Mesh Embedding Research Articles

Visible watermarking for 3D models based on 3D Boolean operation

With the continuous expansion of the application field of 3D models and the convenience of model storage, transmission, and replication, the problems of illegal reproduction, illegal modification, and embezzlement faced by 3D models are gradually becoming severe, which has brought substantial economic losses to the producers of 3D models. Therefore, this study aims to develop a visible watermarking method for 3D model using 3D Boolean operation. First, based on TrueType font library, the 3D model of the watermark is generated through the extraction, positioning and combination of character outline. Next, the spatial registration between the watermark model and the 3D model was carried out according to the embedding position of the watermark. Finally, based on multiple 3D Boolean operations, the copyright information of the 3D watermark model is embedded into the 3D model in various modes, such as embossing, debossing, and surface mesh embedding. The experiments demonstrate that the method of this paper supports embedding watermark information in B-rep, CSG, and voxel models. This method can readily support business applications for visible watermarking of 3D models and has laid a good foundation for researching multipurpose 3D model watermarking algorithms supporting copyright notification and protection.

Effects of coal bedding dip angle on hydraulic fracturing crack propagation

As a commonly used and effective technology for increasing the permeability of coal–rock reservoirs, hydraulic fracturing has been widely used in engineering sites to realize the efficient exploitation and utilization of gas resources in coal–rock reservoirs. The core of hydraulic fracturing is the initiation, propagation, and path of hydraulic cracks. In this paper, the combination of true triaxial physical test and numerical simulation is used to study the influence of coal bedding characteristics on the crack propagation of hydraulic fracturing and to discuss the important role of bedding in hydraulic crack formation. Results show that the control effect of the coal bedding dip angle on the hydraulic crack propagation under the same stress conditions is stronger than that of the maximum principal stress, and the control effect of the bedding on the crack propagation is weaker under the bedding dip angles of 0° and 90°. Reasonable fracturing fluid displacement setting is conducive to the formation of complex hydraulic fracture network structure, small displacement is conducive to the opening of primary natural fractures, and large displacement is conducive to hydraulic cracks that pass through the structural surface and the coal–rock interface. Global and local methods of finite element mesh embedding zero-thickness cohesion element and a pore-pressure node merging method to simulate fracturing are established using Python language and ABAQUS numerical analysis platform, respectively. The numerical simulation results suggest that the main fractures are formed along the principal stress direction, and the secondary branch fractures are formed along the bedding direction under the condition wherein the coal bedding dip angle is 30°. Under the conditions of different stress fields and fracturing fluid discharges, the controlling effect of bedding on hydraulic fracture is closely related to the fracturing parameters.

Realtime Simulation of Thin-Shell Deformable Materials Using CNN-Based Mesh Embedding

We address the problem of accelerating thin-shell deformable object simulations by dimension reduction. We present a new algorithm to embed a high-dimensional configuration space of deformable objects in a low-dimensional feature space, where the configurations of objects and feature points have approximate one-to-one mapping. Our key technique is a graph-based convolutional neural network (CNN) defined on meshes with arbitrary topologies and a new mesh embedding approach based on physics-inspired loss term. We have applied our approach to accelerate high-resolution thin shell simulations corresponding to cloth-like materials, where the configuration space has tens of thousands of degrees of freedom. We show that our physics-inspired embedding approach leads to higher accuracy compared with prior mesh embedding methods. Finally, we show that the temporal evolution of the mesh in the feature space can also be learned using a recurrent neural network (RNN) leading to fully learnable physics simulators. After training our learned simulator runs $500-10000\times$ faster and the accuracy is high enough for robot manipulation tasks.

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes

SummaryThis work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large‐scale sampling‐based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right‐hand side. The stochastic PDE is discretized using the mixed finite element method on an embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. We demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large‐scale 3D MLMC simulations with up to 1.9·109 unknowns.

Stable Real-Time Surgical Cutting Simulation of Deformable Objects Embedded with Arbitrary Triangular Meshes

Surgical simulators need to simulate deformation and cutting of deformable objects. Adaptive octree mesh based cutting methods embed the deformable objects into octree meshes that are recursively refined near the cutting tool trajectory. Deformation is only applied to the octree meshes; thus the deformation instability problem caused by degenerated elements is avoided. Biological tissues and organs usually contain complex internal structures that are ignored by previous work. In this paper the deformable objects are modeled as voxels connected by links and embedded inside adaptive octree meshes. Links swept by the cutting tool are disconnected and object surface meshes are reconstructed from disconnected links. Two novel methods for embedding triangular meshes as internal structures are proposed. The surface mesh embedding method is applicable to arbitrary triangular meshes, but these meshes have no physical properties. The material sub-region embedding method associates the interiors enclosed by the triangular meshes with physical properties, but requires that these meshes are watertight, and have no self-intersections, and their smallest features are larger than a voxel. Some local features are constructed in a pre-calculation stage to increase simulation performance. Simulation tests show that our methods can cut embedded structures in a way consistent with the cutting of the deformable objects. Cut fragments can also deform correctly along with the deformable objects.

Foldover-Free Mesh Warping for Constrained Texture Mapping.

Mapping texture onto 3D meshes with positional constraints is a popular technique that can effectively enhance the visual realism of geometric models. Such a process usually requires constructing a valid mesh embedding satisfying a set of positional constraints, which is known to be a challenging problem. This paper presents a novel algorithm for computing a foldover-free piecewise linear mapping with exact positional constraints. The algorithm begins with an unconstrained planar embedding, followed by iterative constrained mesh transformations. At the heart of the algorithm are radial basis function (RBF)-based warping and the longest edge bisection (LEB)-based refinement. A delicate integration of the RBF-based warping and the LEB-based refinement provides a provably-foldover-free, smooth constrained mesh warping, which can handle a large number of constraints and output a visually pleasing mapping result without extra smoothing optimization. The experiments demonstrate the effectiveness of the proposed algorithm.

3-D Printed Microwave Patch Antenna via Fused Deposition Method and Ultrasonic Wire Mesh Embedding Technique

In this work, the design, fabrication and characterization of a 3-D printed microwave patch antenna is presented. The antenna is fabricated by combining fused filament fabrication method for the dielectric part and ultrasonic metal wire mesh embedding approach for the conductor part. Full wave finite-element simulations for different wire mesh structures and also the entire antenna have been done to make sure the embedded wire mesh has good performance at microwave frequency. A microstrip patch antenna working around 7.5 GHz is printed and characterized to demonstrate the efficiency and accuracy of this technique. The measured reflection coefficient shows a good resonance peak at 7.5 GHz. The measured gain of this antenna is 5.5 dB at the resonance frequency. Good agreement between simulation and measurement is obtained in both reflection coefficient and radiation pattern.

Anisotropic geodesics for live‐wire mesh segmentation

AbstractWe present an interactive method for mesh segmentation that is inspired by the classical live‐wire interaction for image segmentation. The core contribution of the work is the definition and computation of wires on surfaces that are likely to lie at segment boundaries. We define wires as geodesics in a new tensor‐based anisotropic metric, which improves upon previous metrics in stability and feature‐awareness. We further introduce a simple but effective mesh embedding approach that allows geodesic paths in an anisotropic path to be computed efficiently using existing algorithms designed for Euclidean geodesics. Our tool is particularly suited for delineating segmentation boundaries that are aligned with features or curvature directions, and we demonstrate its use in creating artist‐guided segmentations.

Embedding meshes into twisted-cubes

The n-dimensional twisted-cube, TN n , is a variation of the hypercube. In this paper, we study embedding of meshes into TN n . We prove three major results in this paper: (1) For any integer n ⩾ 1, a 2 × 2 n−1 mesh can be embedded into TN n with dilation 1 and expansion 1. (2) For any integer n ⩾ 4, an m × k( m ⩾ 3, k ⩾ 3) mesh cannot be embedded into TN n with dilation 1. (3) For any integer n ⩾ 4, two node-disjoint 4 × 2 n−3 meshes can be embedded into TN n with dilation 2 and expansion 1.

Embedding meshes into locally twisted cubes

As a newly introduced interconnection network for parallel computing, the locally twisted cube possesses many desirable properties. In this paper, mesh embeddings in locally twisted cubes are studied. Let LTQ n ( V, E) denote the n-dimensional locally twisted cube. We present three major results in this paper: (1) For any integer n ⩾ 1, a 2 × 2 n−1 mesh can be embedded in LTQ n with dilation 1 and expansion 1. (2) For any integer n ⩾ 4, two node-disjoint 4 × 2 n−3 meshes can be embedded in LTQ n with dilation 1 and expansion 2. (3) For any integer n ⩾ 3, a 4 × (2 n−2 − 1) mesh can be embedded in LTQ n with dilation 2. The first two results are optimal in the sense that the dilations of all embeddings are 1. The embedding of the 2 × 2 n−1 mesh is also optimal in terms of expansion. We also present the analysis of 2 p × 2 q mesh embedding in locally twisted cubes.

Topology and Geometry of Hexahedral Complex: Combined Approach for Hexahedral Meshing

In present paper a new approach for hexahedral mesh generation is suggested. The process of hexahedral mesh generation for an arbitrary volume is an open subject. Two main stages exist: determining topological connectivity of the mesh and its geometrical embedding. There are many interesting solutions proposed in various methods, which mostly rely on topological validity of the mesh. Nevertheless, the final quality of the mesh strongly depends on the step of mesh embedding, which has direct connection with geometry of the mesh and shapes of the elements. In order to generate hexahedral meshes topologically valid and geometrically qualitative, we propose a new guide for hexahedral meshing that combines both geometrical and topological aspects of hexahedral complex, which is to be generated. This guide includes topological construction of the spine of three-manifold and encoding with a matrix of incidence based on curvature information.

Embedding of meshes in Möbius cubes

The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. Möbius cubes form a class of hypercube variants that give better performance with the same number of edges and vertices. In this paper, we consider embedding of meshes in Möbius cubes. The main results obtained in this paper are: (1) For n ≥ 1 , there exists a 2 × 2 n − 1 mesh that can be embedded in the n -dimensional Möbius cube with dilation 1 and expansion 1. (2) For n ≥ 4 , there exists a 4 × 2 n − 2 mesh that can be embedded in the n -dimensional Möbius cube with dilation 2 and expansion 1. (3) For n ≥ 4 , there are two disjoint 4 × 2 n − 3 meshes that can be embedded in the 0-type n -dimensional Möbius cube with dilation 1. (4) For n ≥ 4 , there are two disjoint 4 × 2 n − 3 meshes that can be embedded in the 1-type n -dimensional Möbius cube with dilation 2. Results of (1) and (3) are optimal in the sense that the dilations of the embeddings are 1.

Texture Mapping with Hard Constraints Using Warping Scheme

Texture mapping with positional constraints is an important and challenging problem in computer graphics. In this paper, we first present a theoretically robust, foldover-free 2D mesh warping algorithm. Then we apply this warping algorithm to handle mapping texture onto 3D meshes with hard constraints. The proposed algorithm is experimentally evaluated and compared with the state-of-the-art method for examples with more challenging constraints. These challenging constraints may lead to large distortions and foldovers. Experimental results show that the proposed scheme can generate more pleasing results and add fewer Steiner vertices on the 3D mesh embedding.

Embedding meshes into crossed cubes

Crossed cubes are important variants of hypercubes. In this paper, we consider embeddings of meshes in crossed cubes. The major research findings in this paper are: (1) For any integer n ⩾ 1, a 2 × 2 n−1 mesh can be embedded in the n-dimensional crossed cube with dilation 1 and expansion 1. (2) For any integer n ⩾ 4, two node-disjoint 4 × 2 n−3 meshes can be embedded in the n-dimensional crossed cube with dilation 1 and expansion 2. The obtained results are optimal in the sense that the dilations of the embeddings are 1. The embedding of the 2 × 2 n−1 mesh is also optimal in terms of expansion because it has the smallest expansion 1.

Efficient simulation of blood flow past complex endovascular devices using an adaptive embedding technique

The simulation of blood flow past endovascular devices such as coils and stents is a challenging problem due to the complex geometry of the devices. Traditional unstructured grid computational fluid dynamics relies on the generation of finite element grids that conform to the boundary of the computational domain. However, the generation of such grids for patient-specific modeling of cerebral aneurysm treatment with coils or stents is extremely difficult and time consuming. This paper describes the application of an adaptive grid embedding technique previously developed for complex fluid structure interaction problems to the simulation of endovascular devices. A hybrid approach is used: the vessel walls are treated with body conforming grids and the endovascular devices with an adaptive mesh embedding technique. This methodology fits naturally in the framework of image-based computational fluid dynamics and opens the door for exploration of different therapeutic options and personalization of endovascular procedures.

A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations

Mesh refinement is desirable for an advantageous use of the finite-difference time-domain (FDTD) solution method of Maxwell’s equations, because higher spatial resolutions, i.e., increased mesh densities, are introduced only in sub-regions where they are really needed, thus preventing computer resources wasting. However, the introduction of high density meshes in the FDTD method is recognized as a source of troubles as far as stability and accuracy are concerned, a problem which is currently dealt with by recursion, i.e., by nesting meshes with a progressively increasing resolution. Nevertheless, such an approach unavoidably raises again the computational burden. In this paper we propose a non-recursive three-dimensional (3-D) algorithm that works with straight embedding of fine meshes into coarse ones which have larger space steps, in each direction, by a factor of 5 or more, while maintaining a satisfactory stability and accuracy. The algorithm is tested against known analytical solutions.

Topological properties of OTIS-networks

We conduct a general study of the topological properties of optical transpose interconnection systems (OTIS). We first obtain their basic topological metrics of size, degree, shortest distance and diameter, and then we obtain results related to the recursive structure and efficient embedding of meshes, cubes, spanning trees and cycles. We also present minimal one-to-one routing and optimal broadcasting algorithms, and we show how to construct node-disjoint paths between any two nodes of an OTIS network. Recent studies have addressed only particular members of the general class of OTIS networks. In this paper, we present unified tools for obtaining the topological properties of an arbitrary OTIS network based on the properties of the corresponding factor network.

Block-cyclic matrix triangulation on the Cartesian product of star graphs

The star graph has drawn a lot of attention recently as an attractive alternative to hypercube. Due to its reduced diameter, the star graph theoretically supports more efficient communication than popular networks such as the hypercube and the mesh. However, practically only limited results have been obtained related to the design of parallel algorithms on the star graph. By its own nature, the star graph seems to be inadequate for certain types of algorithms especially those based on matrix computations. Furthermore, no efficient embeddings of hypercubes or meshes in the star graph are known, which would (had they existed) allow us to simulate the corresponding hypercube or mesh algorithms. In this paper, we show how to overcome these difficulties with the star graph while allowing to take advantage of its communication capabilities. We propose to consider the Cartesian product of star graphs as interconnection networks and we design and evaluate block-cyclic matrix triangulation on these networks. We demonstrate how such star graph based Cartesian product networks are more suitable for real applications than traditional star graphs, while inheriting the theoretically established communication efficiency of star graphs. We present a framework for practical implementation of block-cyclic matrix triangulation on the Cartesian product of star graphs along with a performance evaluation and comparison with other topologies. The proposed techniques for matrix decomposition and mapping are of general use and can be applied to design other matrixbased algorithms on the Cartesian product of star graphs.

Two-Dimensional Mesh Embedding for B-spline Methods

Many factors motivate consideration of B-splines as basis functions for solving partial differential equations. These are arbitrary orders of accuracy and high resolving powers similar to those of compact schemes. Furthermore, if one uses a Galerkin scheme one gets, in addition to conservation of the discretized quantities, conservation of quadratic invariants such as energy. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. An algorithm is presented for constructing a global spline basis that automatically hasd-1 continuous derivatives at mesh-block boundaries as everywhere else (heredis the polynomial degree). The basis functions are simply suitable products of one-dimensional B-splines. Both integer and noninteger refinement ratios are allowed across mesh blocks. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented.

The Hyperstar Interconnection Network

In this paper, a multiprocessor interconnection topology, the hyperstar, based on the Cartesian product of star graphs is studied. The basic properties of the hyperstar are discussed and proved. This includes reduced degree and diameter, hierarchical structure, vertex symmetry, optimal routing, and shortest path characterization. The hyperstar is shown to be a member of the Cayley class of symmetric graphs. Embeddings of hypercubes, star graphs, and meshes are discussed. An optimal one-to-all broadcasting algorithm is obtained and analyzed. Some results on fault tolerance, parallel paths, Hamiltonian cycles, and VLSI layouts are obtained. Furthermore, a comparative study between the hyperstar and seven related networks is conducted. The comparison is based on scalability, broadcasting cost, link requirements, cost/performance ratio, and other static parameters such as degree, diameter, and average diameter.