The Islamic Crossed-Arch Domes in Cordoba: Geometry and Structural Analysis of the “Capilla de Villaviciosa”

Crossed-arch domes are a singular type of ribbed vaults. Their characteristic feature is that the ribs that form the vault are intertwined, forming polygons or stars, leaving an empty space in the centre. The earliest known vaults of this type are found in the Great Mosque of Córdoba, built ca. 960 a.C. The type spread through Spain, and the north of Africa in the 10th to the 16th Centuries, and was used by Guarini and Vittone in the 17th and 18th Centuries in Italy. However, it was used only in a few buildings. Though the literature about the structural behaviour of ribbed Gothic vaults is extensive, so far no structural analysis of crossed arch domes has been made. The purpose of this work is, first to show the way to attack such an analysis within the frame of Modern Limit Analysis of Masonry Structures (Heyman 1995), and then to apply the approach to study the stability of the dome of the Capilla de Villaviciosa. The work may give some clues to art and architectural historians to understand better the origin and development of Islamic dome architecture.

The Ciborium or Lantern Tower of Valencia Cathedral: Geometry, Construction and Stability

Early 18th century treatise writer Tomas Vicente Tosca1 includes in his Tratado de la montea y cortes de Canteria [On Masonry Design and Stone Cutting], what is an important documentary source about the lantern of Valencia Cathedral. Tosca writes about this lantern as an example of vaulting over cross arches without the need of buttresses. A geometrical description is followed by an explanation of the structural behavior which manifests his deep understanding of the mechanics of masonry structures. He tries to demonstrate the absence of buttresses supporting his thesis on the appropriate distribution of loads which will reduce the "empujos" [horizontal thrusts] to the point of not requiring more than the thickness of the walls to stand (Tosca [1727] 1992, 227-230). The present article2 assesses T osca' s appreciation studying how loads and the thrusts they generate are transmitted through the different masonry elements that constitute this ciborium. In order to do so, we first present a geometrical analysis and make considerations regarding its materials and construction methods to, subsequently, analyze its stability adopting an equilibrium approach within the theoretical framework of the lower bound limit analysis.

The Ciborium or Lantern Tower of Valencia Cathedral: Geometry, Construction and Stability

Early 18th century treatise writer Tomas Vicente Tosca1 includes in his Tratado de la montea y cortes de Canteria [On Masonry Design and Stone Cutting], what is an important documentary source about the lantern of Valencia Cathedral. Tosca writes about this lantern as an example of vaulting over cross arches without the need of buttresses. A geometrical description is followed by an explanation of the structural behavior which manifests his deep understanding of the mechanics of masonry structures. He tries to demonstrate the absence of buttresses supporting his thesis on the appropriate distribution of loads which will reduce the "empujos" [horizontal thrusts] to the point of not requiring more than the thickness of the walls to stand (Tosca [1727] 1992, 227-230). The present article2 assesses T osca' s appreciation studying how loads and the thrusts they generate are transmitted through the different masonry elements that constitute this ciborium. In order to do so, we first present a geometrical analysis and make considerations regarding its materials and construction methods to, subsequently, analyze its stability adopting an equilibrium approach within the theoretical framework of the lower bound limit analysis.

Unconstrained and Contactless Hand Geometry Biometrics

This paper presents a hand biometric system for contact-less, platform-free scenarios, proposing innovative methods in feature extraction, template creation and template matching. The evaluation of the proposed method considers both the use of three contact-less publicly available hand databases, and the comparison of the performance to two competitive pattern recognition techniques existing in literature: namely Support Vector Machines (SVM) and k-Nearest Neighbour (k-NN). Results highlight the fact that the proposed method outcomes existing approaches in literature in terms of computational cost, accuracy in human identification, number of extracted features and number of samples for template creation. The proposed method is a suitable solution for human identification in contact-less scenarios based on hand biometrics, providing a feasible solution to devices with limited hardware requirements like mobile devices

Monte-Carlo dosimetry on a realistic cell monolayer geometry exposed to alpha particles

The energy and specific energy absorbed in the main cell compartments (nucleus and cytoplasm) in typical radiobiology experiments are usually estimated by calculations as they are not accessible for a direct measurement. In most of the work, the cell geometry is modelled using the combination of simple mathematical volumes. We propose a method based on high resolution confocal imaging and ion beam analysis (IBA) in order to import realistic cell nuclei geometries in Monte-Carlo simulations and thus take into account the variety of different geometries encountered in a typical cell population. Seventy-six cell nuclei have been imaged using confocal microscopy and their chemical composition has been measured using IBA. A cellular phantom was created from these data using the ImageJ image analysis software and imported in the Geant4 Monte-Carlo simulation toolkit. Total energy and specific energy distributions in the 76 cell nuclei have been calculated for two types of irradiation protocols: a 3 MeV alpha particle microbeam used for targeted irradiation and a 239Pu alpha source used for large angle random irradiation. Qualitative images of the energy deposited along the particle tracks have been produced and show good agreement with images of DNA double strand break signalling proteins obtained experimentally. The methodology presented in this paper provides microdosimetric quantities calculated from realistic cellular volumes. It is based on open-source oriented software that is publicly available.

Design, implementation and evaluation of an unconstrained and contactless biometric system based on hand geometry and stress detection

Esta tesis propone un sistema biométrico de geometría de mano orientado a entornos sin contacto junto con un sistema de detección de estrés capaz de decir qué grado de estrés tiene una determinada persona en base a señales fisiológicas Con respecto al sistema biométrico, esta tesis contribuye con el diseño y la implementación de un sistema biométrico de geometría de mano, donde la adquisición se realiza sin ningún tipo de contacto, y el patrón del usuario se crea considerando únicamente datos del propio individuo. Además, esta tesis propone un algoritmo de segmentación multiescala para solucionar los problemas que conlleva la adquisición de manos en entornos reales. Por otro lado, respecto a la extracción de características y su posterior comparación esta tesis tiene una contribución específica, proponiendo esquemas adecuados para llevar a cabo tales tareas con un coste computacional bajo pero con una alta precisión en el reconocimiento de personas. Por último, este sistema es evaluado acorde a la norma estándar ISO/IEC 19795 considerando seis bases de datos públicas. En relación al método de detección de estrés, esta tesis propone un sistema basado en dos señales fisiológicas, concretamente la tasa cardiaca y la conductancia de la piel, así como la creación de un innovador patrón de estrés que recoge el comportamiento de ambas señales bajo las situaciones de estrés y no-estrés. Además, este sistema está basado en lógica difusa para decidir el grado de estrés de un individuo. En general, este sistema es capaz de detectar estrés de forma precisa y en tiempo real, proporcionando una solución adecuada para sistemas biométricos actuales, donde la aplicación del sistema de detección de estrés es directa para evitar situaciónes donde los individuos sean forzados a proporcionar sus datos biométricos. Finalmente, esta tesis incluye un estudio de aceptabilidad del usuario, donde se evalúa cuál es la aceptación del usuario con respecto a la técnica biométrica propuesta por un total de 250 usuarios. Además se incluye un prototipo implementado en un dispositivo móvil y su evaluación. ABSTRACT: This thesis proposes a hand biometric system oriented to unconstrained and contactless scenarios together with a stress detection method able to elucidate to what extent an individual is under stress based on physiological signals. Concerning the biometric system, this thesis contributes with the design and implementation of a hand-based biometric system, where the acquisition is carried out without contact and the template is created only requiring information from a single individual. In addition, this thesis proposes an algorithm based on multiscale aggregation in order to tackle with the problem of segmentation in real unconstrained environments. Furthermore, feature extraction and matching are also a specific contributions of this thesis, providing adequate schemes to carry out both actions with low computational cost but with certain recognition accuracy. Finally, this system is evaluated according to international standard ISO/IEC 19795 considering six public databases. In relation to the stress detection method, this thesis proposes a system based on two physiological signals, namely heart rate and galvanic skin response, with the creation of an innovative stress detection template which gathers the behaviour of both physiological signals under both stressing and non-stressing situations. Besides, this system is based on fuzzy logic to elucidate the level of stress of an individual. As an overview, this system is able to detect stress accurately and in real-time, providing an adequate solution for current biometric systems, where the application of a stress detection system is direct to avoid situations where individuals are forced to provide the biometric data. Finally, this thesis includes a user acceptability evaluation, where the acceptance of the proposed biometric technique is assessed by a total of 250 individuals. In addition, this thesis includes a mobile implementation prototype and its evaluation.

Influence of loudspeaker directivity and measurement geometry on direct acoustic levels over façades for acoustic insulation tests with the International Standard ISO 140-5

The International Standard ISO 140-5 on field measurements of airborne sound insulation of façades establishes that the directivity of the measurement loudspeaker should be such that the variation in the local direct sound pressure level (ΔSPL) on the sample is ΔSPL < 5 dB (or ΔSPL < 10 dB for large façades). This condition is usually not very easy to accomplish nor is it easy to verify whether the loudspeaker produces such a uniform level. Direct sound pressure levels on the ISO standard façade essentially depend on the distance and directivity of the loudspeaker used. This paper presents a comprehensive analysis of the test geometry for measuring sound insulation and explains how the loudspeaker directivity, combined with distance, affects the acoustic level distribution on the façade. The first sections of the paper are focused on analysing the measurement geometry and its influence on the direct acoustic level variations on the façade. The most favourable and least favourable positions to minimise these direct acoustic level differences are found, and the angles covered by the façade in the reference system of the loudspeaker are also determined. Then, the maximum dimensions of the façade that meet the conditions of the ISO 140-5 standard are obtained for the ideal omnidirectional sound source and the piston radiating in an infinite baffle, which is chosen as the typical radiation pattern for loudspeakers. Finally, a complete study of the behaviour of different loudspeaker radiation models (such as those usually utilised in the ISO 140-5 measurements) is performed, comparing their radiation maps on the façade for searching their maximum dimensions and the most appropriate radiation configurations.

Analysis of the performance of caissons with a yard and cylindrical geometry as a breakwater. Apollonius caisson

En el presente trabajo se analiza el cajón Apolonio como diseño conceptual para controlar la reflexión en monolitos de gravedad sometidos a esfuerzos dinámicos de oleaje.

Mathematical Analysis of the Effect of Rotor Geometry on Cup Anemometer Response

The calibration coefficients of two commercial anemometers equipped with different rotors were studied. The rotor cups had the same conical shape, while the size and distance to the rotation axis varied.The analysis was based on the 2-cup positions analytical model, derived using perturbation methods to include second-order effects such as pressure distribution along the rotating cups and friction.Thecomparison with the experimental data indicates a nonuniformdistribution of aerodynamic forces on the rotating cups, with higher forces closer to the rotating axis. The 2-cup analytical model is proven to be accurate enough to study the effect of complex forces on cup anemometer performance.

Optimal boundary geometry in an elasticity problem: a systematic adjoint approach

In different problems of Elasticity the definition of the optimal gcometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables. Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

NURBS-Based Geometry Parameterization for Aerodynamic Shape Optimization

La motivación de esta tesis es el desarrollo de una herramienta de optimización automática para la mejora del rendimiento de formas aerodinámicas enfocado en la industria aeronáutica. Este trabajo cubre varios aspectos esenciales, desde el empleo de Non-Uniform Rational B-Splines (NURBS), al cálculo de gradientes utilizando la metodología del adjunto continuo, el uso de b-splines volumétricas como parámetros de diseño, el tratamiento de la malla en las intersecciones, y no menos importante, la adaptación de los algoritmos de la dinámica de fluidos computacional (CFD) en arquitecturas hardware de alto paralelismo, como las tarjetas gráficas, para acelerar el proceso de optimización. La metodología adjunta ha posibilitado que los métodos de optimización basados en gradientes sean una alternativa prometedora para la mejora de la eficiencia aerodinámica de los aviones. La formulación del adjunto permite calcular los gradientes de una función de coste, como la resistencia aerodinámica o la sustentación, independientemente del número de variables de diseño, a un coste computacional equivalente a una simulación CFD. Sin embargo, existen problemas prácticos que han imposibilitado su aplicación en la industria, que se pueden resumir en: integrabilidad, rendimiento computacional y robustez de la solución adjunta. Este trabajo aborda estas contrariedades y las analiza en casos prácticos. Como resumen, las contribuciones de esta tesis son: • El uso de NURBS como variables de diseño en un bucle de automático de optimización, aplicado a la mejora del rendimiento aerodinámico de alas en régimen transónico. • El desarrollo de algoritmos de inversión de punto, para calcular las coordenadas paramétricas de las coordenadas espaciales, para ligar los vértices de malla a las NURBS. • El uso y validación de la formulación adjunta para el calculo de los gradientes, a partir de las sensibilidades de la solución adjunta, comparado con diferencias finitas. • Se ofrece una estrategia para utilizar la geometría CAD, en forma de parches NURBS, para tratar las intersecciones, como el ala-fuselaje. • No existen muchas alternativas de librerías NURBS viables. En este trabajo se ha desarrollado una librería, DOMINO NURBS, y se ofrece a la comunidad como código libre y abierto. • También se ha implementado un código CFD en tarjeta gráfica, para realizar una valoración de cómo se puede adaptar un código sobre malla no estructurada a arquitecturas paralelas. • Finalmente, se propone una metodología, basada en la función de Green, como una forma eficiente de paralelizar simulaciones numéricas. Esta tesis ha sido apoyada por las actividades realizadas por el Área de Dinámica da Fluidos del Instituto Nacional de Técnica Aeroespacial (INTA), a través de numerosos proyectos de financiación nacional: DOMINO, SIMUMAT, y CORESFMULAERO. También ha estado en consonancia con las actividades realizadas por el departamento de Métodos y Herramientas de Airbus España y con el grupo Investigación y Tecnología Aeronáutica Europeo (GARTEUR), AG/52. ABSTRACT The motivation of this work is the development of an automatic optimization strategy for large scale shape optimization problems that arise in the aeronautics industry to improve the aerodynamic performance; covering several aspects from the use of Non-Uniform Rational B-Splines (NURBS), the calculation of the gradients with the continuous adjoint formulation, the development of volumetric b-splines parameterization, mesh adaptation and intersection handling, to the adaptation of Computational Fluid Dynamics (CFD) algorithms to take advantage of highly parallel architectures in order to speed up the optimization process. With the development of the adjoint formulation, gradient-based methods for aerodynamic optimization become a promising approach to improve the aerodynamic performance of aircraft designs. The adjoint methodology allows the evaluation the gradients to all design variables of a cost function, such as drag or lift, at the equivalent cost of more or less one CFD simulation. However, some practical problems have been delaying its full implementation to the industry, which can be summarized as: integrability, computer performance, and adjoint robustness. This work tackles some of these issues and analyse them in well-known test cases. As summary, the contributions comprises: • The employment of NURBS as design variables in an automatic optimization loop for the improvement of the aerodynamic performance of aircraft wings in transonic regimen. • The development of point inversion algorithms to calculate the NURBS parametric coordinates from the space coordinates, to link with the computational grid vertex. • The use and validation of the adjoint formulation to calculate the gradients from the surface sensitivities in an automatic optimization loop and evaluate its reliability, compared with finite differences. • This work proposes some algorithms that take advantage of the underlying CAD geometry description, in the form of NURBS patches, to handle intersections and mesh adaptations. • There are not many usable libraries for NURBS available. In this work an open source library DOMINO NURBS has been developed and is offered to the community as free, open source code. • The implementation of a transonic CFD solver from scratch in a graphic card, for an assessment of the implementability of conventional CFD solvers for unstructured grids to highly parallel architectures. • Finally, this research proposes the use of the Green's function as an efficient paralellization scheme of numerical solvers. The presented work has been supported by the activities carried out at the Fluid Dynamics branch of the National Institute for Aerospace Technology (INTA) through national founding research projects: DOMINO, SIMUMAT, and CORESIMULAERO; in line with the activities carried out by the Methods and Tools and Flight Physics department at Airbus and the Group for Aeronautical Research and Technology in Europe (GARTEUR) action group AG/52.

Feo, inútil, inestable: pensamiento crítico contemporáneo y procesos proyectivos en arquitectura = Ugly, useless, unstable: contemporary critical thought and projective processes in architecture

La presente tesis doctoral persigue dos objetivos simultáneos: Determinar el alcance de los criterios clásicos para la evaluación de arquitectura y poner en crisis la prevalencia de esos mismos criterios dentro del marco crítico y productivo actual. En concreto, esta tesis se interroga sobre la posible contribución de determinadas corrientes del pensamiento post-estructuralista y neo-materialista a las tareas de expansión y transformación de los criterios clásicos antes mencionados. Asimismo, se plantea la oportunidad de formalizar estas incorporaciones conceptuales como metodologías para el proyectar arquitectónico. La tesis emplea un análisis pormenorizado de las cualidades implícitas en la triada Firmitas, Utilitas, Venustas elaborada por Vitruvio como vehículo para calibrar la influencia de los paradigmas de pensamiento clásico en nuestras posiciones críticas contemporáneas. Como reacción al carácter dominante de dichos paradigmas, y con la ayuda de una compilación selectiva de ejemplos procedentes de los campos artístico y arquitectónico, la presente tesis procede a examinar y clasificar diversas estrategias arquitectónicas basadas en la no conformidad con los criterios clásicos de evaluación de la disciplina. A la hora de realizar esta tarea, y con el objetivo de superar el dualismo trascendental que caracteriza la gran mayoría de dichos criterios clásicos, se propone un modelo analítico y multidimensional que formula las instancias arquitectónicas como posibles posiciones dentro de un extenso continuo combinatorio de cualidades formales, estructurales y organizativas. Este modelo conceptual permite replantear el aparente antagonismo entre los principios de Vitruvio y sus opuestos, estableciendo en su lugar un dominio operativo continuo de producción arquitectónica. Esta operación abre una ventana de oportunidad para expandir los límites del marco crítico actual más allá de las fronteras establecidas por nuestra herencia clásica. En consecuencia con esta voluntad, la presente tesis pretende habilitar un ámbito para el análisis crítico de las estrategias que caracterizan ciertas corrientes del proyectar contemporáneo, pero también contribuir a informar nuevas aproximaciones metodológicas al proceso de proyecto, desplazando progresivamente su foco desde lo descriptivo hacia lo proyectivo. ABSTRACT This doctoral thesis attempts to simultaneously determine the scope of the classical criteria for the evaluation of architecture and challenge their prevalence within the current framework of architectural production and criticism. It examines how specific strands of post-structuralism and neo-materialism may contribute to both the expansion and the transformation of these criteria and, in doing so, sets itself the goal of mobilising these conceptual incorporations as explicit design methodologies. A detailed analysis of the formal, structural and organisational qualities implicit in Vitruvius’ triad Firmitas, Utilitas, Venustas is used as a starting point to determine the influence of classical paradigms in our current critical positions. As a reaction to this critical pervasiveness, and supported by a curated collection of artistic and architectural works, diverse approaches to non-compliance with the classical criteria of assessment are examined and classified. In order to facilitate this endeavour -and to overcome the transcendental dualism of most classical critical approaches in architecture- this thesis puts forward an analytical, multidimensional model that formulates architectural instances as possible positions within a larger combinatory continuum of formal, structural and organisational qualities. Using this conceptual model, the apparent antagonism between Vitruvius’ principles and its non-compliant opposites is reframed as a continuous operative domain of architectural production, which in turn opens up a window of opportunity to expand the limits of our critical framework beyond the boundaries of classical paradigms. In doing so, this thesis attempts not only to foster a better understanding of some of the strategic approaches that characterise contemporary systems of architectural production, but also to inform future methodological approaches to architectural design, hence situating itself beyond the domain of the descriptive and moving towards the projective.

Tridimensional simulation of the speed, pressure and turbulence fields of the air flow on the geometry of a freight truck inside a wind tunnel

This study shows the air flow behavior through the geometry of a freight truck inside a AF6109 wind tunnel with the purpose to predict the speed, pressure and turbulence fields made by the air flow, to decrease the aerodynamic resistance, to calculate the dragging coefficient, to evaluate the aerodynamics of the geometry of the prototype using the CFD technique and to compare the results of the simulation with the results obtained experimentally with the “PETER 739 HAULER” scaled freight truck model located on the floor of the test chamber. The Geometry went through a numerical simulation process using the CFX 5,7. The obtained results showed the behavior of the air flow through the test chamber, and also it showed the variations of speed and pressure at the exit of the chamber and the calculations of the coefficient and the dragging force on the geometry of the freight truck. The evaluation of the aerodynamics showed that the aerodynamic deflector is a device that helped the reduction the dragging produced in a significant way by the air. Furthermore, the dragging coefficient and force on the prototype freight truck could be estimated establishing an incomplete similarity.

Calibración geométrica de cámaras no métricas. Estudio de metodologías y modelos matemáticos de distorsión

La Fotogrametría, como ciencia y técnica de obtención de información tridimensional del espacio objeto a partir de imágenes bidimensionales, requiere de medidas de precisión y en ese contexto, la calibración geométrica de cámaras ocupa un lugar importante. El conocimiento de la geometría interna de la cámara es fundamental para lograr mayor precisión en las medidas realizadas. En Fotogrametría Aérea se utilizan cámaras métricas (fabricadas exclusivamente para aplicaciones cartográficas), que incluyen objetivos fotográficos con sistemas de lentes complejos y de alta calidad. Pero en Fotogrametría de Objeto Cercano se está trabajando cada vez con más asiduidad con cámaras no métricas, con ópticas de peor calidad que exigen una calibración geométrica antes o después de cada trabajo. El proceso de calibración encierra tres conceptos fundamentales: modelo de cámara, modelo de distorsión y método de calibración. El modelo de cámara es un modelo matemático que aproxima la transformación proyectiva original a la realidad física de las lentes. Ese modelo matemático incluye una serie de parámetros entre los que se encuentran los correspondientes al modelo de distorsión, que se encarga de corregir los errores sistemáticos de la imagen. Finalmente, el método de calibración propone el método de estimación de los parámetros del modelo matemático y la técnica de optimización a emplear. En esta Tesis se propone la utilización de un patrón de calibración bidimensional que se desplaza en la dirección del eje óptico de la cámara, ofreciendo así tridimensionalidad a la escena fotografiada. El patrón incluye un número elevado de marcas, lo que permite realizar ensayos con distintas configuraciones geométricas. Tomando el modelo de proyección perspectiva (o pinhole) como modelo de cámara, se realizan ensayos con tres modelos de distorsión diferentes, el clásico de distorsión radial y tangencial propuesto por D.C. Brown, una aproximación por polinomios de Legendre y una interpolación bicúbica. De la combinación de diferentes configuraciones geométricas y del modelo de distorsión más adecuado, se llega al establecimiento de una metodología de calibración óptima. Para ayudar a la elección se realiza un estudio de las precisiones obtenidas en los distintos ensayos y un control estereoscópico de un panel test construido al efecto. ABSTRACT Photogrammetry, as science and technique for obtaining three-dimensional information of the space object from two-dimensional images, requires measurements of precision and in that context, the geometric camera calibration occupies an important place. The knowledge of the internal geometry of the camera is fundamental to achieve greater precision in measurements made. Metric cameras (manufactured exclusively for cartographic applications), including photographic lenses with complex lenses and high quality systems are used in Aerial Photogrammetry. But in Close Range Photogrammetry is working increasingly more frequently with non-metric cameras, worst quality optical components which require a geometric calibration before or after each job. The calibration process contains three fundamental concepts: camera model, distortion model and method of calibration. The camera model is a mathematical model that approximates the original projective transformation to the physical reality of the lenses. The mathematical model includes a series of parameters which include the correspondents to the model of distortion, which is in charge of correcting the systematic errors of the image. Finally, the calibration method proposes the method of estimation of the parameters of the mathematical modeling and optimization technique to employ. This Thesis is proposing the use of a pattern of two dimensional calibration that moves in the direction of the optical axis of the camera, thus offering three-dimensionality to the photographed scene. The pattern includes a large number of marks, which allows testing with different geometric configurations. Taking the projection model perspective (or pinhole) as a model of camera, tests are performed with three different models of distortion, the classical of distortion radial and tangential proposed by D.C. Brown, an approximation by Legendre polynomials and bicubic interpolation. From the combination of different geometric configurations and the most suitable distortion model, brings the establishment of a methodology for optimal calibration. To help the election, a study of the information obtained in the various tests and a purpose built test panel stereoscopic control is performed.