1,619 research outputs found
A geometric mesh smoothing algorithm related to damped oscillations
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral
and hexahedral meshes whose centerpiece is a simple geometric triangle
transformation. The first part focuses on the mathematical properties of the
element transformation. In particular, the transformation gives rise directly
to a continuous model given by a system of coupled damped oscillations. Derived
from this physical model, adaptive parameters are introduced and their benefits
presented. The second part discusses the mesh smoothing algorithm based on the
element transformation and its numerical performance on example meshes.Comment: 35 pages, 16 figure
T-spline based unifying registration procedure for free-form surface workpieces in intelligent CMM
With the development of the modern manufacturing industry, the free-form surface is widely used in various fields, and the automatic detection of a free-form surface is an important function of future intelligent three-coordinate measuring machines (CMMs). To improve the intelligence of CMMs, a new visual system is designed based on the characteristics of CMMs. A unified model of the free-form surface is proposed based on T-splines. A discretization method of the T-spline surface formula model is proposed. Under this discretization, the position and orientation of the workpiece would be recognized by point cloud registration. A high accuracy evaluation method is proposed between the measured point cloud and the T-spline surface formula. The experimental results demonstrate that the proposed method has the potential to realize the automatic detection of different free-form surfaces and improve the intelligence of CMMs
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
HybridOctree_Hex: Hybrid Octree-Based Adaptive All-Hexahedral Mesh Generation with Jacobian Control
We present a new software package, "HybridOctree_Hex," for adaptive
all-hexahedral mesh generation based on hybrid octree and quality improvement
with Jacobian control. The proposed HybridOctree_Hex begins by detecting
curvatures and narrow regions of the input boundary to identify key surface
features and initialize an octree structure. Subsequently, a strongly balanced
octree is constructed using the balancing and pairing rules. Inspired by our
earlier preliminary hybrid octree-based work, templates are designed to
guarantee an all-hexahedral dual mesh generation directly from the strongly
balanced octree. With these pre-defined templates, the sophisticated hybrid
octree construction step is skipped to achieve an efficient implementation.
After that, elements outside and around the boundary are removed to create a
core mesh. The boundary points of the core mesh are connected to their
corresponding closest points on the surface to fill the buffer zone and build
the final mesh. Coupled with smart Laplacian smoothing, HybridOctree_Hex takes
advantage of a delicate optimization-based quality improvement method
considering geometric fitting, Jacobian and scaled Jacobian, to achieve a
minimum scaled Jacobian that is higher than . We empirically verify the
robustness and efficiency of our method by running the HybridOctree_Hex
software on dozens of complex 3D models without any manual intervention or
parameter adjustment. We provide the HybridOctree_Hex source code, along with
comprehensive results encompassing the input and output files and statistical
data in the following repository: https://github.com/CMU-CBML/HybridOctree_Hex
On a general implementation of - and -adaptive curl-conforming finite elements
Edge (or N\'ed\'elec) finite elements are theoretically sound and widely used
by the computational electromagnetics community. However, its implementation,
specially for high order methods, is not trivial, since it involves many
technicalities that are not properly described in the literature. To fill this
gap, we provide a comprehensive description of a general implementation of edge
elements of first kind within the scientific software project FEMPAR. We cover
into detail how to implement arbitrary order (i.e., -adaptive) elements on
hexahedral and tetrahedral meshes. First, we set the three classical
ingredients of the finite element definition by Ciarlet, both in the reference
and the physical space: cell topologies, polynomial spaces and moments. With
these ingredients, shape functions are automatically implemented by defining a
judiciously chosen polynomial pre-basis that spans the local finite element
space combined with a change of basis to automatically obtain a canonical basis
with respect to the moments at hand. Next, we discuss global finite element
spaces putting emphasis on the construction of global shape functions through
oriented meshes, appropriate geometrical mappings, and equivalence classes of
moments, in order to preserve the inter-element continuity of tangential
components of the magnetic field. Finally, we extend the proposed methodology
to generate global curl-conforming spaces on non-conforming hierarchically
refined (i.e., -adaptive) meshes with arbitrary order finite elements.
Numerical results include experimental convergence rates to test the proposed
implementation
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}
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