A modified Q4/Q4 element for topology optimization

Design variable and displacement fields are distinct. Thus, their respective material and finite element meshes may also be distinct, as well as their actual location of nodes for the two fields. The proposed Q4/Q4M element possesses design variable nodes and displacement nodes which are not coincident. The element has been implemented using different approaches, including continuous approximation of material distribution and nodal approaches. The results obtained demonstrate that the element is effective in generating structural topologies with high resolution. From a numerical point of view, mesh independent solutions can be obtained by means of projection.     

Polygonal multiresolution topology optimization (PolyMTOP) for structural dynamics

We use versatile polygonal elements along with a multiresolution scheme for topology optimization to achieve computationally efficient and high resolution designs for structural dynamics problems. The multiresolution scheme uses a coarse finite element mesh to perform the analysis, a fine design variable mesh for the optimization and a fine density variable mesh to represent the material distribution. The finite element discretization employs a conforming finite element mesh. The design variable and density discretizations employ either matching or non-matching grids to provide a finer discretization for the density and design variables. Examples are shown for the optimization of structural eigenfrequencies and forced vibration problems.     

Selective refinement queries for volume visualization of unstructured tetrahedral meshes

We address the problem of the efficient visualization of large irregular volume data sets by exploiting a multiresolution model based on tetrahedral meshes. Multiresolution models, also called Level-Of-Detail (LOD) models, allow encoding the whole data set at a virtually continuous range of different resolutions. We have identified a set of queries for extracting meshes at variable resolution from a multiresolution model, based on field values, domain location, or opacity of the transfer function. Such queries allow trading off between resolution and speed in visualization. We define a new compact data structure for encoding a multiresolution tetrahedral mesh built through edge collapses to support selective refinement efficiently and show that such a structure has a storage cost from 3 to 5.5 times lower than standard data structures used for tetrahedral meshes. The data structures and variable resolution queries have been implemented together with state-of-the art visualization techniques in a system for the interactive visualization of three-dimensional scalar fields defined on tetrahedral meshes. Experimental results show that selective refinement queries can support interactive visualization of large data sets.     

Topology optimization using the p-version of the finite element method

A multiresolution topology optimization approach is proposed using the p-version finite element method (p-version FEM). Traditional topology optimization, where a density design variable is assigned to each element, is suitable for low-order h-version FEM. However, it cannot take advantage of the higher accuracy of higher-order p-version FEM analysis for generating results with higher resolution. In contrast, the proposed method separates density variables and finite elements so that the resolution of the density field, which defines the structure, can be higher than that of the finite element mesh. Thus, the method can take full advantage of the higher accuracy of p-version FEM.     

Cloth and Skin Deformation with a Triangle Mesh Based Convolutional Neural Network

We introduce a triangle mesh based convolutional neural network. The proposed network structure can be used for problems where input and/or output are defined on a manifold triangle mesh with or without boundary. We demonstrate its applications in cloth upsampling, adding back details to Principal Component Analysis (PCA) compressed cloth, regressing clothing deformation from character poses, and regressing hand skin deformation from bones' joint angles. The data used for training in this work are generated from high resolution extended position based dynamics (XPBD) physics simulations with small time steps and high iteration counts and from an offline FEM simulator, but it can come from other sources. The inference time of our prototype implementation, depending on the mesh resolution and the network size, can provide between 4 to 134 times faster than a GPU based simulator. The inference also only needs to be done for meshes currently visible by the camera.     

A computational paradigm for multiresolution topology optimization (MTOP)

This paper presents a multiresolution topology optimization (MTOP) scheme to obtain high resolution designs with relatively low computational cost. We employ three distinct discretization levels for the topology optimization procedure: the displacement mesh (or finite element mesh) to perform the analysis, the design variable mesh to perform the optimization, and the density mesh (or density element mesh) to represent material distribution and compute the stiffness matrices. We employ a coarser discretization for finite elements and finer discretization for both density elements and design variables. A projection scheme is employed to compute the element densities from design variables and control the length scale of the material density. We demonstrate via various two- and three-dimensional numerical examples that the resolution of the design can be significantly improved without refining the finite element mesh.     

Hierarchical Deformation of Locally Rigid Meshes

We propose a method for calculating deformations of models by deforming a low‐resolution mesh and adding details while ensuring that the details we add satisfy a set of constraints. Our method builds a low‐resolution representation of a mesh by using edge collapses and performs an as‐rigid‐as‐possible deformation on the simplified mesh. We then add back details by reversing edge‐collapses so that the shape of the mesh is locally preserved. While adding details, we deform the mesh to match the predicted positions of constraints so that constraints on the full‐resolution mesh are met. Our method operates on meshes with arbitrary triangulations, satisfies constraints over the full‐resolution mesh and converges quickly.     

Adaptive Compositing and Navigation of Variable Resolution Images

We present a new, high‐quality compositing pipeline and navigation approach for variable resolution imagery. The motivation of this work is to explore the use of variable resolution images as a quick and accessible alternative to traditional gigapixel mosaics. Instead of the common tedious acquisition of many images using specialized hardware, variable resolution images can achieve similarly deep zooms as large mosaics, but with only a handful of images. For this approach to be a viable alternative, the state‐of‐the‐art in variable resolution compositing needs to be improved to match the high‐quality approaches commonly used in mosaic compositing. To this end, we provide a novel, variable resolution mosaic seam calculation and gradient domain color correction. This approach includes a new priority order graph cuts computation along with a practical data structure to keep memory overhead low. In addition, navigating variable resolution images is challenging, especially at the zoom factors targeted in this work. To address this challenge, we introduce a new image interaction for variable resolution imagery: a pan that automatically, and smoothly, hugs available resolution. Finally, we provide several real‐world examples of our approach producing high‐quality variable resolution mosaics with deep zooms typically associated with gigapixel photography.     

Parallel algorithms for moving Lagrangian data on block structured Eulerian meshes

We present a suite of algorithms for migrating Lagrangian data between processors in a parallel environment when the underlying mesh is Eulerian. The collection of algorithms applies to both uniform and adaptive meshes. The algorithms are implemented in, and distributed with, FLASH, a publicly available multiphysics simulation code. Migrating Lagrangian data on an Eulerian mesh is non-trivial because the Eulerian grid points are spatially fixed whereas Lagrangian entities move with the flow of a simulation. Thus, the movement of Lagrangian data cannot use the data migration methods associated with the Eulerian mesh. Additionally, when the mesh is adaptive, as the simulation progresses the grid resolution changes. The resulting regridding process can cause complex Lagrangian data migration.The algorithms presented in this paper describe Lagrangian data movement on a static uniform mesh and on an adaptive octree based block-structured mesh. Some of the algorithms are general enough to be applicable to any block structured mesh, while some others exploit the meta-data and structure of PARAMESH, the adaptive mesh refinement (AMR) package used in FLASH. We also present an analysis of the algorithms’ comparative performances in different parallel environments, and different flow characteristics.     

Model-based human shape reconstruction from multiple views

Image-based modelling allows the reconstruction of highly realistic digital models from real-world objects. This paper presents a model-based approach to recover animated models of people from multiple view video images. Two contributions are made, a multiple resolution model-based framework is introduced that combines multiple visual cues in reconstruction. Second, a novel mesh parameterisation is presented to preserve the vertex parameterisation in the model for animation. A prior humanoid surface model is first decomposed into multiple levels of detail and represented as a hierarchical deformable model for image fitting. A novel mesh parameterisation is presented that allows propagation of deformation in the model hierarchy and regularisation of surface deformation to preserve vertex parameterisation and animation structure. The hierarchical model is then used to fuse multiple shape cues from silhouette, stereo and sparse feature data in a coarse-to-fine strategy to recover a model that reproduces the appearance in the images. The framework is compared to physics-based deformable surface fitting at a single resolution, demonstrating an improved reconstruction accuracy against ground-truth data with a reduced model distortion. Results demonstrate realistic modelling of real people with accurate shape and appearance while preserving model structure for use in animation.     

Adaptive Surface Texture Synthesis Using Round‐Shaped Neighbourhoods

This paper presents a novel surface texture synthesis method, which is capable of producing high‐quality results by performing the synthesis within an effective multi‐resolution scheme using an adaptive texture similarity metric. Compared with related works, our method allows us to directly carry out multi‐resolution synthesis without involving complicated operations such as mesh hierarchy and partitioning on the target surface. Also, the adaptive similarity metric focuses on measuring texture properties at different scales ranging from local to global, allowing for consistency within differently‐sized texture structures. Further, with the introduced round shaped neighbourhoods, we can save considerable amount of computation for the surface texture synthesis over variable texture directions. Experimental results are provided and comparisons are made against other latest works.     

Online Mesh Refinement for Parallel Atmospheric Models

Forecast precisions of climatological models are limited by computing power and time available for the executions. As more and faster processors are used in the computation, the resolution of the mesh adopted to represent the Earth’s atmosphere can be increased, and consequently the numerical forecast is more accurate. However, a finer mesh resolution, able to include local phenomena in a global atmosphere integration, is still not possible due to the large number of data elements to compute in this case. To overcome this situation, different mesh refinement levels can be used at the same time for different areas of the domain. Thus, our paper evaluates how mesh refinement at run time (online) can improve performance for climatological models.The online mesh refinement (OMR) increases dynamically mesh resolution in parts of a domain,when special atmosphere conditions are registered during the execution. Experimental results show that the execution of a model improved by OMR provides better resolution for the meshes, without any significant increase of execution time. The parallel performance of the simulations is also increased through the creation of threads in order to explore different levels of parallelism.     

基于视点的LOD绘制

基于迭代收缩算法（即PM算法）设计了一种新的多分辨率数据结构,给出了基于视点的模型多分辨率实时绘制方法,使得模型的分辨率可以随着视点位置的变化而变化,满足了观察者观察局部细节的要求。     

CPH: A Compact Representation for Hierarchical Meshes Generated by Primal Refinement

We present CPH (Compact Primal Hierarchy): a compact representation of the hierarchical connectivity of surface and volume manifold meshes generated through primal subdivision refinements. CPH is consistently defined in several dimensions and supports multiple kinds of tessellations and refinements, whether regular or adaptive. The basic idea is to store only the finest mesh, encoded in a classical monoresolution structure that is enriched with a minimal set of labels. These labels allow traversal of any intermediate level of the mesh concurrently without having to extract it in an additional structure. Our structure allows attributes to be stored on the cells not only on the finest level, but also on any intermediate level. We study the trade‐off between the memory cost of this compact representation and the time complexity of mesh traversals at any resolution level.     

一种新的多分辨率模型表示方法

提出了一种简洁高效的多分辨率模型表示方法MRM,该方法能对网格简化或精化过程进行编码,并在此基础上实现了一个多分辨率造型与编辑系统。该系统能为给定的模型生成多分辨率表示,并支持对模型的分辨率进行编辑,统一地完成有选择地精化和简化操作。     

Spectral Mesh Simplification

The spectrum of the Laplace-Beltrami operator is instrumental for a number of geometric modeling applications, from processing to analysis. Recently, multiple methods were developed to retrieve an approximation of a shape that preserves its eigenvectors as much as possible, but these techniques output a subset of input points with no connectivity, which limits their potential applications. Furthermore, the obtained Laplacian results from an optimization procedure, implying its storage alongside the selected points. Focusing on keeping a mesh instead of an operator would allow to retrieve the latter using the standard cotangent formulation, enabling easier processing afterwards. Instead, we propose to simplify the input mesh using a spectrum-preserving mesh decimation scheme, so that the Laplacian computed on the simplified mesh is spectrally close to the one of the input mesh. We illustrate the benefit of our approach for quickly approximating spectral distances and functional maps on low resolution proxies of potentially high resolution input meshes.     

Extension of half-edges for the representation of multiresolution subdivision surfaces

We address in this paper the problem of the data structures used for the representation and the manipulation of multiresolution subdivision surfaces. The classically used data structures are based on quadtrees, straightforwardly derived from the nested hierarchy of faces generated by the subdivision schemes. Nevertheless, these structures have some drawbacks: specificity to the kind of mesh (triangle or quad); the time complexity of neighborhood queries is not optimal; topological cracks are created in the mesh in the adaptive subdivision case. We present in this paper a new topological model for encoding multiresolution subdivision surfaces. This model is an extension to the well-known half-edge data structure. It allows instant and efficient navigation at any resolution level of the mesh. Its generality allows the support of many subdivision schemes including primal and dual schemes. Moreover, subdividing the mesh adaptively does not create topological cracks in the mesh. The extension proposed here is formalized in the combinatorial maps framework. This allows us to give a very general formulation of our extension.     

Guaranteed-Quality Simplical Mesh Generation with Cell Size and Grading Control

Unstructured mesh quality, as measured geo-metrically, has long been known to influence solution accuracy and efficiency for finite-element and finite-volume simulations. Recent guaranteed-quality unstructured meshing algorithms are therefore welcome tools. However, these algorithms allow no explicit control over mesh resolution or grading. We define a geometric length scale, similar in principle to the local feature size, which allows automatic global control of mesh resolution and grading. We describe how to compute this length scale efficiently and modify Ruppert’s two-dimensional and Shewchuk’s three-dimensional meshing algorithms to produce meshes matching our length scale. We provide proofs of mesh quality, good grading, and size optimality for both two- and three-dimensions, and present examples, including comparison with existing schemes known to generate good-quality meshes.     

Domino Tiling: A New Method of Real-Time Conforming Mesh Construction for Rendering Changeable Height Fields

In this paper we present a novel GPU-oriented method of creating an inherently continuous triangular mesh for tile-based rendering of regular height fields. The method is based on tiling data-independent semi-regular meshes of non-uniform structure, a technique that is quite different from other mesh tiling approaches. A complete, memory efficient set of mesh patterns is created by an off-line procedure and stored into the graphics adapter's memory at runtime. At rendering time, for each tile, one of the precomputed mesh patterns is selected for rendering. The selected mesh pattern fits the required level of details of the tile and ensures seamless connection with other adjacent mesh patterns, like in a game of dominoes. The scalability potential of the proposed method is demonstrated through quadtree hierarchical grouping of tiles. The efficiency is verified by experimental results on height fields for terrain representation, where the method achieves high frame rates and sustained triangle throughput on high resolution viewports with sub-pixel error tolerance. Frame rate sensitivity to real-time modifications of the height field is measured, and it is shown that the method is very tolerant and consequently well tailored for applications dealing with rapidly changeable phenomena represented by height fields.     

A CAD approach for suppression of power supply noise and performance analysis of some multi-core processors in pre-layout stage

In modern system-on-chip, the number of transistors has grown exponentially. This requires an efficient electrical power distribution network for proper functioning of the chip. Voltages at different nodes with respect to the desired level may vary which correspond to generation of supply noise. This paper deals with the estimation and allocation of decoupling capacitance for reduction of supply noise at the pre-layout level. Usually, decoupling capacitors are placed near the noisy functional modules, which acts as local charge storing devices and effectively reduce the transients. In this work, analysis of various sources of supply noises has been performed. Depending on the amount of supply noise, the decoupling capacitance has been estimated and allocated with minimum increment in power consumption and propagation delay. We have considered 512-points, 1-k point, 2-k point and 4-k point Fast Fourier Transform processors and International Test Conference 1999 (b14 and b17) benchmark circuits as our test circuits. This work reports up to 51.9% reduction of peak supply noise at the cost of 0.48 and 1.44% increase in power consumption and delay respectively. This estimation and subsequent allocation of decoupling capacitances will help for more accurate design and implementation at the layout stage.