175 research outputs found
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 boundaryâbased representations. Tetrahedral meshes and (pure) hexâmeshes are two popular formats in scenarios like CAD applications, offering opposite advantages and disadvantages. Hexâmeshes 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. Hexâdominant 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 hexâdominant meshes, which we term 'atâmostâhexa 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 atâmostâhexa meshes by proposing a frugal and straightforward method to generate highâquality 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 preâcomputations 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 threeâdimensional 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
Quad Meshing
Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing
A Review of 3D Point Clouds Parameterization Methods
3D point clouds parameterization is a very important research topic in the fields of computer graphics and computer vision, which has many applications such as texturing, remeshing and morphing, etc. Different from mesh parameterization, point clouds parameterization is a more challenging task in general as there is normally no connectivity information between points. Due to this challenge, the papers on point clouds parameterization are not as many as those on mesh parameterization. To the best of our knowledge, there are no review papers about point clouds parameterization. In this paper, we present a survey of existing methods for parameterizing 3D point clouds. We start by introducing the applications and importance of point clouds parameterization before explaining some relevant concepts. According to the organization of the point clouds, we first divide point cloud parameterization methods into two groups: organized and unorganized ones. Since various methods for unorganized point cloud parameterization have been proposed, we further divide the group of unorganized point cloud parameterization methods into some subgroups based on the technique used for parameterization. The main ideas and properties of each method are discussed aiming to provide an overview of various methods and help with the selection of different methods for various applications
Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation
Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment
What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives
Intelligent Mesh Generation (IMG) represents a novel and promising field of
research, utilizing machine learning techniques to generate meshes. Despite its
relative infancy, IMG has significantly broadened the adaptability and
practicality of mesh generation techniques, delivering numerous breakthroughs
and unveiling potential future pathways. However, a noticeable void exists in
the contemporary literature concerning comprehensive surveys of IMG methods.
This paper endeavors to fill this gap by providing a systematic and thorough
survey of the current IMG landscape. With a focus on 113 preliminary IMG
methods, we undertake a meticulous analysis from various angles, encompassing
core algorithm techniques and their application scope, agent learning
objectives, data types, targeted challenges, as well as advantages and
limitations. We have curated and categorized the literature, proposing three
unique taxonomies based on key techniques, output mesh unit elements, and
relevant input data types. This paper also underscores several promising future
research directions and challenges in IMG. To augment reader accessibility, a
dedicated IMG project page is available at
\url{https://github.com/xzb030/IMG_Survey}
Natural Parameterization
The objective of this project has been to develop an approach for imitating physical objects with an underlying stochastic variation. The key assumption is that a set of ânatural parametersâ can be extracted by a new subdivision algorithm so they reflect what is called the objectâs âgeometric DNAâ. A case study on one hundred wheat grain crosssections (Triticum aestivum) showed that it was possible to extract thirty-six such parameters and to reuse them for Monte Carlo simulation of ânewâ stochastic phantoms which possessthe same stochastic behavior as the âoriginalâ cross-sections
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 visitorsâ 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.
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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
Understanding the Structure of 3D Shapes
Compact representations of three dimensional objects are very often used
in computer graphics to create effective ways to analyse, manipulate and
transmit 3D models. Their ability to abstract from the concrete shapes and
expose their structure is important in a number of applications, spanning
from computer animation, to medicine, to physical simulations. This thesis
will investigate new methods for the generation of compact shape representations.
In the first part, the problem of computing optimal PolyCube base
complexes will be considered. PolyCubes are orthogonal polyhedra used
in computer graphics to map both surfaces and volumes. Their ability to
resemble the original models and at the same time expose a very simple and
regular structure is important in a number of applications, such as texture
mapping, spline fitting and hex-meshing. The second part will focus on
medial descriptors. In particular, two new algorithms for the generation
of curve-skeletons will be presented. These methods are completely based
on the visual appearance of the input, therefore they are independent from
the type, number and quality of the primitives used to describe a shape,
determining, thus, an advancement to the state of the art in the field
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