58 research outputs found

    Design of decorative 3D models: from geodesic ornaments to tangible assemblies

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    L'obiettivo di questa tesi è sviluppare strumenti utili per creare opere d'arte decorative digitali in 3D. Uno dei processi decorativi più comunemente usati prevede la creazione di pattern decorativi, al fine di abbellire gli oggetti. Questi pattern possono essere dipinti sull'oggetto di base o realizzati con l'applicazione di piccoli elementi decorativi. Tuttavia, la loro realizzazione nei media digitali non è banale. Da un lato, gli utenti esperti possono eseguire manualmente la pittura delle texture o scolpire ogni decorazione, ma questo processo può richiedere ore per produrre un singolo pezzo e deve essere ripetuto da zero per ogni modello da decorare. D'altra parte, gli approcci automatici allo stato dell'arte si basano sull'approssimazione di questi processi con texturing basato su esempi o texturing procedurale, o con sistemi di riproiezione 3D. Tuttavia, questi approcci possono introdurre importanti limiti nei modelli utilizzabili e nella qualità dei risultati. Il nostro lavoro sfrutta invece i recenti progressi e miglioramenti delle prestazioni nel campo dell'elaborazione geometrica per creare modelli decorativi direttamente sulle superfici. Presentiamo una pipeline per i pattern 2D e una per quelli 3D, e dimostriamo come ognuna di esse possa ricreare una vasta gamma di risultati con minime modifiche dei parametri. Inoltre, studiamo la possibilità di creare modelli decorativi tangibili. I pattern 3D generati possono essere stampati in 3D e applicati a oggetti realmente esistenti precedentemente scansionati. Discutiamo anche la creazione di modelli con mattoncini da costruzione, e la possibilità di mescolare mattoncini standard e mattoncini custom stampati in 3D. Ciò consente una rappresentazione precisa indipendentemente da quanto la voxelizzazione sia approssimativa. I principali contributi di questa tesi sono l'implementazione di due diverse pipeline decorative, un approccio euristico alla costruzione con mattoncini e un dataset per testare quest'ultimo.The aim of this thesis is to develop effective tools to create digital decorative 3D artworks. Real-world art often involves the use of decorative patterns to enrich objects. These patterns can be painted on the base or might be realized with the application of small decorative elements. However, their creation in digital media is not trivial. On the one hand, users can manually perform texture paint or sculpt each decoration, in a process that can take hours to produce a single piece and needs to be repeated from the ground up for every model that needs to be decorated. On the other hand, automatic approaches in state of the art rely on approximating these processes with procedural or by-example texturing or with 3D reprojection. However, these approaches can introduce significant limitations in the models that can be used and in the quality of the results. Instead, our work exploits the recent advances and performance improvements in the geometry processing field to create decorative patterns directly on surfaces. We present a pipeline for 2D and one for 3D patterns and demonstrate how each of them can recreate a variety of results with minimal tweaking of the parameters. Furthermore, we investigate the possibility of creating decorative tangible models. The 3D patterns we generate can be 3D printed and applied to previously scanned real-world objects. We also discuss the creation of models with standard building bricks and the possibility of mixing standard and custom 3D-printed bricks. This allows for a precise representation regardless of the coarseness of the voxelization. The main contributions of this thesis are the implementation of two different decorative pipelines, a heuristic approach to brick construction, and a dataset to test the latter

    Moving mesh Virtual Element Methods

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    This thesis explores the development and analysis of moving mesh Virtual Element Methods for partial differential equations on time-dependent domains. This thesis presents the first moving mesh method to purely use the Virtual Element Method, an isoparametric Virtual Element Method for approximating partial differential equations on curved domains and a high-order Arbitrary Lagrangian-Eulerian Virtual Element Method for problems on time-dependent domains with moving boundaries. Each contribution successfully demonstrates the applicability and accuracy of Virtual Element Methods in existing moving mesh algorithms, achieving similar orders of accuracy compared to classical Finite Element Method approaches. The results suggest that the flexibility of moving mesh methods can be greatly improved by incorporating more general mesh structures, including polygons and curved-edged polygons, proving the Virtual Element Method offers an effective extension to classical approaches. This work provides a foundation for future research in Virtual Element Methods for more complex problems on time-dependent domains and developing the analysis to support proposed moving mesh methods

    Modelling, Monitoring, Control and Optimization for Complex Industrial Processes

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    This reprint includes 22 research papers and an editorial, collected from the Special Issue "Modelling, Monitoring, Control and Optimization for Complex Industrial Processes", highlighting recent research advances and emerging research directions in complex industrial processes. This reprint aims to promote the research field and benefit the readers from both academic communities and industrial sectors

    A Real-Time Adaptive Sampling Strategy Optimized by Uncertainty for Spatial Data Analysis on Complex Domains

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    Environmental monitoring is used to reveal the state of the environment, to inform experts and help them to prioritise actions in the context of environmental policies. Environmental sampling is the way the environment is interrogated to get measures of environmental (e.g., physical, chemical) parameters in a limited set of locations (samples). The environmental properties varies from place to place in continuum and there are infinitely many places at which we might record what they are like, but practically we can measure them at only a finite number by sampling. The role of the location in which samples are collected is very crucial. The focus of the thesis is the study of a mathematical framework that supports a reasoned and non-random sampling of environmental variables, with the aim of defining a methodological approach to optimise the number of sampling required while maintaining a target precision. The arrangement of points is not selected or known a priori; conversely, we propose an iterative process where the next-sample location is determined on-the-fly on the basis of the environmental scenario that is delineated more and more accurately at each iteration. At each iteration, the distribution map is updated with the new incoming data. The geostatistical analysis we implement provides a predicted value and the related uncertainty about that value, actually providing an uncertainty map beside the predicted distribution. The system responds to the current state by requiring a measurement in the area with highest uncertainty, to reduce uncertainty and increase accuracy. Environmental survey areas to monitor are often characterised by very complex boundaries. Unstructured grids are more flexible to faithfully represent complex geometries compared to structured grids. The usage of unstructured grids introduces another innovation aspect studied in the thesis, which is the change of support model

    Analysis and Generation of Quality Polytopal Meshes with Applications to the Virtual Element Method

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    This thesis explores the concept of the quality of a mesh, the latter being intended as the discretization of a two- or three- dimensional domain. The topic is interdisciplinary in nature, as meshes are massively used in several fields from both the geometry processing and the numerical analysis communities. The goal is to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. In other words, a good quality mesh that is also cheap to handle, overcoming the typical trade-off between quality and computational cost. To reach this goal, we first need to answer the question: ''How, and how much, does the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depend on the particular mesh adopted to model the problem? And which geometrical features of the mesh most influence the result?'' We present a comparative study of the different mesh types, mesh generation techniques, and mesh quality measures currently available in the literature related to both engineering and computer graphics applications. This analysis leads to the precise definition of the notion of quality for a mesh, in the particular context of numerical simulations of partial differential equations with the virtual element method, and the consequent construction of criteria to determine and optimize the quality of a given mesh. Our main contribution consists in a new mesh quality indicator for polytopal meshes, able to predict the performance of the virtual element method over a particular mesh before running the simulation. Strictly related to this, we also define a quality agglomeration algorithm that optimizes the quality of a mesh by wisely agglomerating groups of neighboring elements. The accuracy and the reliability of both tools are thoroughly verified in a series of tests in different scenarios

    Teaching and Learning of Fluid Mechanics, Volume II

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    This book is devoted to the teaching and learning of fluid mechanics. Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, mechanical, chemical and civil engineering and environmental sciences, each highlighting a different aspect or interpretation of the foundation and applications of fluids. While scholarship in fluid mechanics is vast, expanding into the areas of experimental, theoretical and computational fluid mechanics, there is little discussion among scientists about the different possible ways of teaching this subject. We think there is much to be learned, for teachers and students alike, from an interdisciplinary dialogue about fluids. This volume therefore highlights articles which have bearing on the pedagogical aspects of fluid mechanics at the undergraduate and graduate level

    Virtual Element based formulations for computational materials micro-mechanics and homogenization

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    In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics, which has emerged as an effective tool both to understand the influence of complex microstructure on the macro-mechanical response of engineering materials and to tailor-design innovative materials for specific applications through a proper modification of their microstructure. While the classical continuum approximation does not account for microstructural details within the material, computational micromechanics allows detailed modelling of a heterogeneous material's internal structural arrangement by treating each constituent as a continuum. Such an approach requires modelling a certain material microstructure by considering most of the microstructure's morphological features. The most common numerical technique used in computational micromechanics analysis is the Finite Element Method (FEM). Its use has been driven by the development of mesh generation programs, which lead to the quasi-automatic discretisation of the artificial microstructure domain and the possibility of implementing appropriate constitutive equations for the different phases and their interfaces. In FEM's applications to computational micromechanics, the phase arrangements are discretised using continuum elements. The mesh is created so that element boundaries and, wherever required, special interface elements are located at all interfaces between material's constituents. This approach can be effective in modelling many microstructures, and it is readily available in commercial codes. However, the need to accurately resolve the kinematic and stress fields related to complex material behaviours may lead to very large models that may need prohibitive processing time despite the increasing modern computers' performance. When rather complex microstructure's morphologies are considered, the quasi-automatic discretisation process stated before might fail to generate high-quality meshes. Time-consuming mesh regularisation techniques, both automatic and operator-driven, may be needed to obtain accurate numeric results. Indeed, the preparation of high-quality meshes is today one of the steps requiring more attention, and time, from the analyst. In this respect, the development of computational techniques to deal with complex and evolving geometries and meshes with accuracy, effectiveness, and robustness attracts relevant interest. The computational framework presented in this thesis is based on the Virtual Element Method (VEM), a recently developed numerical technique that has proven to provide robust numerical results even with highly-distorted mesh. These peculiar features have been exploited to analyse two-dimensional representations of heterogeneous materials' microstructures. Ad-hoc polygonal multi-domain meshing strategies have been developed and tested to exploit the discretisation freedom that VEM allows. To further simplify the preprocessing stage of the analysis and reduce the total computational cost, a novel hybrid formulation for analysing multi-domain problems has been developed by combining the Virtual Element Method with the well-known Boundary Element Method (BEM). The hybrid approach has been used to study both composite material's transverse behaviour in the presence of inclusions with complex geometries and damage and crack propagation in the matrix phase. Numerical results are presented that demonstrate the potential of the developed framework

    PAVEL: Decorative Patterns with Packed Volumetric Elements

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    Many real-world hand-crafted objects are decorated with elements that are packed onto the object's surface and deformed to cover it as much as possible. Examples are artisanal ceramics and metal jewelry. Inspired by these objects, we present a method to enrich surfaces with packed volumetric decorations. Our algorithm works by first determining the locations in which to add the decorative elements and then removing the non-physical overlap between them while preserving the decoration volume. For the placement, we support several strategies depending on the desired overall motif. To remove the overlap, we use an approach based on implicit deformable models creating the qualitative effect of plastic warping while avoiding expensive and hard-to-control physical simulations. Our decorative elements can be used to enhance virtual surfaces, as well as 3D-printed pieces, by assembling the decorations onto real-surfaces to obtain tangible reproductions.Comment: 11 page

    Similarity reasoning for local surface analysis and recognition

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    This thesis addresses the similarity assessment of digital shapes, contributing to the analysis of surface characteristics that are independent of the global shape but are crucial to identify a model as belonging to the same manufacture, the same origin/culture or the same typology (color, common decorations, common feature elements, compatible style elements, etc.). To face this problem, the interpretation of the local surface properties is crucial. We go beyond the retrieval of models or surface patches in a collection of models, facing the recognition of geometric patterns across digital models with different overall shape. To address this challenging problem, the use of both engineered and learning-based descriptions are investigated, building one of the first contributions towards the localization and identification of geometric patterns on digital surfaces. Finally, the recognition of patterns adds a further perspective in the exploration of (large) 3D data collections, especially in the cultural heritage domain. Our work contributes to the definition of methods able to locally characterize the geometric and colorimetric surface decorations. Moreover, we showcase our benchmarking activity carried out in recent years on the identification of geometric features and the retrieval of digital models completely characterized by geometric or colorimetric patterns
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