Capilla del M.I.T. de Eero Saarinen, 1950-55 : sincretismo en la armonía de los opuestos

La historia de la arquitectura se ha medido - en parte - por la evolución de las modas, épocas y estilos de la arquitectura religiosa. En la aparición de las nuevas capillas interreligiosas universitarias de los años '50 de Norteamérica, la capilla del M.I.T., bautizada tras su inauguración como “Kresge Chapel” en honor al apellido de su benefactor, fue el máximo exponente como prototipo en esta época marcada por la aparición nuevas conciencias de posguerra. (II Guerra Mundial). La tesis centra su investigación en esta capilla, cómo nació en respuesta a la necesidad de compatibilizar la enseñanza reglada científico tecnológica con una formación religiosa y humanista, para el programa impuesto como ampliación del campus universitario del MIT en el barrio universitario de Cambridge, Boston, Massachussets, en torno a dos edificios principales a proyectar: capilla y auditorio. Desde el trabajo de investigación se aporta la información documental necesaria para saber cómo evolucionó desde sus primeros bocetos hasta su construcción. Su nacimiento como necesidad en la sociedad universitaria no fue nada espontáneo, quedando a medias entre la influencia escandinavo - alemana y la tradición americano-luterana de anteriores iglesias neoclásicas herederas del “Plan Akron”. La formación académica y profesional dirigida por su padre, Eliel Saarinen, suman junto a los viajes del arquitecto, una herencia “genética” para con este prototipo ajeno al emergente “estilo internacional” y ayudan a comprender la dimensión compleja de lo que es capaz de representar la capilla. La capilla es refugio emocional de la luz y es un punto de inflexión notable en la recuperación del tipo centrado renovado y evolucionado, que junto con el doble recurso lumínico - efectista, de la vertical para el altar y horizontal inferior, distribuido desde el perímetro ondulado en el interior, el ejemplo es muestra la promoción de una cierta sensibilidad para con las nuevas formas de la "religión" emergentes en la Norteamérica de los años 50. Desde el sincretismo como mecanismo y principal “modus operandi” proyectual, FE versus RAZÓN, aparecen como dualismo permanente en todas las fases del proyecto, desde un proceso de búsqueda de la armonía de ambos y para cada uno de ellos. Con el estudio del modelo prototípico del MIT, buscamos el "patrón" empleado por el arquitecto en su proyección de "nueva iglesia" adaptado a la diversidad cultural y religiosa y de las nuevas y diferentes sensibilidades humanistas para el proyecto. ----------------------------------------------------- SUMMARY--------------------------------------------------- The history of architecture is measured - in part - by the evolution of fashion, periods and styles of religious architecture. In the emergence of the new interfaith university chapel of the 1950s in North America, the chapel of MIT, named after its inauguration as "Kresge Chapel" in honor of its benefactor, was the best example of a prototype, in this time so marked by the emergence of new postwar consciousnesses. The thesis focuses its research on this chapel; how it came about in response to the need to reconcile formal scientific and technological education with religious and humanist training for the program imposed as an extension of the campus of MIT in the university district of Cambridge, Boston Massachusetts, around two main projected buildings : Chapel and auditorium. From research work has been obtained the documentary information necessary to know how it evolved from the first sketches to its construction. Its creation as a necessity of the university society was not at all spontaneous, being halfway between the Scandinavian influence - German and the American Lutheran tradition of neoclassical churches, the heirs to the "Akron Plan". The academic and professional training directed by his father, Eliel Saarinen, together with the travels of the architect, a "genetic" heritage with this external prototype for the emerging "international style", and help to understand the complex dimension of what the chapel is capable of representing. The chapel is an emotional refuge of light and is a remarkable turning point in the recovery of such focused renewed and evolved, along with the double lumen resource - gimmicky, vertical to the altar and lower horizontal, distributed from the undulating perimeter inside, the example is shown to promote a certain sensitivity to the new forms of "religion" but vague religious profile emerging in the America of the 50s. From the syncretism as a mechanism and main "modus operandi" of the project, FAITH versus REASON appears as permanent dualism in all phases of the project from a process of finding the harmony of both and for each of them. With the study of the prototypical model of MIT, we seek the "pattern" used by the architect in his projection of "new church" adapted to the cultural and religious diversity and new and different humanist sensitivities for the project. El desarrollo vierte la luz suficiente para entender los patrones de lo arquitectónico en la capilla, que hacen de ella, la comunión armónica y perfecta de los nombrados opuestos en el campus universitario del MIT. En el camino, además, la investigación arroja luz y orden sobre las fases del proyecto a través de la contribución, recogida, clasificación y orden de los datos, fechas y documentos gráficos, a día de hoy dispersos y confusamente publicados, debido a la no existencia de un estudio profundo y completo como el que pretende ser este trabajo, por ser una obra fundamental en la historia de la arquitectura moderna. El patrón final demostrará el artificio sincrético de cada una de las partes - cada uno en sí misma y cosidas todas - formando el "Ima Summis" de la capilla; resultado de la acción proyectual deducida de su serie genética descifrada. De esta forma, lo sincrético, aparece como el principal atributo del hecho construido, pasando de lo místico a lo científico, de lo intuitivo a lo razonado y siempre con el vehículo de su arquitectura para la interpretación de lo inefable al interior. En cuanto a la estructura de la tesis, se inicia el desarrollo a partir de una introducción en la que se declaran las intenciones y se describe el contexto de lo investigado en torno a la hipótesis principal anunciada en el subtítulo de la tesis. Frente a consideraciones previas de la capilla y de la propia investigación, se expone y explica la hipótesis principal, junto a otros objetivos secundarios. Para finalizar la introducción, se describe el método seguido como estrategia y se justifica la estructura de redacción del documento para la compresión de este trabajo hacia sus conclusiones. Es en el primer capítulo, el C1, donde se inicia el cuerpo central mediante la exposición historiográfica de la situación y contexto previo a la capilla como antecedentes. En un segundo capítulo, el C2, se aborda el estudio del desarrollo del proyecto y de la obra y construcción de la capilla, base documental necesaria. Para ello se inicia con la descripción del lugar, del encargo y del programa, para pasar a mostrar con detalle las distintas propuestas de cada una de las fases del proyecto. En definitiva, qué se proyecto, cómo evolucionó el proyecto y en qué fases transcurrió, para entre otras cuestiones, entender el cambio de estilo desde una fase influenciada por la capilla de Mies construida en el ITT de Chicago, (denominadas en este trabajo por esta influencia como modelos “miesianos”) y la fase reencuentro con el modus de hacer iniciado por su padre Eliel, a través de un modelo a medias de una herencia escandinavo - alemana y la tradición luterano - americana, (denominada en este trabajo como herencia o modelos “saariniana/os”). The development sheds enough light to understand the architectural patterns of the chapel, making it the perfect and harmonic communion named opposites on the campus of MIT. Along the way, furthermore, the research sheds light and order on the phases of the project through the contribution, collection, sorting and order of data, dates and graphic documents, today scattered and confusingly published, due to inexistence of a deep and comprehensive study like this work is meant to be, in the context of such a seminal work in the history of modern architecture. The final pattern will demonstrate the syncretic artifice of each of the parts - each in itself and all together - forming the "Ima Summis" of the chapel; the result of the project action deducted from its deciphered genetic series. Being the SYNCRETIC, the main attribute of the built matter, passing from the mystical to the scientific, from the intuitive to the reasoned and always with the vehicle of architecture as the representation of the ineffable. As for the structure of the thesis, the development starts from an introduction in which the intentions are declared and the context of that which is investigated is described, in terms of the main hypothesis announced in the subtitle of the thesis. Faced with previous considerations of the chapel and the research itself, the principal hypothesis is expressed and explained, along with other secondary objectives. To conclude the introduction, the method followed is described as a strategy and the structuring of the document is justified for the compression of this work towards its conclusions. It is in the first chapter of the thesis, the C1, where the main body of the work is initiated through the historiographical account of the situation and context prior to the chapel as antecedents. A second chapter, C2, addresses the study of the development of the project and of the work and construction of the chapel, based on the necessary documentary evidence. To this end, the analysis begins with the description of the place, the commission and the program, moving on to analyze in detail the various proposals of each phase. What is projected, how it evolved and through what phases passed the project to, among other questions, understand the change in style between the phase of influence of Mies through the projected chapel in the ITT of Chicago chapel (called in this work as "miesian" influences or models) and the reunion with the modus of making initiated by his father Eliel, through a model equally at once of Scandinavian-German heritage and of the American-Lutheran tradition, (referred to in this work as "saarinian" inheritance or models). Para el tercer capítulo, el C3, se llevan a estudio y análisis, los elementos más destacables en los que se prueban las particularidades llamadas “genéticas” en cada uno de las partes principales detectadas en la capilla. Desde ellas se rastrean las influencias - a veces sinergias - que ayudan a justificar y conformar una clasificación genética en torno a cuatro patrones principales, de los que poder discernir al final del capítulo, el “patrón matriz” de la propia capilla en base a la concurrencia de los órdenes arquitectónicos que los conforman. Una vez obtenida la información y orden necesario, se puede afrontar el punto álgido de esta tesis con el cuarto capítulo, el C4, en el que se justifica la capacidad sincrética de la capilla como respuesta a la hipótesis principal señalada en el subtítulo. Para ello se inicia el capítulo con el enfoque y contexto del término “sincretismo” y “sincrético”, aportando la justificación de sus usos para con esta investigación, antes de explicar que la capilla es sincrética por la suma de dos claves fundamentales. La clave primera, correspondiente a la capacidad interconfesional y aconfesional de la capilla, y su capacidad de trascender al interior desde ambas situaciones además de ser reconocible por el religioso y a la vez por el científico. Y la clave segunda, que corresponde a la suma de las distintas partes sincréticas, cada una en si mismas, capaz de sumar todas juntas, este edificio sincrético de los nombrados opuestos. Una vez discernido las claves de lo sincrético en la capilla y a pesar de su doble carácter SACRO Y PROFANO, una comparativa posiciona a la capilla como único entre los ejemplos interconfesionales construidos en los ´50, sin haberse repetido de igual manera y mismo resultado en el tiempo, ni en ninguna otra universidad o centro tecnológico. Así la exposición de este trabajo finaliza con el último capítulo, el C5, en el que desde esa comparativa, una serie de cuestiones unen y distancian a la del MIT y dan acierto a la apuesta inicial, concluyendo que la hipótesis y el patrón de la misma, es el patrón de lo sincrético que modela el ”modus operandi ” del arquitecto. Tras el desarrollo, la investigación cierra filas en torno a cuatro conclusiones para los cuatro capítulos principales; C2, C3, C4, C5. La capilla del MIT como modelo prototípico no se repite en el tiempo, ni en ninguna otra universidad y se posiciona como el mejor prototipo – hito de una nueva arquitectura religiosa universitaria. In the third chapter, C3, we study and analyze the most notable elements in which are found those particularities referred to as "genetic" in each of the principal parts, (see above C3.1.1... - C3.1.8), where these influences - sometimes synergies - are traced, helping to justify and form a classification based on four of those principals (see above C3.2), from which, at the end of this chapter may be discerned a matrix pattern, that of the chapel itself (see above. C3.3.), based on concurrent architectural orders. Once the necessary information and order is obtained, we come to the decisive point in the fourth chapter, C4, where the syncretic capacity of the chapel in response to the main hypothesis indicated in the subtitle of the thesis is justified. For this, the chapter beings with the focus and context of the terms "syncretism" and "syncretic", providing justification for their use for this research, going on to assert that the chapel is syncretic from the sum of two fundamental aspects: the first corresponds to the interfaith and non-denominational capacities of the chapel, its ability to transcend both situations and be recognizable by both the religious and the scientific. The second corresponds to the sum of the different syncretic parts, each in themselves, capable of making together a syncretic building with the opposite. Once discerned the keys to the syncretic and epic in the chapel and despite its dual character both SACRED and PROFANE, a comparatison positions the chapel as being unique among interfaith examples built in the 1950s, without being repeated in the same way and with the same result over time or in any other university or centre of technology. So, the exhibition of this work ends with the last chapter, C5, in which from that comparison a number of issues come together and to distance themselves from MIT and bear out the initial proposition, concluding that the hypothesis and its pattern, the pattern of the syncretic which models the "modus operandi" of the architect to contain the ineffable. The research closes ranks around four conclusions for the four main chapters; C2, C3, C4, and C5 The chapel of MIT as a prototypical model is not repeated in time, or any other university and is positioned as the best prototype - a landmark of a new universitary religious architecture.

Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape

A new method for fitting a series of Zernike polynomials to point clouds defined over connected domains of arbitrary shape defined within the unit circle is presented in this work. The method is based on the application of machine learning fitting techniques by constructing an extended training set in order to ensure the smooth variation of local curvature over the whole domain. Therefore this technique is best suited for fitting points corresponding to ophthalmic lenses surfaces, particularly progressive power ones, in non-regular domains. We have tested our method by fitting numerical and real surfaces reaching an accuracy of 1 micron in elevation and 0.1 D in local curvature in agreement with the customary tolerances in the ophthalmic manufacturing industry.

Stabilisation of low softening point petroleum pitch fibres by HNO3

This paper deals with the stabilisation of low softening point pitch fibres obtained from petroleum pitches using HNO3 as oxidising agent. This method presents some advantages compared with conventional methods: pitches with low softening point (SP) can be used to prepare carbon fibres (CF), the stabilisation time has been reduced, the CF yields are similar to those obtained after general methods of stabilisation, and the initial treatments to increase SP when low SP pitches are used to prepare CF, are avoided. The parent pitches were characterised by different techniques such as diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), elemental analysis and solvent extraction with toluene and quinoline. The interaction between HNO3 and the pitch fibres, as well as the changes occurring during the heat treatment, have been followed by DRIFTS.

Stabilisation of low softening point petroleum pitch fibres by iodine treatment

A method using iodine has been developed for the stabilisation of low softening point (SP) pitch fibres that avoids air stabilisation in the production of carbon fibres (CF). The interaction between iodine and petroleum pitches has been studied by following the changes in the hydrogen content, aromatic or aliphatic, during the heat treatment of iodine-treated pitch fibres. Two low SP petroleum pitches were used and the iodine-treated pitch fibres were analysed by TGA, DSC, DRIFT, XPS and SEM. The results confirm that using this novel method pitches with low SP can be used to prepare CF with two advantages, compared with conventional methods. The stabilisation time is considerably reduced and treatments to increase the SP, usually required when low SP pitches are used to prepare CF, can be avoided.

Optimizing the number of stations in arrays measurements: experimental outcomes for different array geometries and the f-k method

Array measurements have become a valuable tool for site response characterization in a non-invasive way. The array design, i.e. size, geometry and number of stations, has a great influence in the quality of the obtained results. From the previous parameters, the number of available stations uses to be the main limitation for the field experiments, because of the economical and logistical constraints that it involves. Sometimes, from the initially planned array layout, carefully designed before the fieldwork campaign, one or more stations do not work properly, modifying the prearranged geometry. Whereas other times, there is not possible to set up the desired array layout, because of the lack of stations. Therefore, for a planned array layout, the number of operative stations and their arrangement in the array become a crucial point in the acquisition stage and subsequently in the dispersion curve estimation. In this paper we carry out an experimental work to analyze which is the minimum number of stations that would provide reliable dispersion curves for three prearranged array configurations (triangular, circular with central station and polygonal geometries). For the optimization study, we analyze together the theoretical array responses and the experimental dispersion curves obtained through the f-k method. In the case of the f-k method, we compare the dispersion curves obtained for the original or prearranged arrays with the ones obtained for the modified arrays, i.e. the dispersion curves obtained when a certain number of stations n is removed, each time, from the original layout of X geophones. The comparison is evaluated by means of a misfit function, which helps us to determine how constrained are the studied geometries by stations removing and which station or combination of stations affect more to the array capability when they are not available. All this information might be crucial to improve future array designs, determining when it is possible to optimize the number of arranged stations without losing the reliability of the obtained results.

A new approach for semi-automatic rock mass joints recognition from 3D point clouds

Rock mass characterization requires a deep geometric understanding of the discontinuity sets affecting rock exposures. Recent advances in Light Detection and Ranging (LiDAR) instrumentation currently allow quick and accurate 3D data acquisition, yielding on the development of new methodologies for the automatic characterization of rock mass discontinuities. This paper presents a methodology for the identification and analysis of flat surfaces outcropping in a rocky slope using the 3D data obtained with LiDAR. This method identifies and defines the algebraic equations of the different planes of the rock slope surface by applying an analysis based on a neighbouring points coplanarity test, finding principal orientations by Kernel Density Estimation and identifying clusters by the Density-Based Scan Algorithm with Noise. Different sources of information —synthetic and 3D scanned data— were employed, performing a complete sensitivity analysis of the parameters in order to identify the optimal value of the variables of the proposed method. In addition, raw source files and obtained results are freely provided in order to allow to a more straightforward method comparison aiming to a more reproducible research.

Geometric 3D point cloud compression

The use of 3D data in mobile robotics applications provides valuable information about the robot’s environment but usually the huge amount of 3D information is unmanageable by the robot storage and computing capabilities. A data compression is necessary to store and manage this information but preserving as much information as possible. In this paper, we propose a 3D lossy compression system based on plane extraction which represent the points of each scene plane as a Delaunay triangulation and a set of points/area information. The compression system can be customized to achieve different data compression or accuracy ratios. It also supports a color segmentation stage to preserve original scene color information and provides a realistic scene reconstruction. The design of the method provides a fast scene reconstruction useful for further visualization or processing tasks.

Discontinuity spacing analysis in rock masses using 3D point clouds

The complete characterization of rock masses implies the acquisition of information of both, the materials which compose the rock mass and the discontinuities which divide the outcrop. Recent advances in the use of remote sensing techniques – such as Light Detection and Ranging (LiDAR) – allow the accurate and dense acquisition of 3D information that can be used for the characterization of discontinuities. This work presents a novel methodology which allows the calculation of the normal spacing of persistent and non-persistent discontinuity sets using 3D point cloud datasets considering the three dimensional relationships between clusters. This approach requires that the 3D dataset has been previously classified. This implies that discontinuity sets are previously extracted, every single point is labeled with its corresponding discontinuity set and every exposed planar surface is analytically calculated. Then, for each discontinuity set the method calculates the normal spacing between an exposed plane and its nearest one considering 3D space relationship. This link between planes is obtained calculating for every point its nearest point member of the same discontinuity set, which provides its nearest plane. This allows calculating the normal spacing for every plane. Finally, the normal spacing is calculated as the mean value of all the normal spacings for each discontinuity set. The methodology is validated through three cases of study using synthetic data and 3D laser scanning datasets. The first case illustrates the fundamentals and the performance of the proposed methodology. The second and the third cases of study correspond to two rock slopes for which datasets were acquired using a 3D laser scanner. The second case study has shown that results obtained from the traditional and the proposed approaches are reasonably similar. Nevertheless, a discrepancy between both approaches has been found when the exposed planes members of a discontinuity set were hard to identify and when the planes pairing was difficult to establish during the fieldwork campaign. The third case study also has evidenced that when the number of identified exposed planes is high, the calculated normal spacing using the proposed approach is minor than those using the traditional approach.

Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

Software for video-based multi-point frequency measuring and mapping

Complementary programs

Methods and algorithms for video-based multi-point frequency measuring and mapping

Software for video-based multi-point frequency measuring and mapping: http://hdl.handle.net/10045/53429

A Novel Prediction Method for Early Recognition of Global Human Behaviour in Image Sequences

Human behaviour recognition has been, and still remains, a challenging problem that involves different areas of computational intelligence. The automated understanding of people activities from video sequences is an open research topic in which the computer vision and pattern recognition areas have made big efforts. In this paper, the problem is studied from a prediction point of view. We propose a novel method able to early detect behaviour using a small portion of the input, in addition to the capabilities of it to predict behaviour from new inputs. Specifically, we propose a predictive method based on a simple representation of trajectories of a person in the scene which allows a high level understanding of the global human behaviour. The representation of the trajectory is used as a descriptor of the activity of the individual. The descriptors are used as a cue of a classification stage for pattern recognition purposes. Classifiers are trained using the trajectory representation of the complete sequence. However, partial sequences are processed to evaluate the early prediction capabilities having a specific observation time of the scene. The experiments have been carried out using the three different dataset of the CAVIAR database taken into account the behaviour of an individual. Additionally, different classic classifiers have been used for experimentation in order to evaluate the robustness of the proposal. Results confirm the high accuracy of the proposal on the early recognition of people behaviours.

Evaluation of sampling method effects in 3D non-rigid registration

Since the beginning of 3D computer vision problems, the use of techniques to reduce the data to make it treatable preserving the important aspects of the scene has been necessary. Currently, with the new low-cost RGB-D sensors, which provide a stream of color and 3D data of approximately 30 frames per second, this is getting more relevance. Many applications make use of these sensors and need a preprocessing to downsample the data in order to either reduce the processing time or improve the data (e.g., reducing noise or enhancing the important features). In this paper, we present a comparison of different downsampling techniques which are based on different principles. Concretely, five different downsampling methods are included: a bilinear-based method, a normal-based, a color-based, a combination of the normal and color-based samplings, and a growing neural gas (GNG)-based approach. For the comparison, two different models have been used acquired with the Blensor software. Moreover, to evaluate the effect of the downsampling in a real application, a 3D non-rigid registration is performed with the data sampled. From the experimentation we can conclude that depending on the purpose of the application some kernels of the sampling methods can improve drastically the results. Bilinear- and GNG-based methods provide homogeneous point clouds, but color-based and normal-based provide datasets with higher density of points in areas with specific features. In the non-rigid application, if a color-based sampled point cloud is used, it is possible to properly register two datasets for cases where intensity data are relevant in the model and outperform the results if only a homogeneous sampling is used.

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.