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.     

四边形网格优化中的螺旋条带生成

已有的四边形网格的简化及优化方法大多数都是三角形网格简化在局部几何上的推广.四边形网格的结构受螺旋条带的影响,移除四边形网格中的螺旋条带则可以在拓扑结构上明显提高四边形网格的质量.文中具体讨论了四边形网格上螺旋条带与网格上奇异点的关系及其性质,并根据这个性质给出了四边形网格中螺旋条带的一般生成算法.实验结果表明,该算法可以有效地搜索四边形网格上的螺旋条带,进而通过删除螺旋条带优化四边形网格的拓扑结构.     

基于GPU的高质量隐式曲面四边形化

为了从隐式曲面快速抽取高质量的四边形网格,提出一种基于GPU的高质量隐式曲面四边形化方法.该方法分为初始网格抽取和网格优化2个阶段.利用GPU的并行性能,首先快速抽取一个粗糙的四边形网格,然后对该网格的几何(顶点位置、法向)和规整性(顶点分布、邻接关系)两方面进行迭代优化.实验结果表明,文中方法极大地提高了隐式曲面四边形化的效率,并且能得到高质量的四边形网格.     

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C-C细分的四边形网格上插值光滑Bézier曲面的生成

在任意拓扑的四边形网格上构造光滑的曲面是计算机辅助几何设计中的一个重要问题.基于C-C细分,提出一种从四边形网格上生成插值网格顶点的光滑Bézier曲面片的算法.将输入四边形网格作为C-C细分的初始控制网格,在四边形网格的每张面上对应得到一张Bézier曲面,使Bézier曲面片逼近C-C细分极限曲面.曲面片在与奇异顶点相连的边界上G1连续,其他地方C2连续.为解决C-C细分的收缩问题,给出了基于误差控制的迭代扩张初始控制网格的方法,使从扩张后网格上生成的曲面插值于初始控制网格的顶点.实验结果表明,该算法效率高,生成的曲面具有较好的连续性,适用于对四边化后的网格模型上重建光滑的曲面.     

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。     

面向不规则点消除的四边形网格优化方法

为了改善四边形网格的拓扑连接关系,针对Liu等提出的优化方法[1](Liu Jianfei,Sun Shuli,Chen Yongqiang.A new method of quality improvement for quadrilateral mesh based on small polygon reconnection).Acta Mechanica Sinica,2012,28(1):140-145),提出了面向不规则点消除的四边形网格优化方法.首先引入了一个加速策略,使每次操作可以处理的区域更大,从而提高了消除不规则点的能力;其次将方法拓展至曲面网格的优化.数值实验结果表明,该方法既能够大幅度改善ANSYS等数值模拟软件生成的四边形网格,也能进一步提高使用图形学领域方法得出的四边形网格的质量.     

基于“几何-拓扑”迭代优化的三维网格模型修复算法

针对三维网格模型孔洞保特征修复问题,提出一种基于"几何-拓扑"迭代优化的三维数据修复算法.给定残缺的三角网格模型,首先识别孔洞区域,利用动态规划方法对孔洞区域进行初始的三角剖分,赋予孔洞区域拓扑连接关系;然后识别孔洞边界一对特征点,基于特征点及其法向粗略拟合特征曲线,在特征曲线的指导下调整孔洞局部的拓扑结构,即孔洞区域拓扑连接关系优化;最后基于孔洞及其N环邻域构建保特征的局部总变分能量函数,迭代求解孔洞及其邻域的顶点几何位置,即局部顶点几何位置的优化,重复局部拓扑连接关系优化和顶点几何位置优化,直到拓扑结构优化处理中不再发生连接关系调整,即完成了三维网格模型的修复.在现有的完整三维网格模型上人为去除部分构造带孔洞的残缺模型,以此作为数据,与其他修复算法进行对比实验的结果表明,所提算法可以有效地恢复孔洞区域的显著特征,并且在修复时间和误差统计上占有明显优势.     

三维网格压缩方法综述

针对三维网格大数据量与三维图形引擎处理能力及网络带宽限制之间的矛盾,三维网格压缩编码技术提供了一系列解决方法。本文从静态压缩和递进网格两个角度分类,以拓扑信息驱动和几何信息驱动为两条主线,归纳比较了国内外近十年来三维网格压缩的各种方法,并给出其未采发展趋势。     

一种基于多边形剖分的有限元网格生成方法

在两步网格化过程中,待分析区域首先被剖分为具有三条或四条边的简单子区域部分.然后将利用传递模板法或映射法对这些子区域进行网格生成.本文结合计算几何和有限元网格自动生成问题,给出了一种基于简单多边形剖分的全四边形有限元网格自动生成方法.该方法分两步实现有限元网格生成首先通过权函数的引导,对待分析的简单多边形区域先进行子域剖分,得到一组三角形和凸四边形子域(大单元)的集合;然后利用中点剖分方法,将三角形和凸四边形子域单元剖分为全四边形有限元网格.实践证明,本文提出的方法实现简单、使用灵活,结果网格的质量良好.     

Prediction-based realistic 3D model compression

The benefit of using the geometry image to represent an arbitrary 3D mesh is that the 3D mesh can be re-sampled as a completely regular structure and coded efficiently by common image compression methods. For geometry image-based 3D mesh compression, we need to code the normal-map images while coding geometry images to improve the subjective quality and realistic effects of the reconstructed model. In traditional methods, a geometry image and a normal-map image are coded independently. However a strong correlation exists between these two kinds of images, because both of them are generated from the same 3D mesh and share the same parameterization. In this paper we propose a predictive coding framework, in which the normal-map image is predicted based on the geometric correlation between them. Additionally we utilize the strong geometric correlation among three components of normal-map image to improve the predicting accuracy. The experimental results show the proposed coding framework improves the coding efficiency of normal-map image, meanwhile the realistic effect of a 3D mesh is significantly enhanced.     

Digital Differential Geometry Processing

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.     

蝶形细分面片的光顺

使用蝶形细分法细分一般的初始控制网格得到的细分面片光滑而不光顺 ,面片的视觉效果很差 ,而运用现有的光顺技术 ,又只能直接光顺细分以后的结果 ,其需要保存的数据不仅量大 ,而且会引入误差 .针对这一问题 ,提出了一种新的光顺方法 ,即通过调整初始网格顶点位置来光顺细分以后的结果 .在添加合适的约束后 ,该方法不仅可以在光顺细分面片的同时 ,降低细分面片和三维真实物体表面之间的逼近误差 ,而且由于最终输出的是初始控制网格 ,故需要保存的数据量小 .     

一种通用的网格模型动态数据组织结构

数据结构的组织形式在算法的程序实现中占有重要地位。探讨了网格数据处理中的数据结构组织问题, 提出了一种动态的、有较强适应性的通用流形网格数据组织结构,并以不同实例验证了所提出的数据结构在时间上的即时有效性、存储空间上的自适应性以及实现上的简单性和层次性。该网格数据组织结构可用于各类网格模型数据的处理和计算。     

Retiling scheme: a novel approach of direct anisotropic quad-dominant remeshing

Remeshing has been an active research topic in Digital Geometry Processing. In this paper, a novel approach of direct anisotropic quad-dominant remeshing is proposed. We apply the retiling method to the particular problem of quad-dominant remeshing. Compared with other methods, this method can simply partition the surface of an original triangular mesh into connected quads with the mesh edges aligning to the principal directions. The first step in this method is to estimate and smooth the curvature tensor field of the surface at the vertices, and then the quad-dominant mesh is obtained by retiling the quad surface so that quadrilateral edges are parallel to the local principal curvature directions. In addition, to preserve the sharp feature information during remeshing processes, the feature lines can be extracted using mesh segmentation method, and the intersections between the feature lines and the orthogonal planes can be found during the process of retiling. A feature fusion process is presented to join the feature edges and feature points into the quad-dominant mesh. The experiment results show that this new remeshing method is simple and easy to implement. The resolution of the quadrilateral mesh can be controlled during the remeshing. It is applicable to arbitrary genus meshes and can generate high-quality quad-dominant mesh.     

Differential geometry images: remeshing and morphing with local shape preservation

In this paper, we propose a novel conception of differential geometry images (DGIM), encapsulating differential coordinates to traditional geometry images. DGIM preserves the local geometric characteristics in many graphics applications, such as model remeshing and morphing. The traditional geometry images using Cartesian coordinates require normal maps for correctly rendering models, because they neglect the existence of local geometric details in the image structure, which leads us to compute the normals and curvatures imprecisely. Using our differential geometry images, normals can be reconstructed easily and correctly thereafter normal maps are no longer required. In addition, DGIM can be easily applied to mesh morphing due to its regular topology and well-preserved local details. In this paper, we also demonstrate a variety of plausible mesh morphing results based on DGIM in shape space.     

基于单幅图像的真实感人体动画合成

由于单幅图像缺失三维信息以及完整的纹理信息,基于单幅图像的真实感三维人体动画合成极具挑战性。针对单幅图像三维信息缺失问题,提出了一种基于SMPL参数模型的三维人体几何重建方法。该方法以单幅图像为输入,先根据输入图像人体轮廓信息变形标准的SMPL参数模型分别生成与目标轮廓一致的正反面的三维几何模型,然后利用基于B样条插值的网格拼接融合算法拼接正反面三维几何,最后为了恢复正确的手部几何,利用基于B样条插值的网格拼接融合算法,将重建后的模型上错误的手部几何用标准SMPL参数模型上正确的手部几何替换。同时,针对单幅图像中纹理缺失的问题,提出了一个称为FBN（front to back network）的对抗生成网络,用于恢复被遮挡的人体背面纹理。实验结果表明,该方法生成的具有完整纹理的人体几何能够由3D运动数据驱动运动,生成具有高度真实感的三维人体动画。     

视点相关且拓扑可变的多分辨网格动态构造算法

随着近几年3维扫描和图形建模技术的快速发展,3维模型的数据量不断增大,其在存储、显示及传输上都面临巨大的挑战,因此,必须构造模型的简化表示。通过对当前网格模型动态简化算法的分析,提出了一种网格简化算法来构造拓扑可变的网格模型累进表示,在此基础上,通过对简化后的模型数据进行再组织,为简化模型建立了一种紧凑、灵活的动态多分辨率结构,并相应地给出了基于视点的动态简化算法。理论分析和实验结果表明,新方法能够随着视点参数的变化动态生成适当细节的简化模型,简化结果好,简化后的模型不仅能够较好地保留原模型的基本几何形状,而且能够较好地保留原始模型的颜色等属性特征,具有存储量小、适用范围广和自适应性强等特点。     

Wavelet-based multiresolution analysis of irregular surface meshes

We extend Lounsbery's multiresolution analysis wavelet-based theory for triangular 3D meshes, which can only be applied to regularly subdivided meshes and thus involves a remeshing of the existing 3D data. Based on a new irregular subdivision scheme, the proposed algorithm can be applied directly to irregular meshes, which can be very interesting when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. This is very convenient in CAD (computer-assisted design), when the mesh has attributes such as texture and color information, or when the 3D mesh is used for simulations, and where a different connectivity could lead to simulation errors. The algorithm faces an inverse problem for which a solution is proposed. For each level of resolution, the simplification is processed in order to keep the mesh as regular as possible. In addition, a geometric criterion is used to keep the geometry of the approximations as close as possible to the original mesh. Several examples on various reference meshes are shown to prove the efficiency of our proposal.