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El doblez proyectado es indisoluble de la geometría que lo hace posible. Para establecer un claro control sobre el doblez es necesario realizar un documento proyectivo, un plano. Es por eso que los asuntos ligados a la geometría y al control matemático de los patrones de doblado han sido siempre fundamentales en la construcción de este tipo de diseños. Nos acercamos aquí a uno de los principales referentes y precursores sobre el estudio y desarrollo de los patrones de doblado para fines volumétricos, Ron Resch. Se trata de un desconocido artista y científico computacional norteamericano cuyo trabajo se menciona de modo repetido cuando se habla de arquitectos contemporáneos como Greg Lynn, quien ha aplicado también el uso del ordenador como herramienta de control y desarrollo geométrico. Para situar el momento, veremos el trabajo didáctico de Josef Albers y su manera de “abrir los ojos” mediante la experiencia con la manipulación restringida de la materia. El trabajo de Ron Resch establece una manera científica de aproximarse al problema y de aplicar las por aquel entonces incipientes herramientas computacionales, como son la elaboración de modelos 3D o la utilización de maquinaria CNC para el corte o el marcado. Los sistemas topológicos de Resch son en gran medida el origen de lo que hoy es el diseño paramétrico y la arquitectura de desarrollo con ordenadores.

Optimal viewpoint prediction is an essential task in many computer graphics applications. Unfortunately, common viewpointqualities suffer from two major drawbacks: dependency on clean surface meshes, which are not always available, and the lack ofclosed-form expressions, which requires a costly search involving rendering. To overcome these limitations we propose to sepa-rate viewpoint selection from rendering through an end-to-end learning approach, whereby we reduce the in¿uence of the meshquality by predicting viewpoints from unstructured point clouds instead of polygonal meshes. While this makes our approachinsensitive to the mesh discretization during evaluation, it only becomes possible when resolving label ambiguities that arise inthis context. Therefore, we additionally propose to incorporate the label generation into the training procedure, making the labeldecision adaptive to the current network predictions. We show how our proposed approach allows for learning viewpoint pre-dictions for models from different object categories and for different viewpoint qualities. Additionally, we show that predictiontimes are reduced from several minutes to a fraction of a second, as compared to state-of-the-art (SOTA) viewpoint quality eval-uation. Code and training data is available at https://github.com/schellmi42/viewpoint_learning, whichis to our knowledge the biggest viewpoint quality dataset available. This work was supported in part by project TIN2017-88515-C2-1-R(GEN3DLIVE), from the Spanish Ministerio de Economía yCompetitividad, by 839 FEDER (EU) funds.

Geometric 3D scene classification is a very challenging task. Current methodologies extract the geometric information using only a depth channel provided by an RGB-D sensor. These kinds of methodologies introduce possible errors due to missing local geometric context in the depth channel. This work proposes a novel Residual Attention Graph Convolutional Network that exploits the intrinsic geometric context inside a 3D space without using any kind of point features, allowing the use of organized or unorganized 3D data. Experiments are done in NYU Depth v1 and SUN-RGBD datasets to study the different configurations and to demonstrate the effectiveness of the proposed method. Experimental results show that the proposed method outperforms current state-of-the-art in geometric 3D scene classification tasks. This research was supported by Secretary of Universities and Research of the Generalitat de Catalunya and the European Social Fund via a PhD grant (FI2019) in the framework of project TEC2016-75976-R, financed by the Ministerio de Economía, Industria y Competitividad and the European Regional Development Fund (ERDF).

Motivation Protein–protein interactions (PPIs) are usually modeled as networks. These networks have extensively been studied using graphlets, small induced subgraphs capturing the local wiring patterns around nodes in networks. They revealed that proteins involved in similar functions tend to be similarly wired. However, such simple models can only represent pairwise relationships and cannot fully capture the higher-order organization of protein interactomes, including protein complexes. Results To model the multi-scale organization of these complex biological systems, we utilize simplicial complexes from computational geometry. The question is how to mine these new representations of protein interactomes to reveal additional biological information. To address this, we define simplets, a generalization of graphlets to simplicial complexes. By using simplets, we define a sensitive measure of similarity between simplicial complex representations that allows for clustering them according to their data types better than clustering them by using other state-of-the-art measures, e.g. spectral distance, or facet distribution distance. We model human and baker’s yeast protein interactomes as simplicial complexes that capture PPIs and protein complexes as simplices. On these models, we show that our newly introduced simplet-based methods cluster proteins by function better than the clustering methods that use the standard PPI networks, uncovering the new underlying functional organization of the cell. We demonstrate the existence of the functional geometry in the protein interactome data and the superiority of our simplet-based methods to effectively mine for new biological information hidden in the complexity of the higher-order organization of protein interactomes. Availability and implementation Codes and datasets are freely available at http://www0.cs.ucl.ac.uk/staff/natasa/Simplets/. Supplementary information Supplementary data are available at Bioinformatics online.

Traditional vector field visualization has a close focus on velocity, and is typically constrained to the dynamics of massless particles. In this paper, we present a novel approach to the analysis of the force-induced dynamics of inertial particles. These forces can arise from acceleration fields such as gravitation, but also be dependent on the particle dynamics itself, as in the case of magnetism. Compared to massless particles, the velocity of an inertial particle is not determined solely by its position and time in a vector field. In contrast, its initial velocity can be arbitrary and impacts the dynamics over its entire lifetime. This leads to a four-dimensional problem for 2D setups, and a six-dimensional problem for the 3D case. Our approach avoids this increase in dimensionality and tackles the visualization by an integrated topological analysis approach. We demonstrate the utility of our approach using a synthetic time-dependent acceleration field, a system of magnetic dipoles, and N -body systems both in 2D and 3D.

Kernel-based methods have experienced a substantial progress in the last years, tuning out an essential mechanism for data classification, clustering and pattern recognition. The effectiveness of kernel-based techniques, though, depends largely on the capability of the underlying kernel to properly embed data in the feature space associated to the kernel. However, visualizing how a kernel embeds the data in a feature space is not so straightforward, as the embedding map and the feature space are implicitly defined by the kernel. In this work, we present a novel technique to visualize the action of a kernel, that is, how the kernel embeds data into a high-dimensional feature space. The proposed methodology relies on a solid mathematical formulation to map kernelized data onto a visual space. Our approach is faster and more accurate than most existing methods while still allowing interactive manipulation of the projection layout, a game-changing trait that other kernel-based projection techniques do not have.

We address the problem of tracking and detecting interactions between the different groups of runners that form during a race. In athletic races control points are set to monitor the progress of athletes over the course. Intuitively, a {\it group} is a sufficiently large set of athletes that cross a control point together. After adapting an existing definition of group to our setting we go on to study two types of group evolution patterns. The primary focus of this work are {\it evolution patterns}, i.e. the transformation and interaction of groups of athletes between two consecutive control points. We provide an accurate geometric model of the following evolution patterns: survives, appears, disappears, expands, shrinks, merges, splits, coheres and disbands, and present algorithms to efficiently compute these patterns. Next, based on the algorithms introduced for identifying evolution patterns, algorithms to detect {\it long-term patterns} are introduced. These patterns track global properties over several control points: surviving, traceable forward, traceable backward and related forward and backward. Experimental evaluation of the algorithms provided is presented using real and synthetic data. Using the data currently available, our experiments show how our algorithms can provide valuable insight into how running races develop. Moreover, we also show how, even if dense (synthetic) data is considered, our algorithms are also able to process it in real time.

We present a conformal bisection procedure for local refinement of 4D unstructured simplicial meshes with bounded minimum shape quality. Specifically, we propose a recursive refine to conformity procedure in two stages, based on marking bisection edges on different priority levels and defining specific refinement templates. Two successive applications of the first stage ensure that any 4D unstructured mesh can be conformingly refined. In the second stage, the successive refinements lead to a cycle in the number of generated similarity classes and thus, we can ensure a bound over the minimum shape quality. In the examples, we check that after successive refinement the mesh quality does not degenerate. Moreover, we refine a 4D unstructured mesh and a space-time mesh (3D + 1D) representation of a moving object. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 715546. This work has also received funding from the Generalitat de Catalunya under grant number 2017 SGR 1731. The work of X. Roca has been partially supported by the Spanish Ministerio de Economía y Competitividad under the personal grant agreement RYC-2015-01633.

Dynamic networks naturally appear in a multitude of applications from different fields. Analyzing and exploring dynamic networks in order to understand and detect patterns and phenomena is challenging, fostering the development of new methodologies, particularly in the field of visual analytics. In this work, we propose a novel visual analytics methodology for dynamic networks, which relies on the spectral graph wavelet theory. We enable the automatic analysis of a signal defined on the nodes of the network, making viable the robust detection of network properties. Specifically, we use a fast approximation of a graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The coefficients naturally encode the spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This methodology allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using usage scenarios and comparisons involving real dynamic networks.

Data analysis and knowledge discovery in trajectory databases is an emerging field with a growing number of applications such as managing traffic, planning tourism infrastructures or better understanding wildlife. In this paper, we study the problem of finding flock patterns in trajectory databases. A flock refers to a large enough subset of entities that move close to each other for, at least, a given time interval. We present parallel algorithms, to be run on a Graphics Processing Unit, for reporting three different variants of the flock pattern: (1) all maximal flocks, (2) the largest flock and (3) the longest flock. We also provide their complexity analysis together with experimental results showing the efficiency and scalability of our approach Work partially supported by the Spanish Ministerio de Ciencia e Innovación [TIN2010-20590-C02-02]

The main goal of this work is to develop a methodology for finding nutritional patterns from a variety of individual characteristics which can contribute to better understand the interactions between nutrition and health, provided that the complexity of the phenomenon gives poor performance using classical approaches. An innovative methodology based on a combination of advanced clustering techniques and consistent conceptual interpretation of clusters is proposed to find more understandable patterns or clusters. The Interpreted Integrative Multiview Clustering (I2MC) combines the previously proposed Integrative Multiview Clustering (IMC) with a new interpretation methodology NCIMS. IMC uses crossing operations over the several partitions obtained with the different views. Comparison with other classical clustering techniques is provided to assess the performance of this approach. IMC helps to reduce the high dimensionality of the data based on multiview division of variables. Two innovative Cluster Interpretation methodologies are proposed to support the understanding of the clusters. These are automatic methods to detect the significant variables that describe the clusters; also, a mechanism to deal with the consistency between the interpretations inter clusters of a single partition CI-IMS, or between pairs of nested partitions NCIMS. Some formal concepts are specifically introduced to be used in the NCIMS. I2MC is used to validate the interpretability of the participant’s profiles from an intervention nutritional study. The method has advantages to deal with complex datasets including heterogeneous variables corresponding to different topics and is able to provide meaningful partitions.

Given a set S of n line segments in the plane, we say that a region R R2 is a stabber for S if R contains exactly one endpoint of each segment of S. In this paper we provide optimal or near-optimal algorithms for reporting all combinatorially di erent stabbers for several shapes of stabbers. Speci cally, we consider the case in which the stabber can be described as the intersection of axis-parallel halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). The running times are O(n) (for the halfplane case), O(n log n) (for strips, quadrants, and 3-sided rectangles), and O(n2 log n) (for rectangles). Junta de Andalucía PAI FQM-0164 Ministerio de Economía y Competitividad MTM2014-60127-P

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

We introduce a flexible technique for interactive exploration of vector field data through classification derived from user-specified feature templates. Our method is founded on the observation that, while similar features within the vector field may be spatially disparate, they share similar neighborhood characteristics. Users generate feature-based visualizations by interactively highlighting well-accepted and domain specific representative feature points. Feature exploration begins with the computation of attributes that describe the neighborhood of each sample within the input vector field. Compilation of these attributes forms a representation of the vector field samples in the attribute space. We project the attribute points onto the canonical 2D plane to enable interactive exploration of the vector field using a painting interface. The projection encodes the similarities between vector field points within the distances computed between their associated attribute points. The proposed method is performed at interactive rates for enhanced user experience and is completely flexible as showcased by the simultaneous identification of diverse feature types.

Alya is a multi-physics simulation code developed at Barcelona Supercomputing Center (BSC). From its inception Alya code is designed using advanced High Performance Computing programming techniques to solve coupled problems on supercomputers efficiently. The target domain is engineering, with all its particular features: complex geometries and unstructured meshes, coupled multi-physics with exotic coupling schemes and physical models, ill-posed problems, flexibility needs for rapidly including new models, etc. Since its beginnings in 2004, Alya has scaled well in an increasing number of processors when solving single-physics problems such as fluid mechanics, solid mechanics, acoustics, etc. Over time, we have made a concerted effort to maintain and even improve scalability for multi-physics problems. This poses challenges on multiple fronts, including: numerical models, parallel implementation, physical coupling models, algorithms and solution schemes, meshing process, etc. In this paper, we introduce Alya's main features and focus particularly on its solvers. We present Alya's performance up to 100.000 processors in Blue Waters, the NCSA supercomputer with selected multi-physics tests that are representative of the engineering world. The tests are incompressible flow in a human respiratory system, low Mach combustion problem in a kiln furnace, and coupled electro-mechanical contraction of the heart. We show scalability plots for all cases and discuss all aspects of such simulations, including solver convergence. © 2016 Elsevier B.V. All rights reserved., The authors would like to thank the following fellow researchers and institutions: The Private Sector Program at NCSA and the Blue Waters sustained-petascale computing project-supported by the National Science Foundation (award number OCI 07-25070) and the state of Illinois. Denis Doorly and Alister Bates (Imperial College London, UK), collaborators of the airways study. Part of this work was financed by European PRACE Type B/C projects. The heart geometry was provided by Dr. A. Berruezo (Hospital Clínic de Barcelona) in collaboration with R. Sebastian (UVEG) and O. Camara (UPF), partially financed through project TIN2011-28067 from MINECO, Spain. Part of the cardiac model development was financed by the grant SEV-2011-00067 of Severo Ochoa Program, awarded by the Spanish Government. Part of the kiln model development was financed by the European Commission in the framework of the FP7 Collaborative project “Advanced Technologies for the Production of Cement and Clean Aggregates from Construction and Demolition Waste (C2CA)”, Grant Agreement No. 265189.

The computation of the largest planar region approximating a 3D object is an important problem with wide applications in modeling and rendering. Given a voxelization of the 3D object, we propose an efficient algorithm to solve a discrete version of this problem. The input of the algorithm is the set of grid edges connecting the interior and the exterior of the object (called sticks). Using a voting-based approach, we compute the plane that slices the largest number of sticks and is orientation-compatible with these sticks. The robustness and efficiency of our approach rests on the use of two different parameterizations of the planes with suitable properties. The first of these is exact and is used to retrieve precomputed local solutions of the problem. The second one is discrete and is used in a hierarchical voting scheme to compute the global maximum. This problem has diverse applications that range from finding object signatures to generating simplified models. Here we demonstrate the merits of the algorithm for efficiently computing an optimized set of textured impostors for a given polygonal model. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling

3D registration or matching is a crucial step in 3D model reconstruction. Registration applications span along a variety of research fields, including computational geometry, computer vision, and geometric modeling. This variety of applications produces many diverse approaches to the problem but at the same time yields divergent notations and a lack of standardized algorithms and guidelines to classify existing methods. In this article, we review the state of the art of the 3D rigid registration topic (focused on Coarse Matching) and offer qualitative comparison between the most relevant approaches. Furthermore, we propose a pipeline to classify the existing methods and define a standard formal notation, offering a global point of view of the literature. Our discussion, based on the results presented in the analyzed papers, shows how, although certain aspects of the registration process still need to be tested further in real application situations, the registration pipeline as a whole has progressed steadily. As a result of this progress in all registration aspects, it is now possible to put together algorithms that are able to tackle new and challenging problems with unprecedented data sizes and meeting strict precision criteria This work has been supported by the FP7-ICT-2011-7 project PANDORA-Persistent Autonomy through Learning, Adaptation, Observation and Re-planning (Ref 288273) funded by the European Commission and the project RAIMON-Autonomous Underwater Robot for Marine Fish Farms Inspection and Monitoring (Ref CTM2011-29691-C02-02) funded by the Ministry of Economy and Competitiveness of the Spanish government. Ferran Roure is supported by an FPI scholarship associated with the RAIMON project

Data analysis and knowledge discovery in trajectory databases is an emerging field with a growing number of applications such as managing traffic, planning tourism infrastructures, analyzing professional sport matches or better understanding wildlife. A well-known collection of patterns which can occur for a subset of trajectories of moving objects exists. In this paper, we study the popular places pattern, that is, locations that are visited by many moving objects. We consider two criteria, strong and weak, to establish either the exact number of times that an object has visited a place during its complete trajectory or whether it has visited the place, or not. To solve the problem of reporting popular places, we introduce the popularity map. The popularity of a point is a measure of how many times the moving objects of a set have visited that point. The popularity map is the subdivision, into regions, of a plane where all the points have the same popularity. We propose different algorithms to efficiently compute and visualize popular places, the so-called popular regions and their schematization, by taking advantage of the parallel computing capabilities of the graphics processing units. Finally, we provide and discuss the experimental results obtained with the implementation of our algorithms We thank the reviewers for their suggestions and comments. Authors are partially supported by the Spanish MCI grant TIN2010-20590-C02-02

We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a non-monotonic dependence of the synchronization time on the velocity of the agents. Moreover, we find that mechanisms that drive synchronization are different for different dynamical regimes. We report the extreme situation where an interplay between the time-scales involved in the dynamical processes completely inhibit the achievement of a coherent state. We also provide estimators for the transitions between the different regimes., Submitted to PRL, 5 pages, 3 figures. Suplementary Material: 6 pages, 5 figures

Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the user's own subjective requirements.

Content-based image retrieval is still a challenging issue due to the inherent complexity of images and choice of the most discriminant descriptors. Recent developments in the field have introduced multidimensional projections to burst accuracy in the retrieval process, but many issues such as introduction of pattern recognition tasks and deeper user intervention to assist the process of choosing the most discriminant features still remain unaddressed. In this paper, we present a novel framework to CBIR that combines pattern recognition tasks, class-specific metrics, and multidimensional projection to devise an effective and interactive image retrieval system. User interaction plays an essential role in the computation of the final multidimensional projection from which image retrieval will be attained. Results have shown that the proposed approach outperforms existing methods, turning out to be a very attractive alternative for managing image data sets.

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article surveys several methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy analysed using real images. A summary, accompanied with experimental results, is given.

Public genealogical databases are becoming increasingly populated with historical data and records of the current population's ancestors. As this increasing amount of available information is used to link individuals to their ancestors, the resulting trees become deeper and more dense, which justifies the need for using organized, space-efficient layouts to display the data. Existing layouts are often only able to show a small subset of the data at a time. As a result, it is easy to become lost when navigating through the data or to lose sight of the overall tree structure. On the contrary, leaving space for unknown ancestors allows one to better understand the tree's structure, but leaving this space becomes expensive and allows fewer generations to be displayed at a time. In this work, we propose that the H-tree based layout be used in genealogical software to display ancestral trees. We will show that this layout presents an increase in the number of displayable generations, provides a nicely arranged, symmetrical, intuitive and organized fractal structure, increases the user's ability to understand and navigate through the data, and accounts for the visualization requirements necessary for displaying such trees. Finally, user-study results indicate potential for user acceptance of the new layout.

Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their number is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete.

I comment on a paper describing a method for deducing the hidden topology of an object portrayed in a 2D natural line drawing. The principal problem with this paper is that it cannot be considered an advance on (or even an equal of) the state of the art as the approach it describes makes the same limiting assumptions as approaches proposed 10 years ago. There are also important omissions in the review of related work.

Dynamic geometry systems are tools for geometric visualization. They allow the user to define geometric elements, establish relationships between them and explore the dynamic behavior of the remaining geometric elements when one of them is moved. In this work we propose a modular architecture for dynamic geometry systems built upon a set of functional units which will allow to apply some well known results from the Geometric Constraint Solving field.

In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 x 2 x 2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target con guration. Our algorithms involve a total of O(n²) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n²) parallel steps [7, 9, 4] or do not respect the constraints mentioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω(n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations.

The exploration of complex walkthrough models is often a difficult task due to the presence of densely occluded regions which pose a serious challenge to online navigation. In this paper we address the problem of algorithmic generation of exploration paths for complex walkthrough models. We present a characterization of suitable properties for camera paths and we discuss an efficient algorithm for computing them with little or no user intervention. Our approach is based on identifying the free-space structure of the scene (represented by a cell and portal graph) and an entropy-based measure of the relevance of a view-point. This metric is key for deciding which cells have to be visited and for computing critical way-points inside each cell. Several results on different model categories are presented and discussed.

Automatic computation of best views of objects is very useful. For example, they can be used as the starting point of a scene exploration, or to enrich galleries of objects available through Internet by adding an image a model that may help to decide if it is worth downloading. To select the most interesting viewpoint of an object, we use the so-called viewpoint entropy. The best view is the one which gives the most information of the object being inspected. In this paper we present an adaptive method to compute best views. Our adaptive scheme allows to improve over previous approaches the time of the selection of best views by an order of magnitude, and achieve a nearly interactive rate.

This article presents a new scan-line algorithm for displaying bicubic surfaces. Patches are decomposed on regions of constant sign of the z component of the normal before the scan process. Most of the computations are done in parametric space. The algorithm computes the intersection of the surfaces with only a restricted subset of scan planes and obtains the intersection with other scan planes by linear interpolation between exact instersections. A bound of the algorithm's error is given. Finally, the new method is compared with Whitted's algorithm.

We describe here a properly recent application of the Gröbner Cover algorithm (GC) providing an algebraic support to Dynamic Geometry computations of geometrical loci. It provides a complete algebraic solution of locus computation as well as a suitable taxonomy allowing to distinguish the nature of the different components. We included a new algorithm Locus into the Singular grobcov.lib library for this purpose. A web prototype has been implemented using it in Geogebra.

Given a tetrahedral mesh immersed in a voxel model, we present a method to refine the mesh to reduce the discrepancy between interpolated values based on either scheme at arbitrary locations. An advantage of the method presented is that it requires few subdivisions and all decisions are made locally at each tetrahedron. We discuss the algorithm’s performance and applications.

Trabajo presentado en la IEEE/CVF Conference on Computer Vision and Pattern Recognition, celebrada en Salt Lake City (UT, USA), del 18 al 23 de junio de 2018, We present a novel approach for synthesizing photorealistic images of people in arbitrary poses using generative adversarial learning. Given an input image of a person and a desired pose represented by a 2D skeleton, our model renders the image of the same person under the new pose, synthesizing novel views of the parts visible in the input image and hallucinating those that are not seen. This problem has recently been addressed in a supervised manner [16, 35], i.e., during training the ground truth images under the new poses are given to the network. We go beyond these approaches by proposing a fully unsupervised strategy. We tackle this challenging scenario by splitting the problem into two principal subtasks. First, we consider a pose conditioned bidirectional generator that maps back the initially rendered image to the original pose, hence being directly comparable to the input image without the need to resort to any training image. Second, we devise a novel loss function that incorporates content and style terms, and aims at producing images of high perceptual quality. Extensive experiments conducted on the DeepFashion dataset demonstrate that the images rendered by our model are very close in appearance to those obtained by fully supervised approaches., This work is supported in part by a Google Faculty Research Award, by the Spanish Ministry of Science and Innovation under projects HuMoUR TIN2017- 90086-R, ColRobTransp DPI2016-78957 and Mar´ıa de Maeztu Seal of Excellence MDM-2016-0656; and by the EU project AEROARMS ICT-2014-1-644271. We also thank Nvidia for hardware donation under the GPU Grant Program.

We propose a 3D mesh curving method that converts a straight-sided mesh to an optimal-quality curved high-order mesh that interpolates a CAD boundary representation. The main application of this method is the generation of discrete approximations of curved domains that are valid for simulation analysis with unstructured high-order methods. We devise the method as follows. First, the boundary of a straight-sided high-order mesh is curved to match the curves and surfaces of a CAD model. Second, the method minimizes the volume mesh distortion with respect to the coordinates of the inner nodes and the parametric coordinates of the curve and surface nodes. The proposed minimization features untangling capabilities and therefore, it repairs the invalid elements that may arise from the initial curving step. Compared with other mesh curving methods, the only goal of the proposed residual system is to minimize the volume mesh distortion. Furthermore, it is less constrained since the boundary nodes are free to slide on the CAD curves and surfaces. Hence, the proposed method is well suited to generate curved high-order meshes of optimal quality from CAD models that contain thin parts or high-curvature entities. To illustrate these capabilities, we generate several curved high-order meshes from CAD models with the implementation detailed in this work. Specifically, we detail a node-by-node non-linear iterative solver that minimizes the proposed objective function in a block Gauss–Seidel manner. This research was partially supported by CONACYT-SENER (‘‘Fondo Sectorial CONACYT SENER HIDROCARBUROS’’, grant contract 163723) and by the Spanish Ministerio de Economía y Competitividad under grant CTM2014-55014-C3-3-R.The work of the second author was partially supported by the Boeing Co. and US Air Force Office of Scientific Research and European Commis- sion through the Boeing–MIT Alliance and Computational Math Program and Marie Skłodowska-Curie Actions (HiPerMeGaFlows project),respectively.