基于外存八叉树的大模型多分辨率并行构建

随着3维扫描、计算机辅助设计和科学仿真等技术的发展,包含上千万甚至数十亿几何图元的3维网格模型变得十分普遍,如何实现这些模型的交互式绘制成为日益迫切需要解决的难题。外存多分辨率技术作为提高大模型绘制性能最有效的方法之一,成为近几年计算机图形学领域的研究热点。然而大型3维网格模型多分辨率表示的构建通常需要很长的预处理时间,这非常不利于系统调试和下游应用。针对基于外存八叉树的大模型多分辨率表示的构建,提出了基于子树的任务分割策略和基于基准测试的动态构建任务管理机制,实现大模型多分辨率表示的并行构建和负载平衡,有效地提高了大模型多分辨率表示的构建速度。     

大型网格模型简化和多分辨率技术综述

网格简化和多分辨率绘制是2种对于提高绘制性能非常有效的技术,但对于大型网格模型,这2种技术的设计和实现本身也存在诸多难点.文中综述了大型网格模型简化和多分辨率技术的研究进展,首先分析和比较基于网格分割、基于外存数据结构和基于流式策略的大型网格模型简化方法,然后介绍和比较大型网格模型多分辨率表示的设计、构建和绘制技术.最后总结并展望了该研究领域的发展趋势.     

Generalized B-spline subdivision-surface wavelets for geometry compression

We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail is expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform is computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.     

n-Dimensional multiresolution representation of subdivision meshes with arbitrary topology

We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topological subdivision process that is a key issue to robustly and soundly define mesh hierarchies. It fully supports multiresolution edition what allows the implementation of most mesh processing algorithms – like filtering or compression – for n-dimensional meshes with arbitrary topologies.We illustrate this model, in dimension 3, with an new truly multiresolution representation of subdivision volumes. It allows us to extend classical subdivision schemes to arbitrary polyhedrons and to handle adaptive subdivision with an elegant solution to compliance issues. We propose an implementation of this model as an effective and relatively inexpensive data structure.     

A Shrink Wrapping Approach to Remeshing Polygonal Surfaces

Due to their simplicity and flexibility, polygonal meshes are about to become the standard representation for surface geometry in computer graphics applications. Some algorithms in the context of multiresolution representation and modeling can be performed much more efficiently and robustly if the underlying surface tesselations have the special subdivision connectivity. In this paper, we propose a new algorithm for converting a given unstructured triangle mesh into one having subdivision connectivity. The basic idea is to simulate the shrink wrapping process by adapting the deformable surface technique known from image processing. The resulting algorithm generates subdivision connectivity meshes whose base meshes only have a very small number of triangles. The iterative optimization process that distributes the mesh vertices over the given surface geometry guarantees low local distortion of the triangular faces. We show several examples and applications including the progressive transmission of subdivision surfaces.     

Multiresolution Shape Deformations for Meshes with Dynamic Vertex Connectivity

Multiresolution shape representation is a very effective way to decompose surface geometry into several levels of detail. Geometric modeling with such representations enables flexible modifications of the global shape while preserving the detail information. Many schemes for modeling with multiresolution decompositions based on splines, polygonal meshes and subdivision surfaces have been proposed recently. In this paper we modify the classical concept of multiresolution representation by no longer requiring a global hierarchical structure that links the different levels of detail. Instead we represent the detail information implicitly by the geometric difference between independent meshes. The detail function is evaluated by shooting rays in normal direction from one surface to the other without assuming a consistent tesselation. In the context of multiresolution shape deformation, we propose a dynamic mesh representation which adapts the connectivity during the modification in order to maintain a prescribed mesh quality. Combining the two techniques leads to an efficient mechanism which enables extreme deformations of the global shape while preventing the mesh from degenerating. During the deformation, the detail is reconstructed in a natural and robust way. The key to the intuitive detail preservation is a transformation map which associates points on the original and the modified geometry with minimum distortion. We show several examples which demonstrate the effectiveness and robustness of our approach including the editing of multiresolution models and models with texture.     

Multiresolution Surface Representation Based on Displacement Volumes

We propose a new representation for multiresolution models which uses volume elements enclosed between thedifferent resolution levels to encode the detail information. Keeping these displacement volumes locally constantduring a deformation of the base surface leads to a natural behaviour of the detail features. The correspondingreconstruction operator can be implemented efficiently by a hierarchical iterative relaxation scheme, providingclose to interactive response times for moderately complex models. Based on this representation we implement a multiresolution editing tool for irregular polygon meshes that allowsthe designer to freely edit the base surface of a multiresolution model without having to care about self‐intersectionsin the respective detailed surface. We demonstrate the effectiveness and robustness of the reconstructionby several examples with real‐world data.     

大型网格模型多分辨率的外存构建与交互绘制

结合多分辨率、网格排布和基于视点的绘制技术,提出一种外存多分辨率构建和绘制算法.采用适应性八叉树对模型的包围盒进行划分,自顶向下构建模型的多分辨率层次结构,较好地保持了原模型的细节分布;并对多分辨率结构中每个节点所包含的三角形片段进行网格排布优化,降低了缓存的平均失效率;在实时绘制时,采用基于视点的细节层次选择策略进行模型的细化;最后通过引入数据预取机制来隐藏磁盘I/O延时,进一步提高绘制性能.实验结果表明,该算法在绘制速度与细节保留上均优于同类MRMM算法.     

Multiresolution representation and visualization of volume data

A system to represent and visualize scalar volume data at multiple resolution is presented. The system is built on a multiresolution model based on tetrahedral meshes with scattered vertices that can be obtained from any initial dataset. The model is built off-line through data simplification techniques, and stored in a compact data structure that supports fast on-line access. The system supports interactive visualization of a representation at an arbitrary level of resolution through isosurface and projective methods. The user can interactively adapt the quality of visualization to requirements of a specific application task and to the performance of a specific hardware platform. Representations at different resolutions can be used together to further enhance interaction and performance through progressive and multiresolution rendering     

Adaptive extraction of time-varying isosurfaces

We present an algorithm for adaptively extracting and rendering isosurfaces from compressed time-varying volume data sets. Tetrahedral meshes defined by longest edge bisection are used to create a multiresolution representation of the volume in the spatial domain that is adapted overtime to approximate the time-varying volume. The reextraction of the isosurface at each time step is accelerated with the vertex programming capabilities of modern graphics hardware. A data layout scheme which follows the access pattern indicated by mesh refinement is used to access the volume in a spatially and temporally coherent manner. This data layout scheme allows our algorithm to be used for out-of-core visualization.     

Out-of-core streamline visualization on large unstructured meshes

This paper presents an out-of-core approach for interactive streamline construction on large unstructured tetrahedral meshes containing millions of elements. The out-of-core algorithm uses an octree to partition and restructure the raw data into subsets stored into disk files for fast data retrieval. A memory management policy tailored to the streamline calculations is used such that, during the streamline construction, only a very small amount of data are brought into the main memory on demand. By carefully scheduling computation and data fetching, the overhead of reading data from the disk is significantly reduced and good memory performance results. This out-of-core algorithm makes possible interactive streamline visualization of large unstructured-grid data sets on a single mid-range workstation with relatively low main-memory capacity: 5-15 megabytes. We also demonstrate that this approach is much more efficient than relying on virtual memory and operating system's paging algorithms     

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.     

递进网格的一种快速生成算法

递进网格表示法能高效地存储网格信息，并能生成连续的细节层次模型，支持模型的多分辨率表示、递进传输、网格压缩和有选择精化。此文给出了一种递进网格的生成算法，该算法能有效地控制简化网格与原始网格的误差，速度较快并能很好地保持原模型的边界特征     

Parallel H-Tree Based Data Cubing on Graphics Processors

Graphics processing units (GPUs) have an SIMD architecture and have been widely used recently as powerful general-purpose co-processors for the CPU. In this paper, we investigate efficient GPU-based data cubing because the most frequent operation in data cube computation is aggregation, which is an expensive operation well suited for SIMD parallel processors. H-tree is a hyper-linked tree structure used in both top-k H-cubing and the stream cube. Fast H-tree construction, update and real-time query response are crucial in many OLAP applications. We design highly efficient GPU-based parallel algorithms for these H-tree based data cube operations. This has been made possible by taking effective methods, such as parallel primitives for segmented data and efficient memory access patterns, to achieve load balance on the GPU while hiding memory access latency. As a result, our GPU algorithms can often achieve more than an order of magnitude speedup when compared with their sequential counterparts on a single CPU. To the best of our knowledge, this is the first attempt to develop parallel data cubing algorithms on graphics processors.     

HCCMeshes: Hierarchical‐Culling oriented Compact Meshes

Hierarchical culling is a key acceleration technique used to efficiently handle massive models for ray tracing, collision detection, etc. To support such hierarchical culling, bounding volume hierarchies (BVHs) combined with meshes are widely used. However, BVHs may require a very large amount of memory space, which can negate the benefits of using BVHs. To address this problem, we present a novel hierarchical‐culling oriented compact mesh representation, HCCMesh, which tightly integrates a mesh and a BVH together. As an in‐core representation of the HCCMesh, we propose an i‐HCCMesh representation that provides an efficient random hierarchical traversal and high culling efficiency with a small runtime decompression overhead. To further reduce the storage requirement, the in‐core representation is compressed to our out‐of‐core representation, o‐HCCMesh, by using a simple dictionary‐based compression method. At runtime, o‐HCCMeshes are fetched from an external drive and decompressed to the i‐HCCMeshes stored in main memory. The i‐HCCMesh and o‐HCCMesh show 3.6:1 and 10.4:1 compression ratios on average, compared to a naively compressed (e.g., quantized) mesh and BVH representation. We test the HCCMesh representations with ray tracing, collision detection, photon mapping, and non‐photorealistic rendering. Because of the reduced data access time, a smaller working set size, and a low runtime decompression overhead, we can handle models ten times larger in commodity hardware without the expensive disk I/O thrashing. When we avoid the disk I/O thrashing using our representation, we can improve the runtime performances by up to two orders of magnitude over using a naively compressed representation.     

Volume Preservation of Multiresolution Meshes

Geometric constraints have proved to be efficient for enhancing the realism of shape animation. The present paper addresses the computation and the preservation of the volume enclosed by multiresolution meshes. A wavelet based representation allows the mesh to be handled at any level of resolution. The key contribution is the calculation of the volume as a trilinear form with respect to the multiresolution coefficients. Efficiency is reached thanks to the pre-processing of a sparse 3D data structure involving the transposition of the filters while represented as a lifting scheme. A versatile and interactive method for preserving the volume during a deformation process is then proposed. It is based on a quadratic minimization subject to a linearization of the volume constraint. A closed form of the solution is derived.     

Ternary Sparse Matrix Representation for Volumetric Mesh Subdivision and Processing on GPUs

In this paper, we present a novel volumetric mesh representation suited for parallel computing on modern GPU architectures. The data structure is based on a compact, ternary sparse matrix storage of boundary operators. Boundary operators correspond to the first‐order top‐down relations of k‐faces to their (k ? 1)‐face facets. The compact, ternary matrix storage format is based on compressed sparse row matrices with signed indices and allows for efficient parallel computation of indirect and bottom‐up relations. This representation is then used in the implementation of several parallel volumetric mesh algorithms including Laplacian smoothing and volumetric Catmull‐Clark subdivision. We compare these algorithms with their counterparts based on OpenVolumeMesh and achieve speedups from 3× to 531×, for sufficiently large meshes, while reducing memory consumption by up to 36%.     

√3-Subdivision-Based Biorthogonal Wavelets

A new efficient biorthogonal wavelet analysis based on the radic3 subdivision is proposed in the paper by using the lifting scheme. Since the radic3 subdivision is of the slowest topological refinement among the traditional triangular subdivisions, the multiresolution analysis based on the radic3 subdivision is more balanced than the existing wavelet analyses on triangular meshes and accordingly offers more levels of detail for processing polygonal models. In order to optimize the multiresolution analysis, the new wavelets, no matter whether they are interior or on boundaries, are orthogonalized with the local scaling functions based on a discrete inner product with subdivision masks. Because the wavelet analysis and synthesis algorithms are actually composed of a series of local lifting operations, they can be performed in linear time. The experiments demonstrate the efficiency and stability of the wavelet analysis for both closed and open triangular meshes with radic3 subdivision connectivity. The radic3-subdivision-based biorthogonal wavelets can be used in many applications such as progressive transmission, shape approximation, and multiresolution editing and rendering of 3D geometric models.     

A practical approach to Morse-Smale complex computation: scalability and generality

The Morse-Smale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalar-valued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closure-finite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes. A new divide-and-conquer strategy allows for memory-efficient computation of the MS complex and simplification on-the-fly to control the size of the output. In addition to being able to handle various data formats, the framework supports implementation-specific optimizations, for example, for regular data. We present the complete characterization of critical point cancellations in all dimensions. This technique enables the topology based analysis of large data on off-the-shelf computers. In particular we demonstrate the first full computation of the MS complex for a 1 billion/1024(3) node grid on a laptop computer with 2Gb memory.     

体积保持的多分辨率多边形网格的光顺造型

给出了一个高效的多边形网格的多分辨率光顺造型算法。该算法首先通过引入体积保持约束,快速地实现稠密多边形网格的多分辨率表示,然后结合一个有效的无收缩光顺算法,对网格执行高效的多分辨率光顺编辑,与传统编辑方法不同,该方法利用体积保持约束及优化技术,来自动恢复编辑区域中相应的细节,而无需引入非常损耗资源的局部标架。实验结果表明,该算法计算稳定、高效,能产生复杂的模型。