Optimal Embedding of Multiple Directed Hamiltonian Rings into d-dimensional Meshes

In this paper, we consider the embedding of multiple directed Hamiltonian rings into d-dimensional meshes M_d. Assuming two adjacent nodes in M_d are connected by two directed links with opposite directions, we aim to embed as many directed Hamiltonian rings as possible in a way that they are link-disjoint. In particular, we construct d link-disjoint directed Hamiltonian rings in d-dimensional N₁×…×N_d mesh, where each N_i⩾2d is even.     

Embedding Meshes on the Star Graph

We develop algorithms for mapping n-dimensional meshes on a star graph of degree n with expansion 1 and dilation 3. We show that an n-degree star graph can efficiently simulate an n-dimensional mesh.     

Valence-Driven Connectivity Encoding for 3D Meshes

In this paper, we propose a valence-driven, single-resolution encoding technique for lossless compression of triangle mesh connectivity. Building upon a valence-based approach pioneered by Touma and Gotsman²² , we design a new valence-driven conquest for arbitrary meshes that always guarantees smaller compression rates than the original method. Furthermore, we provide a novel theoretical entropy study of our technique, hinting the optimality of the valence-driven approach. Finally, we demonstrate the practical efficiency of this approach (in agreement with the theoretical prediction) on a series of test meshes, resulting in the lowest compression ratios published so far, for both irregular and regular meshes, small or large.     

Embedding a family of disjoint 3D meshes into a crossed cube

Crossed cubes are an important class of hypercube variants. This paper addresses how to embed a family of disjoint 3D meshes into a crossed cube. Two major contributions of this paper are: (1) for n?4, a family of two disjoint 3D meshes of size 2×2×2^n-3 can be embedded in an n-D crossed cube with unit dilation and unit expansion, and (2) for n?6, a family of four disjoint 3D meshes of size 4×2×2^n-5 can be embedded in an n-D crossed cube with unit dilation and unit expansion. These results mean that a family of two or four 3D-mesh-structured parallel algorithms can be executed on a same crossed cube efficiently and in parallel. Our work extends the results recently obtained by Fan and Jia [J. Fan, X. Jia, Embedding meshes into crossed cubes, Information Sciences 177(15) (2007) 3151-3160].     

Optimized Topological Surgery for Unfolding 3D Meshes

Constructing a 3D papercraft model from its unfolding has been fun for both children and adults since we can reproduce virtual 3D models in the real world. However, facilitating the papercraft construction process is still a challenging problem, especially when the shape of the input model is complex in the sense that it has large variation in its surface curvature. This paper presents a new heuristic approach to unfolding 3D triangular meshes without any shape distortions, so that we can construct the 3D papercraft models through simple atomic operations for gluing boundary edges around the 2D unfoldings. Our approach is inspired by the concept of topological surgery, where the appearance of boundary edges of the unfolded closed surface can be encoded using a symbolic representation. To fully simplify the papercraft construction process, we developed a genetic‐based algorithm for unfolding the 3D mesh into a single connected patch in general, while optimizing the usage of the paper sheet and balance in the shape of that patch. Several examples together with user studies are included to demonstrate that the proposed approach works well for a broad range of 3D triangular meshes.     

Interactive Planarization and Optimization of 3D Meshes

Constraining 3D meshes to restricted classes is necessary in architectural and industrial design, but it can be very challenging to manipulate meshes while staying within these classes. Specifically, polyhedral meshes—those having planar faces—are very important, but also notoriously difficult to generate and manipulate efficiently. We describe an interactive method for computing, optimizing and editing polyhedral meshes. Efficiency is achieved thanks to a numerical procedure combining an alternating least‐squares approach with the penalty method. This approach is generalized to manipulate other subsets of polyhedral meshes, as defined by a variety of other constraints.     

三维有限元网格的快速显示

应用OpengGL三维图形库,结合三维有限元网格的特点,提出了一种方便,实用的三维有限元网格的快速消隐显示方法,使得三维图形显示速度大为提高,并对显示中出现的网格线间断、缺线问题提出了相应的解决措施。     

不规则三维网格纹理映射的均匀化

采用单一纹理对不规则三维网格进行纹理映射,常常使网格密集处映射不足;而采用纹理地图集方法又使映射过程变得复杂。因此文章提出一种新的方法:通过离散保角变换方法,先将三维网格无遮挡地映射到平面正方形中,随后通过一种离散均匀面积变换方法,使其平面网格较均匀地分布,然后求得其纹理坐标,从而有效实现不规则三维网格的纹理映射。该方法算法快速、稳定,纹理映射均匀化效果良好。     

Approximate Symmetry Detection in Partial 3D Meshes

Symmetry is a common characteristic in natural and man‐made objects. Its ubiquitous nature can be exploited to facilitate the analysis and processing of computational representations of real objects. In particular, in computer graphics, the detection of symmetries in 3D geometry has enabled a number of applications in modeling and reconstruction. However, the problem of symmetry detection in incomplete geometry remains a challenging task. In this paper, we propose a vote‐based approach to detect symmetry in 3D shapes, with special interest in models with large missing parts. Our algorithm generates a set of candidate symmetries by matching local maxima of a surface function based on the heat diffusion in local domains, which guarantee robustness to missing data. In order to deal with local perturbations, we propose a multi‐scale surface function that is useful to select a set of distinctive points over which the approximate symmetries are defined. In addition, we introduce a vote‐based scheme that is aware of the partiality, and therefore reduces the number of false positive votes for the candidate symmetries. We show the effectiveness of our method in a varied set of 3D shapes and different levels of partiality. Furthermore, we show the applicability of our algorithm in the repair and completion of challenging reassembled objects in the context of cultural heritage.     

基于骨架的三维网格局部编辑

复杂网格的编辑是三维动画设计的关键技术,已经出现了多种比较成功的方案和算法。在研究了三维网格的骨架生成及其优化方法的基础上,提出了一种基于骨架的局部网格编辑算法。先由用户确定编辑区域,绘出与变形后的骨架相对应的编辑曲线,再根据网格顶点与骨架曲线及编辑曲线之间的对应关系,实现网格结点的平移和旋转等编辑操作。实验证明,该算法的实现具有编辑直观、易于控制等特点,能够很好地应用于网格的局部特征编辑。     

曲面浅浮雕生成算法

为了在三维网格上快速生成曲面浅浮雕造型,提出一种利用三维模型半自动生成曲面浅浮雕的算法.首先利用图像的边缘检测方法来获取模型在透视场景中的边缘点,并将其与被贴的曲面载体进行位置匹配,获得Poisson方程的Dirichlet边界值;然后对模型高度场的梯度值进行压缩;最后利用确定边界条件的Poisson方程对模型压缩后的梯度场进行求解,还原生成浮雕模型.利用文中算法可以生成贴于曲面上的浅浮雕模型.     

Optimally Embedding 3-Ary n-Cubes into Grids

Journal of Computer Science and Technology - The 3-ary n-cube, denoted as $$ {Q}_n^3 $$ , is an important interconnection network topology proposed for parallel computers, owing to its many...     

Reconstruction of 3D Object Meshes from Silhouette Images

In this work we propose a method for computing mesh representations of 3D objects reconstructed from a set of silhouette images. Our method is based on the polygonization of volumetric reconstructions by using a modified version of the dual contouring method. In order to apply dual contouring on volumetric reconstruction from silhouettes we devised a method that is able to determine the discrete topology of the surface in relation to the octree cells. We also developed a new scheme for computing hermitian data representing the intersections of conic volumes with the octree cells and their corresponding normals with subpixel accuracy. Due to the discrete and extremely noisy nature of the data used in the reconstruction we had to devise a different criterion for mesh simplification that applies topological consistency tests only when the geometric error measure is beyond a given tolerance. We present results of the application of the proposed method in the extraction of a mesh corresponding to the surface of objects of a real scene.     

Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

We present a new two-step “intermediate mortar” approach that efficiently extends the Mortar Element Method (MEM) to 3D meshes with nonconforming discretizations. The technique utilizes projection matrices derived in 2D, thereby avoiding the need to explicitly form large matrices for the 3D cases. The method also allows more flexibility for both h- and p-type adaptation. Parallel implementations with OpenMP and multithreading compiler directives are used to solve a moving heat source problem on SGI Origin and Cray MTA machines. Numerical results demonstrate the advantages of adaptive nonconforming meshes with MEM over uniformly fine meshes.     

Seamless,Static Multi‐Texturing of 3D Meshes

In the context of 3D reconstruction, we present a static multi‐texturing system yielding a seamless texture atlas calculated by combining the colour information from several photos from the same subject covering most of its surface. These pictures can be provided by shooting just one camera several times when reconstructing a static object, or a set of synchronized cameras, when dealing with a human or any other moving object. We suppress the colour seams due to image misalignments and irregular lighting conditions that multi‐texturing approaches typically suffer from, while minimizing the blurring effect introduced by colour blending techniques. Our system is robust enough to compensate for the almost inevitable inaccuracies of 3D meshes obtained with visual hull–based techniques: errors in silhouette segmentation, inherently bad handling of concavities, etc.     

Dilation-5 Embedding of 3-Dimensional Grids into Hypercubes

We present an algorithm to map the nodes of a 3-dimensional grid to the nodes of its optimal hypercube on a one-to-one basis with dilation at most 5.     

子分元素法:一种体网格压缩算法

提出了一个包含六面体,四面体,金字塔以及三棱柱单元的混合体网格的压缩与解压算法。首先对非四面体单元按照最小节点标号策略进行子分,然后利用修改的增长缝合算法压缩子分后的四面体网格,解压阶段再通过面删除操作来恢复原始网格。压缩后每个四面体约需10bits的存储,初步试验表明,对于通常的六面体网格,能将数据模型压缩至原先的1／4。     

All-To-All Personalized Communication in Wormhole-Routed 2D/3D Meshes and Multidimensional Interconnection Networks

2004.29计算机工程与应用1INTRODUCTIONInamessage-passingmulti-computernetwork,processorsoftenneedtocommunicatewitheachotherforvariousrea-sons,suchasloadbalancing,eventsynchronization,anddataexchange.Basedonthenumberofsendingandreceivingpro-cessors,thesecommunicationscanbeclassifiedintocommuni-cationpatternssuchasone-to-one(unicast),one-to-many(multicast),one-to-all(broadcast),andall-to-all.Thenatureofthemessagetobesentcanbeclassifiedaspersonalizedornon-personalized.Theall-to-allpersonalized…