Subdivision surface fitting to a dense mesh using ridges and umbilics

Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach

At-Most-Hexa Meshes

AbstractVolumetric polyhedral meshes are required in many applications, especially for solving partial differential equations on finite element simulations. Still, their construction bears several additional challenges compared to boundary‐based representations. Tetrahedral meshes and (pure) hex‐meshes are two popular formats in scenarios like CAD applications, offering opposite advantages and disadvantages. Hex‐meshes are more intricate to construct due to the global structure of the meshing, but feature much better regularity, alignment, are more expressive, and offer the same simulation accuracy with fewer elements. Hex‐dominant meshes, where most but not all cell elements have a hexahedral structure, constitute an attractive compromise, potentially unlocking benefits from both structures, but their generality makes their employment in downstream applications difficult. In this work, we introduce a strict subset of general hex‐dominant meshes, which we term 'at‐most‐hexa meshes', in which most cells are still hexahedral, but no cell has more than six boundary faces, and no face has more than four sides. We exemplify the ease of construction of at‐most‐hexa meshes by proposing a frugal and straightforward method to generate high‐quality meshes of this kind, starting directly from hulls or point clouds, for example, from a 3D scan. In contrast to existing methods for (pure) hexahedral meshing, ours does not require an intermediate parameterization of other costly pre‐computations and can start directly from surfaces or samples. We leverage a Lloyd relaxation process to exploit the synergistic effects of aligning an orientation field in a modified 3D Voronoi diagram using the norm for cubical cells. The extracted geometry incorporates regularity as well as feature alignment, following sharp edges and curved boundary surfaces. We introduce specialized operations on the three‐dimensional graph structure to enforce consistency during the relaxation. The resulting algorithm allows for an efficient evaluation with parallel algorithms on GPU hardware and completes even large reconstructions within minutes

Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error {\delta}, minimal interior angle {\theta} and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound {\delta} as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. In this way our optimization framework greedily searches for the coarsest mesh with minimal interior angle above {\theta} and approximation error bounded by {\delta}. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization and Computer Graphic

Retopology: a comprehensive study of current automation solutions from an artist’s workflow perspective

Dissertação de mestrado em Engenharia InformáticaTopology (the density, organization and flow of a 3D mesh’s connectivity) constrains the suitability of a 3D model for any given purpose, be it surface showcasing through renders, use in real-time engines, posing or animation. While some of these use cases might not have very strict topology requirements, others may demand optimized polygon counts for performance reasons, or even specific geometry distribution in order to take deformation directions into account. Many processes for creating 3D models such as sculpting try to make the user unaware of the inner workings of geometry, by providing flexible levels of surface detailing through dynamic geometry allocation. The resulting models have a dense, unorganized topology that is inefficient and unfit for most use cases, with the additional drawback of being hard to work with manually. Retopology is the process of providing a new topology to a model such as these, while maintaining the shape of its surface. It’s a technical and time-consuming process that clashes with the rest of the artist’s workflow, which is mainly composed of creative processes. While there’s abundant research in this area focusing on polygon distribution quality based on surface shape, artists are still left with no options but to resort to manual work when it comes to deformation-optimized topology. This document exposes this disconnect, along with a proposed framework that attempts to provide a more complete retopology solution for 3D artists. This framework combines traditional mesh extraction algorithms with adapting manually-made meshes in a pipeline that tries to understand the input on a higher level, in order to solve deficiencies that are present in current retopology tools. Our results are very positive, presenting an improvement over state of the art solutions, which could possibly steer discussion and research in this area to be more in line with the needs of 3D artists.A topologia (a densidade, organização e direções tomadas pela conectividade de uma mesh 3D) limita a adequação de um modelo 3D para um leque variado de usos, entre os quais, visualização da superfície através de renders, uso em motores real-time, poses ou animações. Embora muitos destes usos não possuam requerimentos de topologia muito rigorosos, outros podem exigir número de polígonos mais baixos por questões de performance, ou até distribuição de geometria específica para acomodar direções de deformação corretamente. Muitos processos de criação de modelos 3D, como escultura, permitem que o utilizador não esteja ciente do que se passa em termos de funcionamento da geometria por debaixo da utilização. Isto é conseguido oferecendo níveis de detalhe flexíveis, alocando geometria de forma dinâmica. Os modelos resultantes têm uma topologia densa e desorganizada, que é ineficiente e pouco apropriada para a maior parte dos casos de uso, com a desvantagem adicional de ser difícil de trabalhar com a mesma manualmente. A retopologia é o processo de gerar uma nova topologia para um modelo, ao mesmo tempo que se mantém a forma da superfície. É um processo técnico e demorado, que entra em conflito com o resto do fluxo de trabalho do artista, que é composto maioritariamente por processos artísticos. Apesar de haver investigação abundante nesta área focada na qualidade da distribuição de polígonos baseada na forma da superfície, os artistas continuam a ter de recorrer ao trabalho manual quando se trata de topologia otimizada para deformações. Este documento expõe esta divergência, propondo, em conjunto, uma framework que tenta oferecer uma solução mais completa para os artistas 3D. Esta framework combina algoritmos de extração de meshes tradicionais com adaptação de meshes feitas manualmente, numa pipeline que tenta compreender o input a um nível superior, resolvendo as deficiências presentes nas ferramentas de retopologia atuais. Os nossos resultados são bastante positivos, apresentando melhorias em relação a soluções de estado da arte, facto que poderá mudar o rumo da discussão e investigação neste campo, para melhor se adequar às necessidades dos artistas 3D

Connectivity Control for Quad-Dominant Meshes

abstract: Quad-dominant (QD) meshes, i.e., three-dimensional, 2-manifold polygonal meshes comprising mostly four-sided faces (i.e., quads), are a popular choice for many applications such as polygonal shape modeling, computer animation, base meshes for spline and subdivision surface, simulation, and architectural design. This thesis investigates the topic of connectivity control, i.e., exploring different choices of mesh connectivity to represent the same 3D shape or surface. One key concept of QD mesh connectivity is the distinction between regular and irregular elements: a vertex with valence 4 is regular; otherwise, it is irregular. In a similar sense, a face with four sides is regular; otherwise, it is irregular. For QD meshes, the placement of irregular elements is especially important since it largely determines the achievable geometric quality of the final mesh. Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Structured meshes: composition and remeshing guided by the Curve-Skeleton

Virtual sculpting is currently a broadly used modeling metaphor with rising popularity especially in the entertainment industry. While this approach unleashes the artists' inspiration and creativity and leads to wonderfully detailed and artistic 3D models, it has the side effect, purely technical, of producing highly irregular meshes that are not optimal for subsequent processing. Converting an unstructured mesh into a more regular and struc- tured model in an automatic way is a challenging task and still open prob- lem. Since structured meshes are useful in different applications, it is of in- terest to be able to guarantee such property also in scenarios of part based modeling, which aim to build digital objects by composition, instead of modeling them from a scratch. This thesis will present methods for obtaining structured meshes in two different ways. First is presented a coarse quad layout computation method which starts from a triangle mesh and the curve-skeleton of the shape. The second approach allows to build complex shapes by procedural composition of PAM's. Since both quad layouts and PAMs exploit their global struc- ture, similarities between the two will be discussed, especially how their structure has correspondences to the curve-skeleton describing the topology of the shape being represented. Since both the presented methods rely on the information provided by the skeleton, the difficulties of using automat- ically extracted curve-skeletons without processing are discussed, and an interactive tool for user-assisted processing is presented

3D photogrammetric data modeling and optimization for multipurpose analysis and representation of Cultural Heritage assets

This research deals with the issues concerning the processing, managing, representation for further dissemination of the big amount of 3D data today achievable and storable with the modern geomatic techniques of 3D metric survey. In particular, this thesis is focused on the optimization process applied to 3D photogrammetric data of Cultural Heritage assets. Modern Geomatic techniques enable the acquisition and storage of a big amount of data, with high metric and radiometric accuracy and precision, also in the very close range field, and to process very detailed 3D textured models. Nowadays, the photogrammetric pipeline has well-established potentialities and it is considered one of the principal technique to produce, at low cost, detailed 3D textured models. The potentialities offered by high resolution and textured 3D models is today well-known and such representations are a powerful tool for many multidisciplinary purposes, at different scales and resolutions, from documentation, conservation and restoration to visualization and education. For example, their sub-millimetric precision makes them suitable for scientific studies applied to the geometry and materials (i.e. for structural and static tests, for planning restoration activities or for historical sources); their high fidelity to the real object and their navigability makes them optimal for web-based visualization and dissemination applications. Thanks to the improvement made in new visualization standard, they can be easily used as visualization interface linking different kinds of information in a highly intuitive way. Furthermore, many museums look today for more interactive exhibitions that may increase the visitors’ emotions and many recent applications make use of 3D contents (i.e. in virtual or augmented reality applications and through virtual museums). What all of these applications have to deal with concerns the issue deriving from the difficult of managing the big amount of data that have to be represented and navigated. Indeed, reality based models have very heavy file sizes (also tens of GB) that makes them difficult to be handled by common and portable devices, published on the internet or managed in real time applications. Even though recent advances produce more and more sophisticated and capable hardware and internet standards, empowering the ability to easily handle, visualize and share such contents, other researches aim at define a common pipeline for the generation and optimization of 3D models with a reduced number of polygons, however able to satisfy detailed radiometric and geometric requests. iii This thesis is inserted in this scenario and focuses on the 3D modeling process of photogrammetric data aimed at their easy sharing and visualization. In particular, this research tested a 3D models optimization, a process which aims at the generation of Low Polygons models, with very low byte file size, processed starting from the data of High Poly ones, that nevertheless offer a level of detail comparable to the original models. To do this, several tools borrowed from the game industry and game engine have been used. For this test, three case studies have been chosen, a modern sculpture of a contemporary Italian artist, a roman marble statue, preserved in the Civic Archaeological Museum of Torino, and the frieze of the Augustus arch preserved in the city of Susa (Piedmont- Italy). All the test cases have been surveyed by means of a close range photogrammetric acquisition and three high detailed 3D models have been generated by means of a Structure from Motion and image matching pipeline. On the final High Poly models generated, different optimization and decimation tools have been tested with the final aim to evaluate the quality of the information that can be extracted by the final optimized models, in comparison to those of the original High Polygon one. This study showed how tools borrowed from the Computer Graphic offer great potentialities also in the Cultural Heritage field. This application, in fact, may meet the needs of multipurpose and multiscale studies, using different levels of optimization, and this procedure could be applied to different kind of objects, with a variety of different sizes and shapes, also on multiscale and multisensor data, such as buildings, architectural complexes, data from UAV surveys and so on

Structured meshes: composition and remeshing guided by the Curve-Skeleton

Virtual sculpting is currently a broadly used modeling metaphor with rising popularity especially in the entertainment industry. While this approach unleashes the artists' inspiration and creativity and leads to wonderfully detailed and artistic 3D models, it has the side effect, purely technical, of producing highly irregular meshes that are not optimal for subsequent processing. Converting an unstructured mesh into a more regular and struc- tured model in an automatic way is a challenging task and still open prob- lem. Since structured meshes are useful in different applications, it is of in- terest to be able to guarantee such property also in scenarios of part based modeling, which aim to build digital objects by composition, instead of modeling them from a scratch. This thesis will present methods for obtaining structured meshes in two different ways. First is presented a coarse quad layout computation method which starts from a triangle mesh and the curve-skeleton of the shape. The second approach allows to build complex shapes by procedural composition of PAM's. Since both quad layouts and PAMs exploit their global struc- ture, similarities between the two will be discussed, especially how their structure has correspondences to the curve-skeleton describing the topology of the shape being represented. Since both the presented methods rely on the information provided by the skeleton, the difficulties of using automat- ically extracted curve-skeletons without processing are discussed, and an interactive tool for user-assisted processing is presented

An optimised workflow for the interactive experience with cultural heritage through reality-based 3d models: Cases study in archaeological and urban complexes

The paper compares two workflows for the achievement of 3D models aimed at in-depth studies on the geometric features of Cultural Heritage artefacts and their dissemination. The purpose is the outlining of pros and cons of different techniques coming from entertainment and video games industry, starting from highly reliable 3D documentation of cultural assets, i.e. architectural/archaeological/urban sites. Two different possible applications are described: (i) procedural modelling used for understanding and visualising reconstruction hypotheses of the vaulted pavilions at Hadrian\u2019s Villa, Tivoli, Rome; (ii) optimisation of 3D high-detailed models, as input files, turned into visual reliable and highly portable assets for game-engines. The first case study is focussed on creating a flexible model for evalueting reconstruction hypotheses and supplying restorers with useful hints for shape completion of ruined pavilions. The second case study makes available detailed digital contents for storytelling historical and cultural events in an attractive way, as in the case of the urban explorative model of Chiuro, a small town in northern Italy