共查询到18条相似文献,搜索用时 156 毫秒
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《计算机辅助设计与图形学学报》2017,(12)
共形映射又称为保角映射,在计算机图形学、几何信息处理和参数化领域扮演着重要角色.调和映射易于计算并且有严密的理论基础,为了计算高亏格曲面的共形映射,提出一种基于调和映射的非线性扩散方法.首先使用贪心算法在高亏格曲面上找到一个同伦群基底;然后通过求解一个线性系统来计算曲面的调和映射,将该映射的结果作为非线性扩散计算的初始条件;再使用拉普拉斯切向法来调节曲面边界的调和能量,调和能量下降的过程即非线性扩散过程;最后最小化调和能量,以获得曲面的共形映射.实验结果表明,文中方法是稳定的,映射结果可以很好地保证曲面三角网格的角度关系;算法对模型网格质量要求不高,具有更高的鲁棒性;与经典的共形映射方法相比,该方法得到的结果更均匀,共形效果更好.该方法可以在参数化、纹理映射、曲面注册等领域得到很好应用. 相似文献
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提出了用实体模型表示复杂组合曲面的方法,以水电站结构中的弯时肝形尾水管型腔面为例,提出用参数化实体造型解决具有相同结构而尺寸为系列化的复杂组合曲面的计算机自动绘图问题。 相似文献
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在对HUST-CAID(哈尔滨理工大学计算机辅助工业造型设计)系统进行研究的基础上,首先引入了自由曲面特征,然后结合HUST-CAID系统定义了自由曲面特征的分类和参数化,应用这种分类和参数化的方法创建了一个自由曲面特征,提出了一种基于FFDP配置的附加自由曲面特征的构造框架。此框架可以使自由曲面整体模型的构造完全参数化。最后建立了基于这个框架构造的自由曲面附加特征的有效性维护机制,从而达到对自由曲面附加特征进行有效性维护的目的。 相似文献
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针对多亏格曲面参数化变形较大、运算复杂度高的问题,提出一种改进的基于全纯1-形式的全局参数化方法。该方法以参数化的梯度场为出发点,采用更快速的同调群和上同调群计算方法。首先,利用简化的割图法计算曲面的同调群以确定其拓扑结构;其次,定义特定的调和函数计算闭合1-形式来构造由梯度场形成的线性空间的上同调群;然后,最小化调和能量将上同调群扩散为调和1-形式;最后,线性组合调和1-形式构造出全纯1-形式并在基本域上积分即得到参数化。由上同调群、同调群相关理论分析表明,该方法所得参数化是一种全局的、边界自由的共形映射。基于多组高亏格模型的实验证明,与原有基于全纯1-形式的全局参数化算法相比,本算法视觉效果更好,平均误差更小,运算效率更高。 相似文献
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晶格结构因其具备特殊的机械性能,已成为增材制造复杂结构设计和制造的重要研究领域之一。
针对传统的模型晶格结构生成方法需要通过对参数化建模的晶格结构网格进行裁剪或对其网格进行保形变形
实现,且生成效率较低的问题,提出一种基于参数曲面的增材制造保形晶格结构生成方法,实现晶格结构对曲
面空间的适应和高效生成。首先,基于一种矩阵方法完成晶格结构骨架的表达和构造。其次,利用点与曲面、
曲线与曲面、曲面与曲面所形成的 3 种封闭空间,对晶格结构骨架进行保形变形,使晶格结构适应曲面空间。
最后,采用基于晶格结构骨架的网格生成和拼接方法,生成保形晶格结构的网格模型。通过组件应用架构(CAA)
二次开发方法提取计算机辅助三维交互应用软件(CATIA)模型的参数曲面,实现保形晶格结构模型的高效生成,
并表现出良好的曲面空间适应性,证明该方法具有一定工程价值。 相似文献
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网格参数化研究进展 总被引:1,自引:0,他引:1
网格参数化是计算机图形学和数字几何处理的基本工具,有着广泛的应用背景.对网格参数化的研究进展进行了综述,主要从参数域和参数化质量两个方面介绍了网格参数化的研究现状.根据参数域的不同,讨论了平面参数化、基网格参数化、球面参数化以及曲面间的交叉参数化;根据参数化质量的不同,介绍了保长度的参数化、保特征的参数化以及致力于参数域简单的参数化.对参数化进行了分类介绍和讨论分析,概括介绍了每类方法的主要思想,讨论了每类方法的主要特性,对其中一些方法进行了比较分析,并对参数化方法存在的难点问题和未来可能的研究方向进行了总结,以期对参数化的研究进展有全面的了解. 相似文献
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Yong‐Liang Yang Ren Guo Feng Luo Shi‐Min Hu Xianfeng Gu 《Computer Graphics Forum》2009,28(7):2005-2014
Surface Ricci flow is a powerful tool to design Riemannian metrics by user defined curvatures. Discrete surface Ricci flow has been broadly applied for surface parameterization, shape analysis, and computational topology. Conventional discrete Ricci flow has limitations. For meshes with low quality triangulations, if high conformality is required, the flow may get stuck at the local optimum of the Ricci energy. If convergence to the global optimum is enforced, the conformality may be sacrificed. This work introduces a novel method to generalize the traditional discrete Ricci flow. The generalized Ricci flow is more flexible, more robust and conformal for meshes with low quality triangulations. Conventional method is based on circle packing, which requires two circles on an edge intersect each other at an acute angle. Generalized method allows the two circles either intersect or separate from each other. This greatly improves the flexibility and robustness of the method. Furthermore, the generalized Ricci flow preserves the convexity of the Ricci energy, this ensures the uniqueness of the global optimum. Therefore the algorithm won't get stuck at the local optimum. Generalized discrete Ricci flow algorithms are explained in details for triangle meshes with both Euclidean and hyperbolic background geometries. Its advantages are demonstrated by theoretic proofs and practical applications in graphics, especially surface parameterization. 相似文献
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Rongjie Lai Zaiwen Wen Wotao Yin Xianfeng Gu Lok Ming Lui 《Journal of scientific computing》2014,58(3):705-725
Surface conformal maps between genus-0 surfaces play important roles in applied mathematics and engineering, with applications in medical image analysis and computer graphics. Previous work (Gu and Yau in Commun Inf Syst 2(2):121–146, 2002) introduces a variational approach, where global conformal parameterization of genus-0 surfaces was addressed through minimizing the harmonic energy, with two weaknesses: its gradient descent iteration is slow, and its solutions contain undesired parameterization foldings when the underlying surface has long sharp features. In this paper, we propose an algorithm that significantly accelerates the harmonic energy minimization and a method that iteratively removes foldings by taking advantages of the weighted Laplace–Beltrami eigen-projection. Experimental results show that the proposed approaches compute genus-0 surface harmonic maps much faster than the existing algorithm in Gu and Yau (Commun Inf Syst 2(2):121–146, 2002) and the new results contain no foldings. 相似文献
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Conformal parameterization for surfaces into various parameter domains is a fundamental task in computer graphics. Prior research on discrete Ricci flow provided us with promising inspirations from methods derived via Riemannian geometry, which is rigorous in theory and effective inpractice. In this paper, we propose a unified conformal parameterization approachfor turning triangle meshes into planar and spherical domains using discrete Calabi flow onpiecewise linear metric. We incorporate edge‐flipping surgery to guarantee convergence as well as other significant improvements including approximate Newton's method, optimal step‐lengths, priority embedding and boundary customizing, which achieve better performance and functionality with robustness and accuracy. 相似文献
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Guo X Li X Bao Y Gu X Qin H 《IEEE transactions on visualization and computer graphics》2006,12(3):375-385
This paper presents a new approach to the physically-based thin-shell simulation of point-sampled geometry via explicit, global conformal point-surface parameterization and meshless dynamics. The point-based global parameterization is founded upon the rigorous mathematics of Riemann surface theory and Hodge theory. The parameterization is globally conformal everywhere except for a minimum number of zero points. Within our parameterization framework, any well-sampled point surface is functionally equivalent to a manifold, enabling popular and powerful surface-based modeling and physically-based simulation tools to be readily adapted for point geometry processing and animation. In addition, we propose a meshless surface computational paradigm in which the partial differential equations (for dynamic physical simulation) can be applied and solved directly over point samples via moving least squares (MLS) shape functions defined on the global parametric domain without explicit connectivity information. The global conformal parameterization provides a common domain to facilitate accurate meshless simulation and efficient discontinuity modeling for complex branching cracks. Through our experiments on thin-shell elastic deformation and fracture simulation, we demonstrate that our integrative method is very natural, and that it has great potential to further broaden the application scope of point-sampled geometry in graphics and relevant fields. 相似文献
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Yang YL Kim J Luo F Hu SM Gu X 《IEEE transactions on visualization and computer graphics》2008,14(5):1054-1066
Mesh parameterization is a fundamental technique in computer graphics. Our paper focuses on solving the problem of finding the best discrete conformal mapping that also minimizes area distortion. Firstly, we deduce an exact analytical differential formula to represent area distortion by curvature change in the discrete conformal mapping, giving a dynamic Poisson equation. Our result shows the curvature map is invertible. Furthermore, we give the explicit Jacobi matrix of the inverse curvature map. Secondly, we formulate the task of computing conformal parameterizations with least area distortions as a constrained nonlinear optimization problem in curvature space. We deduce explicit conditions for the optima. Thirdly, we give an energy form to measure the area distortions, and show it has a unique global minimum. We use this to design an efficient algorithm, called free boundary curvature diffusion, which is guaranteed to converge to the global minimum. This result proves the common belief that optimal parameterization with least area distortion has a unique solution and can be achieved by free boundary conformal mapping. Major theoretical results and practical algorithms are presented for optimal parameterization based on the inverse curvature map. Comparisons are conducted with existing methods and using different energies. Novel parameterization applications are also introduced. 相似文献
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The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods. 相似文献