闭合三角网格的优化切割与保角映射

提出一种自动地将任意闭合三角网格切开并保角映射到二维平面域的算法.通过对自动提取的模型初始切割线逐步优化得到模型切割线,优化过程由一个与保角映射扭曲度和合法性相关的成本函数控制.为了减小映射扭曲,算法中不预先固定参数域边界,而在参数化过程中自动地确定网格的自然边界.实验结果表明,该算法通过优化切割线和参数域边界有效地降低了三角形形状扭曲,并保证了参数化结果的合法性.     

全局各向异性四边形主导网格重建方法

四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡.为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格.重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样;再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除;如此循环,直至达到理想的采样密度.该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征.同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格.     

基于块的任意曲面上的纹理合成

一种新的曲面纹理合成技术被提出,它采用求最小割集来解决块拼接时的礁缝走样问题。算法在预处理期对模型的三维网格进行了重建,使其规则并且建立网格点与参数化栅格采样后的图像点一一对应的关系,无论对合成的速度和质量都有很大的提高。提出了在曲面上进行纹理粘贴的算法,对于渲染存在不完整性的自然物体取得了较好的效果。     

全局各向异性四边形主导网格重建方法?

四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡。为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格。重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样;再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除;如此循环,直至达到理想的采样密度。该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征。同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格。     

基于弹塑性变形的快速展平算法与网格参数化

针对复杂CAD模型的展平问题,提出在三角网格上数值模拟汽车覆盖件一步逆成形的优化算法,实现了对车身零件毛坯料的快速估计.首先对初始网格进行补洞与局部重新网格化等预处理,得到辅助网格;为了减少变形,采用基于能量释放的初始解预示算法,并用基于金属板材弹塑性变形的一步逆算法进行迭代优化,得到修正的展平网格,经后处理得到最终参数化结果.将文中算法应用到自由边界网格参数化上,通过大量数值实验和比较结果表明,该算法不仅适用于工业上的坯料预估,而且在网格参数化的面积、扭曲变形方面有明显改善,同时具有较好的保角效果.     

一种用于表面重建的网格点生成算法

表面重建需要建立表面的多边形(通常为三角形)网格模型,该文给出的算法通过两项参数来控制边缘轮廓上生成的网格点,所生成的网格点不但能够体现边缘的主要特征,而且可以避免在重建时产生斜三角形。该算法具有速度快、适应性强以及可灵活调整重建精度的特点,已在医学影像工作站上的三维重建系统中获得了较好的应用。     

基于网格变形的从图像重建三维人脸

从图像重建高质量三维人脸一直是计算机视觉和图形学的一个重要研究问题.不同于传统的基于立体匹配的窄基线多视几何和数据驱动的人脸形变方法,提出一种结合网格变形技术和立体视觉原理的、从图像重建高质量三维人脸模型方法.给定从不同视角拍摄的几幅人脸图像,基于健壮图像特征获得可靠的相机外部参数和稀疏三维点;在此基础上,提出一种结合几何细节保持和图像一致性约束的三维人脸变形算法重建三维人脸,通过对人脸模板的网格变形,使得变形人脸在多幅图像中的可见投影具有一致性的图像颜色强度.基于模板的人脸变形可以有效地解决三维模型成像中的遮挡问题,采用健壮估计法消除噪声、离群点和光照对目标函数收敛性的影响,对目标函数的多次非线性优化求解进一步改进了人脸重建的质量.采用合成人脸图像和真实人脸图像重建三维人脸的实验结果表明,文中算法可以从几幅宽基线图像重建高质量的三维人脸模型.     

自适应T样条曲面重建

为了进行快速高精度的曲面重建,提出了一种新的基于T样条的曲面自动重建算法。由于T样条控制网格具有特殊性质,因此在使用T样条进行曲面重建时,一个关键的问题是如何构造好一个T网格。该新算法在进行曲面重建时,用三角网格的参数化方法,先将数据点同胚映射到平面,然后再利用平面四叉树细分的方法将无结构散乱数据自动生成合理有效的T网格,最后将曲面重构模型转化为最优化问题,并由最小二乘法求解,同时在误差较大的区域辅以T样条的局部修正,以使重建曲面与原网格面的最大误差小于指定的误差值。由于该新的曲面重建方法是一个基于细节的重建方法,因此采样点密集区域所插入的T网格点也就相应地增多,这样既抓住了网格曲面的特征,又能很好地减少过多的T网格控制顶点,这就提高了算法效率。另外,该新算法还具有高效、易操作、能适应复杂曲面重建、曲面自动生成且满足相应精度要求等优点。重构结果显示,该新的曲面重建算法不仅重构应用范围广,且重构精度高。     

一种网格融合算法

快速建模是三维游戏动画领域的重要技术,从已有模型经过修改、编辑、融合构建出新的模型是一种高效的建模方法.本文提出了一种网格模型融合算法,该算法首先将需要的部分网格从源模型上交互剪切下来,并将其配准对齐;然后将两网格模型转化成点模型表示,并将点模型转化成RBF隐函数表示;再对两隐函数进行布尔运算;最后将布尔运算生的隐函数曲面在两网格接合区域进行三角形化,得到最终的网格模型.算法定义了隐函数曲面的影响区域,有效控制融合过渡.采用边界扩展的三角形化方法,保留了融合区域以外源模型的特征.实验结果表明,本文算法具有很好的网格融合结果,可用于游戏动画中快速造型.     

四边曲面重建中的边界优化算法

文中针对Floater“保形参数化”方法存在的局限性,研究了四边曲面重建中,边界曲折程度的评定方法。通过比较边界上网格点的曲率值,构造形式上的四边拓扑曲面;通过对边界网格的优化剖分,获得相对平滑的边界曲线。与Floater算法相比,提出了曲折边界的平滑剖分方法,改善了重建曲面边界上的扭曲变形,为Floater重建算法在工程CAD模型中的推广提供了实用途径。     

基于多层k路划分的三维网格并行任务分配策略

为解决传统任务划分方法在三维网格并行计算任务分配阶段产生的通信开销大的问题,提出了一种基于多层k路划分算法的并行任务分配策略.首先利用多层k路划分算法划分三维网格,将任务划分问题转化为图划分问题,然后基于图划分结果给出一个任务映射并行算法将计算任务分配到各计算结点.在深腾1800上求解三维网格模型最短路径问题的实验结果表明,相比于传统的行列划分任务分配策略,该策略在保证负裁平衡的同时有效地降低了通信开销,算法的运行时间减少,加速比得到提高.     

A new approach to automatic and a priori mesh adaptation around circular holes for finite element analysis

Through our research on the integration of finite element analysis in the design and manufacturing process with CAD, we have proposed the concept of mesh pre-optimization. This concept consists in converting shape and analysis information in a size map (a mesh sizing function) with respect to various adaptation criteria (refining the mesh around geometric form features, minimizing the geometric discretization error, boundary conditions, etc.). This size map then represents a constraint that has to be respected by automatic mesh generation procedures. This paper introduces a new approach to automatic mesh adaptation around circular holes. This tool aims at optimizing, before any FEA, the mesh of a CAD model around circular holes. This approach, referred to as “a priori” mesh adaptation, should not be regarded as an alternative to adaptive a posteriori mesh refinement but as an efficient way to obtain reasonably accurate FEA results before a posteriori adaptation, which is particularly interesting when evaluating design scenarios. The approach is based on performing many offline FEA analyses on a reference case and deriving, from results and error distributions obtained, a relationship between mesh size and FEA error. This relationship can then be extended to target user specified FEA accuracy objectives in a priori mesh adaptation for any distribution of circular holes. The approach being purely heuristic, fulfilling FEA accuracy objectives, in all cases, cannot be theoretically guaranteed. However, results obtained using varying hole diameters and distributions in 2D show that this heuristic approach is reliable and useful. Preliminary results also show that extension of the method can be foreseen towards a priori mesh adaptation in 3D and mesh adaptation around other types of 2D features.     

Processing of 3D meshed surfaces using spherical wavelets

This paper presents an efficient technique for processing of 3D meshed surfaces via spherical wavelets.More specifically,an input 3D mesh is firstly transformed into a spherical vector signal by a fast low distortion spherical parameterization approach based on symmetry analysis of 3D meshes.This signal is then sampled on the sphere with the help of an adaptive sampling scheme.Finally,the sampled signal is transformed into the wavelet domain according to spherical wavelet transform where many 3D mesh processing operations can be implemented such as smoothing,enhancement,compression,and so on.Our main contribution lies in incorporating a fast low distortion spherical parameterization approach and an adaptive sampling scheme into the frame for processing 3D meshed surfaces by spherical wavelets,which can handle surfaces with complex shapes.A number of experimental examples demonstrate that our algorithm is robust and efficient.     

Geometric signal compression

Compression of mesh attributes becomes a challenging problem due to the great need for efficient storage and fast transmission. This paper presents a novel geometric signal compression framework for all mesh attributes, including position coordinates, normal, color, texture, etc. Within this framework, mesh attributes are regarded as geometric signals defined on mesh surfaces. A planar parameterization algorithm is first proposed to map 3D meshes to 2D parametric meshes. Geometric signals are then transformed into 2D signals, which are sampled into 2D regular signals using an adaptive sampling method. The JPEG2000 standard for still image compression is employed to effectively encode these regular signals into compact bit-streams with high rate/distortion ratios. Experimental results demonstrate the great application potentials of this framework.     

Mesh Segmentation via Spectral Embedding and Contour Analysis

We propose a mesh segmentation algorithm via recursive bisection where at each step, a sub-mesh embedded in 3D is first spectrally projected into the plane and then a contour is extracted from the planar embedding. We rely on two operators to compute the projection: the well-known graph Laplacian and a geometric operator designed to emphasize concavity. The two embeddings reveal distinctive shape semantics of the 3D model and complement each other in capturing the structural or geometrical aspect of a segmentation. Transforming the shape analysis problem to the 2D domain also facilitates our segmentability analysis and sampling tasks. We propose a novel measure of the segmentability of a shape, which is used as the stopping criterionfor our segmentation. The measure is derived from simple area- and perimeter-based convexity measures. We achieve invariance to shape bending through multi-dimensional scaling (MDS) based on the notion of inner distance. We also utilize inner distances to develop a novel sampling scheme to extract two samples along a contour which correspond to two vertices residing on different parts of the sub-mesh. The two samples are used to derive a spectral linear ordering of the mesh faces. We obtain a final cut via a linear search over the face sequence based on part salience, where a choice of weights for different factors of part salience is guided by the result from segmentability analysis.     

一种基于小波变换的三维网格模型水印算法

提出了一种基于小波变换的强壮三维网格模型数字水印算法。首先采用一种平面参数化算法将三维网格模型映射为二维参数网格，三维网格模型表面的几何信号相应转换为二维信号，然后采用一种自适应小波水印算法加入水印。实验结果显示该水印算法能够抵抗各种几何信号处理攻击。     

可调度的小波网格变形

三维网格模型的Morphing是计算机动画研究的重要内容,利用频谱工具控制变形成份出现的次序是对变形路径进行控制的有效方法之一。但在三维网格模型上无法直接进行频谱分析,使得该技术一直无法在网格模型的Morphing中发挥作用。论文在数字几何处理框架的基础上,提出了利用小波分析进行可控网格变形的新方法。针对变形研究和数字几何处理中的关键问题——特征点对齐和采样,分别提出了基于Harmonic映射的参数化网格warping的特征对齐方法以及新型的自适应采样方法。实验表明,该方法稳定可靠,计算量适中,变形结果更为丰富。     

Watermarking 3D mesh by spherical parameterization

In this paper, a robust 3D trianglular mesh watermarking algorithm is presented by applying spherical parameterization. First, we transform the coordinate signals of the 3D triangular mesh into spherical signals using a global spherical parameterization and an even sampling scheme. Then, spherical harmonic transformation is used to generate some data for embedding watermarks. As a result, the watermarks can be embedded in the Fourier-frequency domain of the original mesh. Experimental results show that our watermarking algorithm is robust since watermarks can be extracted without mesh alignment or re-meshing under a variety of attacks, including noise addition, crop, filtering, enhancement, rotation, translation, scale and re-sampling.