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User-controllable polycube map for manifold spline construction 用户可控制的多立方体映射,用于流形样条构造
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364958
Hongyu Wang, Miao Jin, Ying He, X. Gu, Hong Qin
Polycube T-spline has been formulated elegantly that can unify T-splines and manifold splines to define a new class of shape representations for surfaces of arbitrary topology by using polycube map as its parametric domain. In essense, The data fitting quality using polycube T-splines hinges upon the construction of underlying polycube maps. Yet, existing methods for polycube map construction exhibit some disadvantages. For example, existing approaches for polycube map construction either require projection of points from a 3D surface to its polycube approximation, which is therefore very difficult to handle the cases when two shapes differ significantly; or compute the map by conformally deforming the surfaces and polycubes to the common canonical domain and then construct the map using function composition, which is challenging to control the location of singularities and makes it hard for the data-fitting and hole-filling processes later on. This paper proposes a novel framework of user-controllable polycube maps, which can overcome disadvantages of the conventional methods and is much more efficient and accurate. The current approach allows users to directly select the corner points of the polycubes on the original 3D surfaces, then construct the polycube maps by using the new computational tool of discrete Euclidean Ricci flow. We develop algorithms for computing such polycube maps, and show that the resulting user-controllable polycube map serves as an ideal parametric domain for constructing spline surfaces and other applications. The location of singularities can be interactively placed where no important geometric features exist. Experimental results demonstrate that the proposed polycube maps introduce lower area distortion and retain small angle distortion as well, and subsequently make the entire hole-filling process much easier to accomplish.
将t样条和流形样条统一起来,以多立方映射作为参数域,定义了一类新的任意拓扑曲面的形状表示。从本质上讲,使用多立方t样条的数据拟合质量取决于底层多立方映射的构造。然而,现有的多立方体地图构建方法存在一些缺点。例如,现有的多立方体地图构建方法要么需要将点从3D表面投影到其多立方体近似值,因此很难处理两个形状差异很大的情况;或者通过将曲面和聚立方体共形变形到公共规范域来计算映射,然后使用函数组合来构造映射,这既难以控制奇异点的位置,也给后续的数据拟合和填充过程带来了困难。本文提出了一种新的用户可控多立方体映射框架,克服了传统方法的不足,提高了映射的效率和精度。目前的方法允许用户直接在原始三维曲面上选择聚立方体的角点,然后使用新的离散欧几里得-里奇流计算工具构建聚立方体映射。我们开发了计算这种多立方体映射的算法,并表明由此产生的用户可控多立方体映射可以作为构造样条曲面和其他应用的理想参数域。奇点的位置可以交互式地放置在不存在重要几何特征的地方。实验结果表明,所提出的多立方体图引入了较低的面积畸变,并保留了较小的角度畸变,从而使整个填孔过程更容易完成。
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引用次数: 51
Exact arrangements on tori and Dupin cyclides 在tori和Dupin自行车上的精确安排
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364912
Eric Berberich, Michael Kerber
An algorithm and implementation is presented to compute the exact arrangement induced by arbitrary algebraic surfaces on a parametrized ring dupin cyclide. The family of dupin cyclides contains as a special case the torus. The intersection of an algebraic surface of degree n with a reference cyclide is represented as a real algebraic curve of bi-degree (2n, 2n) in the two-dimensional parameter space of the cyclide. We use eigenwillig and kerber: "exact and efficient 2D-Arrangements of arbitrary algebraic Curves", SODA 2008, to compute a planar arrangement of such curves and extend their approach to obtain more asymptotic information about curves approaching the boundary of the cyclide's parameter space. With that, we can base our implementation on the general software framework by berberich et. al.: "sweeping and maintaining two-dimensional arrangements on surfaces: A first Step", ESA 2007. Our contribution provides the demanded techniques to model the special geometry of surfaces intersecting a cyclide and the special topology of the reference surface of genus one. The contained implementation is complete and does not assume generic position. Our experiments show that the combinatorial overhead of the framework does not harm the efficiency of the method. Our experiments show that the overall performance is strongly coupled to the efficiency of the implementation for arrangements of algebraic plane curves.
给出了一种计算任意代数曲面在参数化环上精确排列的算法和实现。dupin自行车族包含环面作为一个特例。在参考环的二维参数空间中,将n次代数曲面与参考环的交点表示为二次(2n, 2n)实代数曲线。我们使用特征威利和kerber:“精确和有效的任意代数曲线的二维排列”,SODA 2008,计算了这些曲线的平面排列,并扩展了他们的方法,以获得接近环参数空间边界的曲线的更多渐近信息。有了这些,我们可以将我们的实现建立在berberich等人的通用软件框架上:“在表面上清扫和维护二维排列:第一步”,ESA 2007。我们的贡献提供了所需的技术来模拟与一个周期相交的曲面的特殊几何形状和参考面1的特殊拓扑结构。所包含的实现是完整的,不具有通用地位。实验表明,该框架的组合开销不会影响该方法的效率。我们的实验表明,总体性能与代数平面曲线排列的实现效率密切相关。
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引用次数: 15
Converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for FEM accuracy and efficiency 将四面体网格转换为棱镜-四面体混合网格以提高有限元精度和效率
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364941
Soji Yamakawa, K. Shimada
This paper presents a computational method for converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for improved solution accuracy and computational efficiency of finite element analysis. The proposed method inserts layers of prism elements and deletes tetrahedral elements in sweepable sub-domains, in which cross-sections remain topologically identical and geometrically similar along a certain sweeping path. The total number of finite elements is reduced because roughly three tetrahedral elements are converted to one prism element. The solution accuracy of the finite element analysis improves since a prism element yields a more accurate solution than a tetrahedral element. Only previously known method for creating such a prism-tetrahedral mesh was to manually decompose a target volume into sweepable and non-sweepable sub-volumes and mesh each sub-volume separately. The proposed method starts from a cross-section of a tetrahedral mesh and replaces the tetrahedral elements with layers of prism elements until prescribed quality criteria can no longer be satisfied. The method applies a sequence of edge-collapse, local-transformation, and smoothing operations to remove or displace nodes located within the volume to be replaced with a layer of prism elements. Series of computational fluid dynamics simulations and structural analyses have been conducted, and the results verified a better performance of prismtetrahedral hybrid mesh in finite element simulations.
为了提高有限元分析的求解精度和计算效率,提出了一种将四面体网格转换为棱镜-四面体混合网格的计算方法。该方法在可扫描的子域中插入棱柱单元层并删除四面体单元,在该子域中沿一定的扫描路径截面保持拓扑相同和几何相似。由于大致将三个四面体单元转换为一个棱镜单元,因此减少了有限元的总数。由于棱镜单元比四面体单元产生更精确的解,因此提高了有限元分析的解精度。以前已知的创建这种棱镜-四面体网格的方法是手动将目标体分解为可扫描和不可扫描的子体,并分别对每个子体进行网格划分。该方法从四面体网格的截面开始,用多层棱镜单元替换四面体单元,直到不能满足规定的质量标准。该方法采用一系列边缘折叠、局部变换和平滑操作来移除或置换待替换为一层棱镜单元的体内节点。进行了一系列的计算流体力学模拟和结构分析,结果验证了棱镜-四面体混合网格在有限元模拟中的良好性能。
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引用次数: 12
Solid height-map sets: modeling and visualization 实体高度图集:建模和可视化
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364953
P. I. N. Santos, Rodrigo de Toledo, M. Gattass
Height maps are a very efficient surface representation, initially developed for terrain modeling and visualization. They are also present in other applications, such as mesostructure rendering. However, height maps are incapable of representing overhangs or self-folding surfaces, as well as several occluding objects. In this paper we propose a novel representation to overcome these limitations. A Solid Height-map Set is used to represent arbitrary solid geometry. We also describe a procedure to convert polygonal meshes into our scheme. In addition, we develop a visualization algorithm capable of efficiently rendering this novel representation and implement it using GPU programming. Results achieve an order of magnitude in memory savings as well as high performance independent of the original mesh size.
高度图是一种非常有效的表面表示,最初是为地形建模和可视化而开发的。它们也出现在其他应用程序中,例如介观结构渲染。然而,高度图无法表示悬垂或自折叠表面,以及一些遮挡物体。在本文中,我们提出了一种新的表示来克服这些限制。立体高度映射集用于表示任意立体几何。我们还描述了将多边形网格转换为我们的方案的过程。此外,我们开发了一种可视化算法,能够有效地呈现这种新颖的表示,并使用GPU编程实现它。结果实现了一个数量级的内存节省以及独立于原始网格大小的高性能。
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引用次数: 11
Visibility-based feature extraction from discrete models 基于可见性的离散模型特征提取
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364951
A. Chica
In this paper, we present a new visibility-based feature extraction algorithm from discrete models as dense point clouds resulting from laser scans. Based on the observation that one can characterize local properties of the surface by what can be seen by an imaginary creature on the surface, we propose algorithms that extract features using an intermediate representation of the model as a discrete volume for computational efficiency. We describe an efficient algorithm for computing the visibility map among voxels, based on the properties of a discrete erosion. The visibility information obtained in this first step is then used to extract the model components (faces, edges and vertices) --- which may be curved---and to compute the topological connectivity graph in a very efficient and robust way. The results are discussed through several examples.
在本文中,我们提出了一种新的基于可见性的特征提取算法,将激光扫描产生的密集点云作为离散模型。基于观察到人们可以通过在表面上想象的生物可以看到的东西来表征表面的局部属性,我们提出了使用模型的中间表示作为离散体积来提取特征的算法,以提高计算效率。我们描述了一种有效的算法来计算体素之间的可见性映射,基于离散侵蚀的性质。在第一步中获得的可见性信息然后用于提取模型组件(面,边和顶点)-可能是弯曲的-并以非常有效和稳健的方式计算拓扑连接图。通过几个算例对结果进行了讨论。
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引用次数: 7
Fast mesh segmentation using random walks 使用随机游走的快速网格分割
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364927
Yu-Kun Lai, Shimin Hu, Ralph Robert Martin, Paul L. Rosin
3D mesh models are now widely available for use in various applications. The demand for automatic model analysis and understanding is ever increasing. Mesh segmentation is an important step towards model understanding, and acts as a useful tool for different mesh processing applications, e.g. reverse engineering and modeling by example. We extend a random walk method used previously for image segmentation to give algorithms for both interactive and automatic mesh segmentation. This method is extremely efficient, and scales almost linearly with increasing number of faces. For models of moderate size, interactive performance is achieved with commodity PCs. It is easy-to-implement, robust to noise in the mesh, and yields results suitable for downstream applications for both graphical and engineering models.
3D网格模型现在广泛用于各种应用。对自动模型分析和理解的需求日益增长。网格分割是模型理解的重要一步,也是不同网格处理应用的有用工具,例如逆向工程和实例建模。我们扩展了先前用于图像分割的随机漫步方法,以提供交互式和自动网格分割的算法。这种方法非常有效,并且随着人脸数量的增加几乎呈线性增长。对于中等大小的模型,交互性能是用普通pc实现的。它易于实现,对网格中的噪声具有鲁棒性,并且产生适合于图形和工程模型的下游应用的结果。
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引用次数: 168
Toward superrobust geometric computation 走向超鲁棒几何计算
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364905
K. Sugihara
To make geometric computation robust against numerical errors is one of the most important issues for practical applications of geometric algorithms. We first review existing approaches to robust geometric computation, and next show that there still remain many difficulties. Finally we discuss possible directions to overcome these difficulties and thus to achieve superrobustness.
如何使几何计算对数值误差具有鲁棒性是几何算法实际应用的重要问题之一。我们首先回顾了现有的鲁棒几何计算方法,然后表明仍然存在许多困难。最后讨论了克服这些困难的可能方向,从而实现超鲁棒性。
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引用次数: 1
Parametric triangular Bézier surface interpolation with approximate continuity 具有近似连续性的参数三角形bsamizier曲面插值
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364956
Yingbin Liu, Stephen Mann
A piecewise quintic interpolation scheme with approximate G1 continuity is presented. For a given triangular mesh of arbitrary topology, one quintic triangular Bézier patch is constructed for each data triangle. Although the resulting surface has G1 continuity at the data vertices, we only require approximate G1 continuity along the patch boundaries so as to lower the patch degree. To reduce the normal discontinuity along boundaries, neighbouring patches are adjusted to have identical normals at the middle point of their common boundary. In most cases, the surfaces generated by this scheme have the same level of visual smoothness compared to an existing sextic G1 continuous interpolation scheme. Further, using the new boundary construction method presented in this paper, better shape quality is observed for sparse data sets than the surfaces of the original G1 continuous scheme, upon which the new scheme is based.
提出了一种近似G1连续性的分段五次插值格式。对于给定的任意拓扑三角形网格,为每个数据三角形构造一个五次三角形bsamzier patch。虽然得到的曲面在数据顶点处具有G1连续性,但是为了降低patch度,我们只要求沿patch边界近似G1连续性。为了减少沿边界的法线不连续性,将相邻的块调整为在其公共边界的中点具有相同的法线。在大多数情况下,与现有的六阶G1连续插值方案相比,该方案生成的表面具有相同的视觉平滑度。此外,使用本文提出的新边界构造方法,稀疏数据集的表面形状质量优于原G1连续方案的表面,新方案基于G1连续方案。
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引用次数: 13
Identification of sections from engineering drawings based on evidence theory 基于证据理论的工程图纸剖面图识别
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364907
Jie-Hui Gong, Hui Zhang, Bin Jiang, Jiaguang Sun
View identification is the basal process for solid reconstruction from engineering drawings. A new method is presented to label various views from a section-involved drawing and identify geometric planes through the object at which the sections are to be located. In the approach, a graph representation is developed for describing multiple relationships among various views in the 2D drawing space, and a reasoning technique based on evidence theory is implemented to validate view relations that are used to fold views and sections in the 3D object space. This is the first automated approach which can handle multiple sections in diverse arrangements, especially accommodating the aligned section for the first time. Experimental results are given to show that the proposed solution makes a breakthrough in the field and builds a promising basis for further expansibility, although it is not a complete one.
视图识别是根据工程图纸进行实体重建的基础过程。提出了一种新的方法,从涉及剖面的绘图中标记各种视图,并通过要定位的剖面所在的对象识别几何平面。在该方法中,开发了一种图形表示来描述二维绘图空间中各种视图之间的多种关系,并实现了基于证据理论的推理技术来验证用于折叠三维对象空间中的视图和部分的视图关系。这是第一个可以处理不同排列的多个部分的自动化方法,特别是第一次适应对齐的部分。实验结果表明,该解决方案在该领域取得了突破,并为进一步的可扩展性奠定了良好的基础,尽管它还不是一个完整的基础。
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引用次数: 10
An incremental approach to feature aligned quad dominant remeshing 特征对齐四主导重划分的增量方法
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364921
Yu-Kun Lai, L. Kobbelt, Shimin Hu
In this paper we present a new algorithm which turns an unstructured triangle mesh into a quad-dominant mesh with edges aligned to the principal directions of the underlying geometry. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, we simply apply an iterative relaxation scheme which incrementally aligns the mesh edges to the principal directions. The quad-dominant mesh is eventually obtained by dropping the not-aligned diagonals from the triangle mesh. A post-processing stage is introduced to further improve the results. The major advantage of our algorithm is its conceptual simplicity since it is merely based on elementary mesh operations such as edge collapse, flip, and split. The resulting meshes exhibit a very good alignment to surface features and rather uniform distribution of mesh vertices. This makes them very well-suited, e.g., as Catmull-Clark Subdivision control meshes.
本文提出了一种将非结构化三角形网格转化为边缘与底层几何主方向对齐的四主导网格的新算法。代替计算全局光滑参数化或沿切向量场积分曲率线,我们简单地应用迭代松弛方案,使网格边缘增量对齐到主方向。通过从三角形网格中去掉未对齐的对角线,最终得到四主导网格。为了进一步改善结果,引入了后处理阶段。我们的算法的主要优点是它的概念简单,因为它仅仅基于基本的网格操作,如边缘折叠,翻转和分裂。所得到的网格与表面特征的对齐非常好,网格顶点分布相当均匀。这使得它们非常适合,例如,作为Catmull-Clark细分控制网格。
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引用次数: 62
期刊
Symposium on Solid and Physical Modeling
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