamme ou robot mobile), les derniers travaux présentés s'intéressent aux techniques de commande prédictive à modèle afin de calculer en temps-réel la vitesse maximale admissible, qui assure l'évolution du critère de stabilité choisi dans un domaine de stabilité. Les modèles, les observateurs, la prédiction du TCLa et les 2 systèmes de prévention présentés dans ce mémoire ont été validés et testés au travers de simulations avancées et d'essais expérimentaux réalisés sur un quad agricole et un robot autonome. Il apparaît alors qu'en plus d'être efficace pour la prévention des risques de renversement à hautes dynamiques, le système de sécurité est industriellement viable. Cela a été rendu possible grâce à une conception reposant uniquement sur des actionneurs et un système sensoriel, dont les coûts sont en adéquation avec le prix d'un VLTT. / This dissertation addresses the topic of lateral dynamic stability of light All-Terrain Vehicles (ATV) in a o-road environment. In particular, the developments are focused on the design of active security system allowing both to prevent the driver of the rollover risk and to ensure the vehicle stability within a safety margin. As the experimental framework is focused on light ATV (e.g. quad bikes), the main limitation of the project has been to keep a low cost sensing equipment in order to keep a possible industrialization. First, the stability metrics (Lateral and Longitudinal Load Transfer : LaLT and LoLT) have been chosen thanks to a preliminary study on the ATV stability. Then, two 2D models (roll and pitch) are proposed allowing to estimate the LaLT and the LoLT from the only acceleration measures and within the driver displacements on the vehicle. However, as the anticipation of lateral risk is mandatory for the next stage of the work, a 2D yaw model is also proposed in order to obtain an analytic model of the vehicle lateral dynamic. Then, the different observation techniques are presented to estimate the variables and parameters of the yaw model, who are not directly measurable and who inuence the lateral stability : sliding, grip conditions and vehicle slopes. Several observers are proposed, whose the last one permits to estimate separately the grip conditions between the front and rear axle thanks to a particular use of the acceleration measure. It allows to take into account the switch between the under- and over-steering behaviour influencing largely the vehicle stability. Thus, the sliding estimations are always relevant what permits to obtain a better prediction of the lateral stability metric (LaTT) whatever the vehicle behaviour. Then, thanks to the observer estimations combined with the vehicle dynamic models and an extrapolation of the driver inputs on a prediction horizon, the Lateral Load Transfer can be predicted. This latter value as well as the online estimations of the two stability metrics are the input of the active security system, which is based on the generation of a counter-force on the trigger. Thus, this system allows first to inform continuously the driver of the incurred risk thanks to a trigger feel harder to press. Secondly, if the risk is too important, the system is able to force the full return of the trigger, what reduces the vehicle speed and consequently the risk. Finally, a control law based on the Predictive Functional Control (PFC) theory has been designed to ensure the lateral stability of the vehicle. This control law allows to calculate in real time the maximal speed ensuring the evolution of the stability metric into a safety range. Nevertheless, this solution is only available for vehicles where it is possible to regulate their speed thanks to a control system on the brake. The models, the observers, the prediction of the LaLT and the two prevention systems presented in this dissertation have been validated and tested through several advanced simulations, a actual quad bike and autonomous mobile robot. Moreover, the security system appears to be directly integrated to industry, as its design rests upon low cost actuators and sensors compared to the price of actual quad bikes.

Silicon nanowire based multiple gate metal oxide field effect transistors(MG-MOSFET) appear as replacements for conventional bulk transistors in post 45nm technology nodes. In such transistors the short channel effect(SCE) is controlled by the device geometry, and hence an undoped (or, lightly doped) ultra-thin body silicon nanowire is used to sustain the channel. The use of undoped body also solves several issues in bulk MOSFETs e.g., random dopant fluctuations, mobility degradation and compatibility with midgap metal gates. The electrostatic integrity of such devices increases with the scaling down of the body thickness. Since the quantization of electron energy cannot be ignored in such ultra-thin body devices, it is extremely important to consider quantum effects in their threshold voltage models. Most of the models reported so far are valid for long channel double gate devices. Only Munteanu et al. [Journal of non-crystalline solids vol 351 pp 1911-1918 2005] have reported threshold voltage model for short channel symmetric double gate MOSFET, however it involves unphysical fitting parameters. Only Munteanu et al.[Molecular simulation vol 31 pp 839-845 2005] reported threshold voltage model for quad gate transistor which is implicit in nature. On the other hand no modeling work has been reported for other types of MG-MOSFETs (e.g., tri gate, cylindrical body)apart from numerical simulation results. In this work we report physically based closed form quantum threshold voltage models for short channel symmetric double gate, quad gate and cylindrical body gate-all-around MOSFETs. In these devices quantum effects aries mainly due to the structural confinement of electron energy. Proposed models are based on the analytical solution of two or three-dimensional Poisson equation and one or two-dimensional Schrodinger equation depending on the device geometries. Judicial approximations have been taken to simplify the models in order to make them closed form and efficient for large scale circuit simulation. Effort has also been put to model the quantum threshold voltage of tri gate MOSFET. However it is found that the energy quantization in tri gate devices are mainly due to electronic confinement and hence it is very difficult to develop closed form analytical equations for the threshold voltage. Thus in this work the modeling of tri gate devices have been limited to long channel cases. All the models are validated against the professional numerical simulator.

Aquesta tesi està dedicada al disseny i a l'anàlisi d'estructures de dades multidimensionals, és a dir, estructures de dades que serveixen per emmagatzemar registres $K$-dimensionals que solen representar-se com a punts en l'espai $[0,1]^K$. Aquestes estructures tenen aplicacions en diverses àrees de la informàtica com poden ser els sistemes d'informació geogràfica, la robòtica, el processament d'imatges, la world wide web, el data mining, entre d'altres. Les estructures de dades multidimensionals també es poden utilitzar com a indexos d'estructures de dades que emmagatzemen, possiblement en memòria externa, dades més complexes que els punts.Les estructures de dades multidimensionals han d'oferir la possibilitat de realitzar operacions d'inserció i esborrat de claus dinàmicament, a més de permetre realitzar cerques anomenades associatives. Exemples d'aquest tipus de cerques són les cerques per rangs ortogonals (quins punts cauen dintre d'un hiper-rectangle donat?) i les cerques del veí més proper (quin és el punt més proper a un punt donat?).Podem dividir les contribucions d'aquesta tesi en dues parts: La primera part està relacionada amb el disseny d'estructures de dades per a punts multidimensionals. Inclou el disseny d'arbres binaris $K$-dimensionals al·leatoritzats (Randomized $K$-d trees), el d'arbres quaternaris al·leatoritzats (Randomized quad trees) i el d'arbres multidimensionals amb punters de referència (Fingered multidimensional trees).La segona part analitza el comportament de les estructures de dades multidimensionals. En particular, s'analitza el cost mitjà de les cerques parcials en arbres $K$-dimensionals relaxats, i el de les cerques per rang en diverses estructures de dades multidimensionals. Respecte al disseny d'estructures de dades multidimensionals, proposem algorismes al·leatoritzats d'inserció i esborrat de registres per als arbres $K$-dimensionals i per als arbres quaternaris. Aquests algorismes produeixen arbres aleatoris, independentment de l'ordre d'inserció dels registres i desprès de qualsevol seqüència d'insercions i esborrats. De fet, el comportament esperat de les estructures produïdes mitjançant els algorismes al·leatoritzats és independent de la distribució de les dades d'entrada, tot i conservant la simplicitat i la flexibilitat dels arbres $K$-dimensionals i quaternaris estàndard. Introduïm també els arbres multidimensionals amb punters de referència. Això permet que les estructures multidimensionals puguin aprofitar l'anomenada localitat de referència en cerques associatives altament correlacionades.I respecte de l'anàlisi d'estructures de dades multidimensionals, primer analitzem el cost esperat de las cerques parcials en els arbres $K$-dimensionals relaxats. Seguidament utilitzem aquest resultat com a base per a l'anàlisi de les cerques per rangs ortogonals, juntament amb arguments combinatoris i geomètrics. D'aquesta manera obtenim un estimat asimptòtic precís del cost de les cerques per rangs ortogonals en els arbres $K$-dimensionals aleatoris. Finalment, mostrem que les tècniques utilitzades es poden estendre fàcilment a d'altres estructures de dades i per tant proporcionem una anàlisi exacta del cost mitjà de cerques per rang en estructures de dades com són els arbres $K$-dimensionals estàndard, els arbres quaternaris, els tries quaternaris i els tries $K$-dimensionals. / Esta tesis está dedicada al diseño y al análisis de estructuras de datos multidimensionales; es decir, estructuras de datos específicas para almacenar registros $K$-dimensionales que suelen representarse como puntos en el espacio $[0,1]^K$. Estas estructuras de datos tienen aplicaciones en diversas áreas de la informática como son: los sistemas de información geográfica, la robótica, el procesamiento de imágenes, la world wide web o data mining, entre otras.Las estructuras de datos multidimensionales suelen utilizarse también como índices de estructuras que almacenan, posiblemente en memoria externa, datos complejos.Las estructuras de datos multidimensionales deben ofrecer la posibilidad de realizar operaciones de inserción y borrado de llaves de manera dinámica, pero además deben permitir realizar búsquedas asociativas en los registros almacenados. Ejemplos de búsquedas asociativas son las búsquedas por rangos ortogonales (¿qué puntos de la estructura de datos están dentro de un hiper-rectángulo dado?) y las búsquedas del vecino más cercano (¿cuál es el punto de la estructura de datos más cercano a un punto dado?).Las contribuciones de esta tesis se dividen en dos partes:La primera parte está dedicada al diseño de estructuras de datos para puntos multidimensionales, que incluye el diseño de los árboles binarios $K$-dimensionales aleatorios (Randomized $K$-d trees), el de los árboles cuaternarios aleatorios (Randomized quad trees), y el de los árboles multidimensionales con punteros de referencia (Fingered multidimensional trees).La segunda parte contiene contribuciones al análisis del comportamiento de las estructuras de datos para puntos multidimensionales. En particular, damos el análisis del costo promedio de las búsquedas parciales en los árboles $K$-dimensionales relajados y el de las búsquedas por rango en varias estructuras de datos multidimensionales.Con respecto al diseño de estructuras de datos multidimensionales, proponemos algoritmos aleatorios de inserción y borrado de registros para los árboles $K$-dimensionales y los árboles cuaternarios que producen árboles aleatorios independientemente del orden de inserción de los registros y después de cualquier secuencia de inserciones y borrados intercalados. De hecho, con la aleatorización garantizamos un buen rendimiento esperado de las estructuras de datos resultantes, que es independiente de la distribución de los datos de entrada, conservando la flexibilidad y la simplicidad de los árboles $K$-dimensionales y de los árboles cuaternarios estándar. También proponemos los árboles multidimensionales con punteros de referencia, una técnica que permite que las estructuras de datos multidimensionales exploten la localidad de referencia en búsquedas asociativas que se presentan altamente correlacionadas.Con respecto al análisis de estructuras de datos multidimensionales, comenzamos dando un análisis preciso del costo esperado de las búsquedas parciales en los árboles $K$-dimensionales relajados. A continuación, utilizamos este resultado como base para el análisis de las búsquedas por rangos ortogonales, combinándolo con argumentos combinatorios y geométricos. Como resultado obtenemos un estimado asintótico preciso del costo de las búsquedas por rango en los árboles $K$-dimensionales relajados. Finalmente, mostramos que las técnicas utilizadas pueden extenderse fácilmente a otras estructuras de datos y por tanto proporcionamos un análisis preciso del costo promedio de búsquedas por rango en estructuras de datos como los árboles $K$-dimensionales estándar, los árboles cuaternarios, los tries cuaternarios y los tries $K$-dimensionales. / This thesis is about the design and analysis of point multidimensional data structures: data structures that store $K$-dimensional keys which we may abstract as points in $[0,1]^K$. These data structures are present in many applications of geographical information systems, image processing or robotics, among others. They are also frequently used as indexes of more complex data structures, possibly stored in external memory.Point multidimensional data structures must have capabilities such as insertion, deletion and (exact) search of items, but in addition they must support the so called {em associative queries}. Examples of these queries are orthogonal range queries (which are the items that fall inside a given hyper-rectangle?) and nearest neighbour queries (which is the closest item to some given point?).The contributions of this thesis are two-fold:Contributions to the design of point multidimensional data structures: the design of randomized $K$-d trees, the design of randomized quad trees and the design of fingered multidimensional search trees;Contributions to the analysis of the performance of point multidimensional data structures: the average-case analysis of partial match queries in relaxed $K$-d trees and the average-case analysis of orthogonal range queries in various multidimensional data structures.Concerning the design of randomized point multidimensional data structures, we propose randomized insertion and deletion algorithms for $K$-d trees and quad trees that produce random $K$-d trees and quad trees independently of the order in which items are inserted into them and after any sequence of interleaved insertions and deletions. The use of randomization provides expected performance guarantees, irrespective of any assumption on the data distribution, while retaining the simplicity and flexibility of standard $K$-d trees and quad trees.Also related to the design of point multidimensional data structures is the proposal of fingered multidimensional search trees, a new technique that enhances point multidimensional data structures to exploit locality of reference in associative queries.With regards to performance analysis, we start by giving a precise analysis of the cost of partial matches in randomized $K$-d trees. We use these results as a building block in our analysis of orthogonal range queries, together with combinatorial and geometric arguments and we provide a tight asymptotic estimate of the cost of orthogonal range search in randomized $K$-d trees. We finally show that the techniques used apply easily to other data structures, so we can provide an analysis of the average cost of orthogonal range search in other data structures such as standard $K$-d trees, quad trees, quad tries, and $K$-d tries.

Les schémas de subdivision et les schémas de subdivision inverse sont largement utilisés en informatiquegraphique; les uns pour lisser des objets 3D, et les autres pour minimiser le coût d'encodagede l'information. Ce sont les deux aspects abordés dans cette thèse.Les travaux présentés dans le cadre de la subdivision décrivent l'études et la construction d'un nouveautype de schémas de subdivision. Celui-ci unifie deux schémas de subdivision de type géométriquesdifférents. Cela permet de modéliser des objets 3D composés de zones issues de l'applicationd'un schéma approximant et de zones issues de l'application d'un schéma interpolant. Dans le cadrede la subdivision inverse, Nous présentons une méthode de construction des schémas de subdivisionbi-réguliers inverses (quadrilatères et triangles)