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Solving global geometric constraints on free-form curves 求解自由曲线的全局几何约束
Pub Date : 2009-10-05 DOI: 10.1145/1629255.1629295
Iddo Hanniel, Kirk Haller
Constraint-based geometric modeling is the standard modeling paradigm in current modern CAD systems. Generally, the user defines constraints on the geometric objects and a solver is applied to find a configuration of the geometry, which satisfies these constraints. Proper application of these constraints allows rapid modification of the geometry without loss of design intent. However, in current CAD systems, constraint solving for free-form geometric objects is generally limited. In particular, constraining global features such as limits on a curve's curvature values, are not supported. In this paper we present a general method, within the constraint-based framework, to construct global constraints on free-form curves. The method starts by defining sufficient conditions on the curves in terms of an inequality expression, unlike local constraints the global constraint expression will be defined for all the domain of the curves. We then transform the expression into a symbolic polynomial, whose coefficients are symbolic expressions of the original curves. In the final step, a set of inequality constraints is applied in terms of the symbolic coefficients. These inequality constraints enforce the positivity of the symbolic polynomial. The final inequality constraints are fed into the solver along with any other local constraints, which the user has provided on the curves. Therefore, the solution returned by the solver satisfies both the global constraints and any other local constraints the user supplies. We have implemented a prototype of our method using existing commercial constraint solvers. We present results on several problems, which are handled as global geometric constraints using our method.
基于约束的几何建模是当前现代CAD系统的标准建模范式。通常,用户在几何对象上定义约束,并应用求解器来找到满足这些约束的几何结构。适当应用这些约束可以在不丧失设计意图的情况下快速修改几何形状。然而,在目前的CAD系统中,对自由形状几何对象的约束求解通常是有限的。特别是,不支持约束全局特征,如曲线曲率值的限制。本文提出了一种在约束框架下构造自由曲线全局约束的一般方法。该方法首先根据不等式表达式定义曲线上的充分条件,与局部约束不同,将为曲线的所有域定义全局约束表达式。然后将表达式转换为符号多项式,其系数是原始曲线的符号表达式。在最后一步中,根据符号系数应用一组不等式约束。这些不等式约束强化了符号多项式的正性。最终的不等式约束与用户在曲线上提供的任何其他局部约束一起输入求解器。因此,求解器返回的解既满足全局约束,也满足用户提供的任何其他局部约束。我们已经使用现有的商业约束求解器实现了我们方法的原型。我们给出了几个用我们的方法作为全局几何约束来处理的问题的结果。
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引用次数: 6
Accelerated wave-based acoustics simulation 加速波基声学模拟
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364916
N. Raghuvanshi, Nico Galoppo, M. Lin
We present an efficient technique to model sound propagation accurately in an arbitrary 3D scene by numerically integrating the wave equation. We show that by performing an offline modal analysis and using eigenvalues from a refined mesh, we can simulate sound propagation with reduced dispersion on a much coarser mesh, enabling accelerated computation. Since performing a modal analysis on the complete scene is usually not feasible, we present a domain decomposition approach to drastically shorten the pre-processing time. We introduce a simple, efficient and stable technique for handling the communication between the domain partitions. We validate the accuracy of our approach against cases with known analytical solutions. With our approach, we have observed up to an order of magnitude speedup compared to a standard finite-difference technique.
本文提出了一种通过对波动方程进行数值积分来精确模拟任意三维场景中声音传播的有效方法。我们表明,通过执行离线模态分析并使用来自精细网格的特征值,我们可以在更粗糙的网格上模拟具有减少色散的声音传播,从而实现加速计算。由于对整个场景进行模态分析通常是不可行的,我们提出了一种域分解方法来大大缩短预处理时间。我们介绍了一种简单、高效和稳定的技术来处理域分区之间的通信。我们验证了我们的方法的准确性与已知的分析解决方案的情况下。通过我们的方法,与标准有限差分技术相比,我们已经观察到高达一个数量级的加速。
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引用次数: 23
Negotiating design specifications: evolving functional constraints in mechanical assembly design 协商设计规范:机械装配设计中演化的功能约束
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364948
M. Dabbeeru, A. Mukerjee
Traditionally it has been assumed "Design Specifications" are given a priori, and constitute the primary constraints on the process of search that is design. This view is under challenge in emergentist accounts of design, where it is seen that for well-understood functional needs, experienced designers are able to come up with good designs very quickly. It is hypothesized that this is possible because search is minimized using novel functional constraints that emerge from experience. These emergent aspects are difficult to model in a computational framework, and this work is a preliminary attempt in this direction. "Well-understood functions" are assumed to be quantifiable in terms of some performance metrics, which permits us to identify regions of high functional validity as emergent constraint regions in the design space. In addition, designers often change the design space itself, and negotiate the initial specs in many ways. We show that small changes in the design space may result in large changes in this mapping, which is why such emergent knowledge is limited to a specific embodiment. By introducing such measures into future solid modeling systems, it may reduce the human designer's search to the more ill-posed aspects of the problem.
传统上,人们认为“设计规范”是先验的,构成了对搜索过程(即设计)的主要约束。这种观点在新兴设计理论中受到了挑战,在新兴设计理论中,经验丰富的设计师能够很快地提出好的设计方案,以满足人们对功能需求的充分理解。假设这是可能的,因为使用从经验中产生的新功能约束最小化了搜索。这些涌现的方面很难在计算框架中建模,而这项工作是在这个方向上的初步尝试。“被充分理解的功能”被假定为根据某些性能指标可量化的,这允许我们将高功能有效性的区域识别为设计空间中的紧急约束区域。此外,设计师经常改变设计空间本身,并以多种方式协商初始规格。我们表明,设计空间中的小变化可能导致该映射的大变化,这就是为什么这种突发知识仅限于特定的体现。通过将这些措施引入未来的实体建模系统,它可以减少人类设计师对问题的病态方面的搜索。
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引用次数: 1
Pattern computation for compression garment 压缩服装的花样计算
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364929
Charlie C. L. Wang, K. Tang
This paper addresses the problem of computing planar patterns for compression garments. In the garment industry, the compression garment has been more and more widely used to retain a shape of human body, where certain strain (or normal pressure) is designed at some places on the compression garment. Variant values and distribution of strain can only be generated by sewing different 2D patterns and warping them onto the body. We present a physical/geometric approach to compute 2D meshes that, when folded onto the 3D body, can generate a user-defined strain distribution through proper distortion. This is opposite to the widely studied mesh parameterization problem, whose objective is to minimize the distortion between the 2D and 3D meshes in angle, area or length.
本文研究了压缩服装平面图案的计算问题。在服装工业中,为了保持人体的某种形状,在压缩服装的某些部位设计一定的应变(或常压),压缩服装已得到越来越广泛的应用。应变的变化值和分布只能通过缝制不同的二维图案并将它们翘曲到身体上来产生。我们提出了一种物理/几何方法来计算二维网格,当折叠到三维体上时,可以通过适当的变形产生用户定义的应变分布。这与广泛研究的网格参数化问题相反,网格参数化问题的目标是最小化二维和三维网格在角度,面积或长度上的畸变。
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引用次数: 5
Surface matching using consistent pants decomposition 表面匹配使用一致的裤子分解
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364920
Xin Li, X. Gu, Hong Qin
Surface matching is fundamental to shape computing and various downstream applications. This paper develops a powerful pants decomposition framework for computing maps between surfaces with arbitrary topologies. We first conduct pants decomposition on both surfaces to segment them into consistent sets of pants patches (here a pants patch is intuitively defined as a genus-zero surface with three boundaries). Then we compose global mapping between two surfaces by harmonic maps of corresponding patches. This framework has several key advantages over other state-of-the-art techniques. First, the surface decomposition is automatic and general. It can automatically construct mappings for surfaces with same but complicated topology, and the result is guaranteed to be one-to-one continuous. Second, the mapping framework is very flexible and powerful. Not only topology and geometry, but also the semantics can be easily integrated into this framework with a little user involvement. Specifically, it provides an easy and intuitive human-computer interaction mechanism so that mapping between surfaces with different topologies, or with additional point/curve constraints, can be properly obtained within our framework. Compared with previous user-guided, piecewise surface mapping techniques, our new method is more intuitive, less labor-intensive, and requires no user's expertise in computing complicated surface map between arbitrary shapes. We conduct various experiments to demonstrate its modeling potential and effectiveness.
曲面匹配是形状计算和各种下游应用的基础。本文开发了一个强大的分解框架,用于计算任意拓扑曲面之间的映射。我们首先在两个表面上进行裤子分解,将它们分割成一致的裤子补丁集(在这里,裤子补丁直观地定义为具有三个边界的属零表面)。然后用对应块的调和映射构成两个曲面之间的全局映射。与其他最先进的技术相比,该框架具有几个关键优势。首先,表面分解是自动的和通用的。它可以自动构造具有相同但复杂拓扑的曲面的映射,并保证映射结果是一对一连续的。其次,映射框架非常灵活和强大。不仅拓扑和几何,而且语义也可以很容易地集成到这个框架中,只需少量的用户参与。具体来说,它提供了一种简单直观的人机交互机制,以便在我们的框架内适当地获得具有不同拓扑结构或附加点/曲线约束的表面之间的映射。与以往以用户为导向的分段曲面映射技术相比,我们的方法更直观,劳动强度更低,并且不需要用户的专业知识来计算任意形状之间的复杂曲面映射。我们进行了各种实验来证明其建模潜力和有效性。
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引用次数: 20
Probabilistic model of triangulation 三角测量的概率模型
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364943
Xiaoyun Li, D. Hunter
This paper analyses the probability that randomly deployed sensor nodes triangulate any point within the target area. Its major result is the probability of triangulation for any point given the number of nodes lying up to a specific distance (2 units) from it, employing a graph representation where an edge exists between any two nodes close than 2 units from one another. The expected number of un-triangulated coverage holes, i.e. uncovered areas which cannot be triangulated by adjacent nodes, in a finite target area is derived. Simulation results corroborate the probabilistic analysis with low error, for any node density. These results will find applications in triangulation-based or trilateration-based pointing analysis, or any computational geometry application within the context of triangulation.
本文分析了随机部署的传感器节点对目标区域内任意点进行三角剖分的概率。它的主要结果是对任何点进行三角剖分的概率,给定的节点数量在距离它的特定距离(2个单位)内,使用图表示,其中任何两个节点之间的边缘存在于彼此之间的距离小于2个单位。导出有限目标区域内未三角剖分覆盖孔(即相邻节点无法三角剖分的未覆盖区域)的期望数量。仿真结果证实了任意节点密度下的概率分析误差较小。这些结果将应用于基于三角测量或基于三边测量的指向分析,或任何基于三角测量的计算几何应用。
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引用次数: 7
Multiresolution sphere packing tree: a hierarchical multiresolution 3D data structure 多分辨率球体包装树:分层多分辨率三维数据结构
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364954
Jiro Inoue, A. J. Stewart
Sphere packing arrangements are frequently found in nature, exhibiting efficient space-filling and energy minimization properties. Close sphere packings provide a tight, uniform, and highly symmetric spatial sampling at a single resolution. We introduce the Multiresolution Sphere Packing Tree (MSP-tree): a hierarchical spatial data structure based on sphere packing arrangements suitable for 3D space representation and selective refinement. Compared to the commonly used octree, MSP-tree offers three advantages: a lower fanout (a factor of four compared to eight), denser packing (about 24% denser), and persistence (sphere centers at coarse resolutions persist at finer resolutions). We present MSP-tree both as a region-based approach that describes the refinement mechanism succintly and intuitively, and as a lattice-based approach better suited for implementation. The MSP-tree offers a robust, highly symmetric tessellation of 3D space with favorable image processing properties.
自然界中经常出现球形堆积排列,它具有高效的空间填充和能量最小化特性。紧密的球体堆积可以在单一分辨率下提供紧密、均匀和高度对称的空间采样。我们介绍了多分辨率球体堆积树(MSP-tree):一种基于球体堆积排列的分层空间数据结构,适用于三维空间表示和选择性细化。与常用的八叉树相比,MSP-树有三个优点:扇出更低(比八叉树低四倍)、堆积更密集(密集度约为 24%)和持久性(粗分辨率下的球体中心在更高分辨率下依然存在)。我们提出的 MSP-tree 既是一种基于区域的方法,能简洁直观地描述细化机制,也是一种基于网格的方法,更适合实施。MSP-tree 是一种稳健、高度对称的三维空间细分方法,具有良好的图像处理特性。
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引用次数: 2
Multi-component heart reconstruction from volumetric imaging 容积成像的多分量心脏重建
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364928
C. Bajaj, S. Goswami
Computer Tomography (CT) and in particular super fast, 64 and 256 detector CT has rapidly advanced over recent years, such that high resolution cardiac imaging has become a reality. In this paper, we briefly introduce a framework that we have built to construct three dimensional (3D) finite-element and boundary element mesh models of the human heart directly from high resolution CT imaging data. Although, the overall IMAGING-MODELING framework consists of image processing, geometry processing and meshing algorithms, our main focus in this paper will revolve around three key geometry processing steps which are parts of the so-called IMAGING-MODELING framework. These three steps are geometry cleanup or CURATION, anatomy guided annotation or SEGMENTATION and construction of GENERALIZED OFFSET SURFACE. These three algorithms, due to the very nature of the computation involved, can also be thought as parts of a more generalized modeling technique, namely geometric modeling with distance function. As part of the results presented in the paper, we will show that our algorithms are robust enough to effectively deal with the challenges posed by the real-world patient CT data collected from our radiologist collaborators.
计算机断层扫描(CT),特别是超快的64和256探测器CT近年来迅速发展,使高分辨率心脏成像成为现实。在本文中,我们简要介绍了我们建立的一个框架,该框架可以直接从高分辨率CT成像数据中构建人类心脏的三维(3D)有限元和边界元网格模型。尽管整个成像建模框架由图像处理、几何处理和网格算法组成,但我们在本文中的主要重点将围绕三个关键的几何处理步骤展开,这些步骤是所谓的成像建模框架的一部分。这三个步骤分别是几何清理或整理、解剖引导注释或分割以及广义偏移曲面的构造。由于所涉及的计算的本质,这三种算法也可以被认为是更广义的建模技术的一部分,即具有距离函数的几何建模。作为论文中提出的结果的一部分,我们将展示我们的算法足够强大,可以有效地处理从我们的放射科医生合作者收集的真实世界患者CT数据所带来的挑战。
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引用次数: 12
Triangulation of hierarchical hexagon meshes 分层六边形网格的三角剖分
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364944
Matthew Guenette, A. J. Stewart
We present an algorithm to triangulate a multi-resolution hierarchical hexagon mesh. The triangulation provides good triangle strips, which result in efficient rendering of the hexagon mesh, and well proportioned triangles, which avoid rendering artifacts.
提出了一种多分辨率分层六边形网格三角剖分算法。三角剖分提供了良好的三角形条,从而实现六边形网格的高效渲染,三角形比例合理,避免了渲染伪影。
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引用次数: 3
Isosurface extraction and interpretation on very large datasets in geophysics 地球物理中超大数据集的等值面提取与解释
Pub Date : 2008-06-02 DOI: 10.1145/1364901.1364932
G. Dupuy, B. Jobard, S. Guillon, N. Keskes, D. Komatitsch
In order to deal with the heavy trend in size increase of volumetric datasets, research in isosurface extraction has focused in the past few years on related aspects such as surface simplification and load balanced parallel algorithms. We present in this paper a parallel, bloc-wise extension of the tandem algorithm [Attali et al. 2005], which simplifies on the fly an isosurface being extracted. Our approach minimizes the overall memory consumption using an adequate bloc splitting and merging strategy and with the introduction of a component dumping mechanism that drastically reduces the amount of memory needed for particular datasets such as those encountered in geophysics. As soon as detected, surface components are migrated to the disk along with a meta-data index (oriented bounding box, volume, etc) that will allow further improved exploration scenarios (small components removal or particularly oriented components selection for instance). For ease of implementation, we carefully describe a master and slave algorithm architecture that clearly separates the four required basic tasks. We show several results of our parallel algorithm applied on a 7000x1600x2000 geophysics dataset.
为了应对体积数据集规模急剧增长的趋势,近年来等值面提取的研究主要集中在曲面简化和负载均衡并行算法等相关方面。我们在本文中提出了对串联算法的并行、分组扩展[Attali et al. 2005],它简化了正在提取的等值面。我们的方法使用适当的块分割和合并策略,并引入组件转储机制,从而最大限度地减少了特定数据集(如地球物理学中遇到的数据集)所需的内存量,从而最大限度地减少了总体内存消耗。一旦检测到,表面组件将与元数据索引(定向边界框,体积等)一起迁移到磁盘,这将允许进一步改进勘探场景(例如小组件移除或特定定向组件选择)。为了便于实现,我们仔细描述了一个主从算法架构,它清楚地分离了四个所需的基本任务。我们展示了并行算法在7000x1600x2000地球物理数据集上的几个应用结果。
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引用次数: 2
期刊
Symposium on Solid and Physical Modeling
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