145 research outputs found
3D mesh metamorphosis from spherical parameterization for conceptual design
Engineering product design is an information intensive decision-making
process that consists of several phases including design specification
definition, design concepts generation, detailed design and analysis,
and manufacturing. Usually, generating geometry models for
visualization is a big challenge for early stage conceptual design.
Complexity of existing computer aided design packages constrains
participation of people with various backgrounds in the design
process. In addition, many design processes do not take advantage of
the rich amount of legacy information available for new concepts
creation.
The research presented here explores the use of advanced graphical
techniques to quickly and efficiently merge legacy information with
new design concepts to rapidly create new conceptual product designs.
3D mesh metamorphosis framework 3DMeshMorpher was created to
construct new models by navigating in a shape-space of registered
design models. The framework is composed of: i) a fast spherical
parameterization method to map a geometric model (genus-0) onto a unit
sphere; ii) a geometric feature identification and picking technique
based on 3D skeleton extraction; and iii) a LOD controllable 3D
remeshing scheme with spherical mesh subdivision based on the
developedspherical parameterization. This efficient software framework
enables designers to create numerous geometric concepts in real time
with a simple graphical user interface.
The spherical parameterization method is focused on closed genus-zero
meshes. It is based upon barycentric coordinates with convex boundary.
Unlike most existing similar approaches which deal with each vertex in
the mesh equally, the method developed in this research focuses
primarily on resolving overlapping areas, which helps speed the
parameterization process. The algorithm starts by normalizing the
source mesh onto a unit sphere and followed by some initial relaxation
via Gauss-Seidel iterations. Due to its emphasis on solving only
challenging overlapping regions, this parameterization process is much
faster than existing spherical mapping methods.
To ensure the correspondence of features from different models, we
introduce a skeleton based feature identification and picking method
for features alignment. Unlike traditional methods that align single
point for each feature, this method can provide alignments for
complete feature areas. This could help users to create more
reasonable intermediate morphing results with preserved topological
features. This skeleton featuring framework could potentially be
extended to automatic features alignment for geometries with similar
topologies. The skeleton extracted could also be applied for other
applications such as skeleton-based animations.
The 3D remeshing algorithm with spherical mesh subdivision is
developed to generate a common connectivity for different mesh models.
This method is derived from the concept of spherical mesh subdivision.
The local recursive subdivision can be set to match the desired LOD
(level of details) for source spherical mesh. Such LOD is controllable
and this allows various outputs with different resolutions. Such
recursive subdivision then follows by a triangular correction process
which ensures valid triangulations for the remeshing. And the final
mesh merging and reconstruction process produces the remeshing model
with desired LOD specified from user. Usually the final merged model
contains all the geometric details from each model with reasonable
amount of vertices, unlike other existing methods that result in big
amount of vertices in the merged model. Such multi-resolution outputs
with controllable LOD could also be applied in various other computer
graphics applications such as computer games
Surface parameterization over regular domains
Surface parameterization has been widely studied and it has been playing a critical role in many geometric processing tasks in graphics, computer-aided design, visualization, vision, physical simulation and etc. Regular domains, such as polycubes, are favored due to their structural regularity and geometric simplicity. This thesis focuses on studying the surface parameterization over regular domains, i.e. polycubes, and develops effective computation algorithms. Firstly, the motivation for surface parameterization and polycube mapping is introduced. Secondly, we briefly review existing surface parameterization techniques, especially for extensively studied parameterization algorithms for topological disk surfaces and parameterizations over regular domains for closed surfaces. Then we propose a polycube parameterization algorithm for closed surfaces with general topology. We develop an efficient optimization framework to minimize the angle and area distortion of the mapping. Its applications on surface meshing, inter-shape morphing and volumetric polycube mapping are also discussed
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
Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D
Signal transduction and cell function are governed by the spatiotemporal
organization of membrane-associated molecules. Despite significant advances in
visualizing molecular distributions by 3D light microscopy, cell biologists
still have limited quantitative understanding of the processes implicated in
the regulation of molecular signals at the whole cell scale. In particular,
complex and transient cell surface morphologies challenge the complete sampling
of cell geometry, membrane-associated molecular concentration and activity and
the computing of meaningful parameters such as the cofluctuation between
morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap
arbitrarily complex 3D cell surfaces and membrane-associated signals into
equivalent lower dimensional representations. The mappings are bidirectional,
allowing the application of image processing operations in the data
representation best suited for the task and to subsequently present the results
in any of the other representations, including the original 3D cell surface.
Leveraging this surface-guided computing paradigm, we track segmented surface
motifs in 2D to quantify the recruitment of Septin polymers by blebbing events;
we quantify actin enrichment in peripheral ruffles; and we measure the speed of
ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D
provides access to spatiotemporal analyses of cell biological parameters on
unconstrained 3D surface geometries and signals.Comment: 49 pages, 10 figure
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}
Non-rigid registration of 2-D/3-D dynamic data with feature alignment
In this work, we are computing the matching between 2D manifolds and 3D manifolds with temporal constraints, that is we are computing the matching among a time sequence of 2D/3D manifolds. It is solved by mapping all the manifolds to a common domain, then build their matching by composing the forward mapping and the inverse mapping. At first, we solve the matching problem between 2D manifolds with temporal constraints by using mesh-based registration method. We propose a surface parameterization method to compute the mapping between the 2D manifold and the common 2D planar domain. We can compute the matching among the time sequence of deforming geometry data through this common domain. Compared with previous work, our method is independent of the quality of mesh elements and more efficient for the time sequence data. Then we develop a global intensity-based registration method to solve the matching problem between 3D manifolds with temporal constraints. Our method is based on a 4D(3D+T) free-from B-spline deformation model which has both spatial and temporal smoothness. Compared with previous 4D image registration techniques, our method avoids some local minimum. Thus it can be solved faster and achieve better accuracy of landmark point predication. We demonstrate the efficiency of these works on the real applications. The first one is applied to the dynamic face registering and texture mapping. The second one is applied to lung tumor motion tracking in the medical image analysis. In our future work, we are developing more efficient mesh-based 4D registration method. It can be applied to tumor motion estimation and tracking, which can be used to calculate the read dose delivered to the lung and surrounding tissues. Thus this can support the online treatment of lung cancer radiotherapy
Geometric modeling and optimization over regular domains for graphics and visual computing
The effective construction of parametric representation of complicated geometric objects can facilitate many design, analysis, and simulation tasks in Computer-Aided Design (CAD), Computer-Aided Manufacturing (CAM), and Computer-Aided Engineering (CAE). Given a 3D shape, the procedure of finding such a parametric representation upon a canonical domain is called geometric parameterization. Regular geometric regions, such as polycubes and spheres, are desirable domains for parameterization. Parametric representations defined upon regular geometric domains have many desirable mathematical properties and can facilitate or simplify various surface/solid modeling and processing computation. This dissertation studies the construction of parameterization on regular geometric domains and explores their applications in shape modeling and computer-aided design. Specifically, we studies (1) the surface parameterization on the spherical domain for closed genus-zero surfaces; (2) the surface parameterization on the polycube domain for general closed surfaces; and (3) the volumetric parameterization for 3D-manifolds embedded in 3D Euclidean space. We propose novel computational models to solve these geometric problems. Our computational models reduce to nonlinear optimizations with various geometric constraints. Hence, we also need to explore effective optimization algorithms. The main contributions of this dissertation are three-folded. (1) We developed an effective progressive spherical parameterization algorithm, with an efficient nonlinear optimization scheme subject to the spherical constraint. Compared with the state-of-the-art spherical mapping algorithms, our algorithm demonstrates the advantages of great efficiency, lower distortion, and guaranteed bijectiveness, and we show its applications in spherical harmonic decomposition and shape analysis. (2) We propose a first topology-preserving polycube domain optimization algorithm that simultaneously optimizes polycube domain together with the parameterization to balance the mapping distortion and domain simplicity. We develop effective nonlinear geometric optimization algorithms dealing with variables with and without derivatives. This polycube parameterization algorithm can benefit the regular quadrilateral mesh generation and cross-surface parameterization. (3) We develop a novel quaternion-based optimization framework for 3D frame field construction and volumetric parameterization computation. We demonstrate our constructed 3D frame field has better smoothness, compared with state-of-the-art algorithms, and is effective in guiding low-distortion volumetric parameterization and high-quality hexahedral mesh generation
A Comparative Study on Polygonal Mesh Simplification Algorithms
Polygonal meshes are a common way of representing three dimensional surface models in many different areas of computer graphics and geometry processing. However, with the evolution of the technology, polygonal models are becoming more and more complex. As the complexity of the models increase, the visual approximation to the real world objects get better but there is a trade-off between the cost of processing these models and better visual approximation. In order to reduce this cost, the number of polygons in a model can be reduced by mesh simplification algorithms. These algorithms are widely used such that nearly all of the popular mesh editing libraries include at least one of them. In this work, polygonal simplification algorithms that are embedded in open source libraries: CGAL, VTK and OpenMesh are compared with the Metro geometric error measuring tool. By this way we try to supply a guidance for developers for publicly available mesh libraries in order to implement polygonal mesh simplification
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