实时网格编辑的扩展中值坐标方法

为了克服凸长和复杂网格较难克隆的问题,提出一种基于扩展中值坐标的交互式网格编辑方法.首先由用户选择源网格中感兴趣的区域,使用垂直投影参数化方法将其映射为二维区域,并将映射后的网格顶点二维拓扑信息保存为图像元放置于目标网格相应位置;然后通过扩展中值坐标参数和外部的边界环,在被粘贴的图像元基础上恢复出三维信息;最终粘贴网格部分被变形使得与目标网格光滑拼接.该方法采用GPU对网格复制进行加速.实验结果表明,文中方法能够在三维模型之间实时地复制、替换任意不规则网格区域.     

基于切平面中值坐标的Laplacian网格变形算法

网格模型变形往往需要保持局部几何细节,Laplacian网格变形算法能够较好地保持局部几何细节特征,但细节特征描述子-Laplacian坐标的计算欠缺精确性.从平面多边形中值坐标的角度出发,对Laplacian坐标进行重新定义,将顶点的一阶邻域投影到顶点处切平面上,根据顶点相对投影点的中值坐标构建的Laplacian坐标能够精确地描述模型的局部几何细节特征,实验验证能够获得较好的编辑效果.     

基于层次B样条的网格模型变形技术

针对常用的网格模型提出了一个基于层次B样条控制的三维网格空间变形框架．首先由用户交互地选取编辑区域,由程序完成编辑区域的参数化和均匀重采样;然后用层次B样条光顺拟合这些均匀采样点,所得的R样条曲面作为网格模型的基曲面,计算待编辑区域中网格顶点相对该B样条基曲面的局部坐标,该局部坐标平移、旋转不变,可视为模型的内蕴几何特征,并作为变形操作中的不变量．用户通过编辑层次B样条基曲面或者直接编辑三维网格模型,可实现多分辨率变形．实验结果表明：该方法操作直观方便,无论对整体还是局部变形,都能取得可控、可靠的变形效果,且采刚B样条曲面的控制手段易于与已有的造型系统合成．     

邻域表示的形状刚性操作实现方法

角色动画编辑的核心技术之一,是形状既能实现刚性变形,又能实现实时操作。在形状刚性操作计算中,通过定义三角网格顶点的面邻域和点邻域的平方差度量,简化自由顶点与约束顶点的坐标分离。这种表示法,在整体拟合中使得x坐标与y坐标能够独立求解。在算法实现中,设计恰当的系数矩阵和常数项向量的链表结构,采用矩阵索引存储和共轭梯度求解,减少数据的重复计算。实验表明,在普通的PC机上能够实现约1 000个顶点的网格实时交互变形操作。     

利用调和映射的复杂网格曲面螺旋刀轨生成算法

针对截平面法规划的复杂网格曲面刀轨的加工效率不高问题,提出一种复杂网格曲面螺旋刀轨生成算法.首先采用调和映射的方法对网格曲面进行参数化,然后根据残留高度确定参数网格中的参数环,在相邻参数环的参数点之间进行“分组匹配”,并依次计算初始和精确的对角参数螺旋线;在此基础上采用“区域划分”的方法快速生成了无干涉的网格曲面螺旋刀轨.对于复杂网格曲面的实验结果表明,文中的螺旋刀轨能够有效地提高截平面法刀轨的加工效率,且能够保证较好的加工质量.     

基于弹簧-质点模型的不规则曲面纹理映射

针对三角网格表示的不规则曲面的纹理映射问题,提出一种基于弹簧-质点模型的简单、高效、失真小的纹理映射算法。结合调和映射的参数化方法以及弹簧-质点模型的复杂平面展开方法,保持拓扑关系地将三维曲面投影于平面内;通过建立三角网格表示的投影面的弹簧-质点模型,将不规则曲面参数化于给定大小的矩形域;利用参数化的结果计算不规则曲面各顶点的纹理坐标,进行纹理贴图。实验结果表明,该算法能够实现纹理高效、均匀、变形小地映射于任意不规则曲面上。     

任意拓扑三角形网格的全局参数化

提出了一种零亏格的任意拓扑流形三角形网格自动全局参数化方法 .算法首先采用顶点对合并的网格简化方法构造一个网格的累进表示 ,在进行网格简化的同时 ,对被删除的顶点相对于顶点合并操作所得到的新顶点的邻域进行局部参数化 ,由此得到一个带局部参数化信息的累进网格 ;然后将网格简化所得到的基网格进行中心投影到一个单位球面上 ,并采用累进恢复的方法将删除的顶点按与删除时相反的顺序逐次添加回网格上来 ,所添加顶点的坐标不再是其删除前的坐标值 ,而是由局部参数化信息计算得到 ,并且保证是位于单位球面上的 .由此得到原始网格的单位球面参数化网格     

均匀准保角球面参数化

针对闭的或者单边界亏格为0的三角网格,提出一种球面参数化方法．通过立体投影将现有的平面参数化方法推广到球面上,得到一个初始的球面参数化;为了减小变形,引入质心坐标进行全局优化;最后用Moebius变换均匀化最终的球面网格．该方法能够避免立体投影出现三角形折叠的情况,保证最后的映射是双射．通过大量典型的三维模型实验和比较可以看出：文中的参数化方法变形小,在复杂网格的纹理映射中的均匀化效果较现有的保角、保面积变换有明显的改善．     

一种基于网格的从明暗恢复形状方法

针对目前“从明暗恢复形状”时存在计算复杂及收敛性差等问题,提出一种基于网格的解决方法。首先通过图像预处理及区域划分操作将原始图像分割成多个亮度离散的多边形区域,并逐步转换成平面三角形网格,然后根据Lambert定律建立关于空间网格顶点坐标的方程组,在使用最小二乘法求解后,直接将结果应用到OpenGL或DirectX等实时渲染引擎的图形管道中,实现模型的建立与显示。经仿真实验证明该方法计算方便,可逼真重建原始物体的形状。     

保相似的网格参数化

网格参数化是数字几何处理中的重要问题,而三角网格又是典型的一种网格表示形式。为能够快速求解三角网格的平面参数化,同时减少参数化带来的三角形的扭曲,提出了一种保持形状相似的三角网格平面参数化方法—保相似参数化,该方法使得参数化后的网格的相邻两边夹角和长度比例在最小二乘意义下整体上保持不变,从而建立对应三角形的相似性。通过三角形的相邻两条边的夹角和两边的比例值建立线性方程组,在给定初始条件后可以快速地求解该线性方程组,从而得到参数化后的平面网格。该方法也适用于添加任何线性约束条件,而且整个算法是线性的。与现有的一些方法相比,该算法几何意义直观,操作简便。实例表明,该方法可以得到较好的参数化结果,非常适合于纹理映射等计算机图形学的应用。     

Interactive mesh cloning driven by boundary loop

In order to copy arbitrary irregular mesh between two models continuously, this paper presents an interactive mesh cloning approach based on pyramid spherical coordinates driven by boundary loop. The approach extends an existing algorithm for computing offset membrane on mesh. A parametric paint brush is constructed to define canvas both on the source mesh and the target mesh. They are mapped onto a 2D parametric domain using discrete geodesic polar maps to register correspondingly. During cloning, the boundary loop of the region of interest (ROI) on the target mesh is fitted in real time by B-spline curve to register the boundary loop of the source ROI. Via the reconstructed boundary loop, the ROI is deformed to register the target mesh by pyramid spherical coordinates to ensure that the clone result is seamless and natural. Our approach can clone arbitrary irregular meshes between two 3D models, even if the mesh is non-manifold. The cloning process is operated in real time by GPU acceleration. Experimental results demonstrate the effectiveness of our interactive mesh cloning.     

GeoBrush: Interactive Mesh Geometry Cloning

We propose a method for interactive cloning of 3D surface geometry using a paintbrush interface, similar to the continuous cloning brush popular in image editing. Existing interactive mesh composition tools focus on atomic copy‐and‐paste of preselected feature areas, and are either limited to copying surface displacements, or require the solution of variational optimization problems, which is too expensive for an interactive brush interface. In contrast, our GeoBrush method supports real‐time continuous copying of arbitrary high‐resolution surface features between irregular meshes, including topological handles. We achieve this by first establishing a correspondence between the source and target geometries using a novel generalized discrete exponential map parameterization. Next we roughly align the source geometry with the target shape using Green Coordinates with automatically‐constructed cages. Finally, we compute an offset membrane to smoothly blend the pasted patch with C continuity before stitching it into the target. The offset membrane is a solution of a bi‐harmonic PDE, which is computed on the GPU in real time by exploiting the regular parametric domain. We demonstrate the effectiveness of GeoBrush with various editing scenarios, including detail enrichment and completion of scanned surfaces.     

网格修补的特征配准方法

目的 网格重建和编辑会产生几何特征缺失的模型,填补这些空洞具有重要的意义。为了克服复杂曲面修补中网格融合难以配准的问题,提出了环驱动球坐标结合基于曲率及法向ICP(iterative closest point)迭代配准的网格修补方法。方法 首先用户查找合适的源网格面片放入空洞处周围;然后对目标网格空洞环建立B样条曲线,将带修补网格包边界置于B样条曲线上,构架环驱动球坐标,将源网格变形初步配准目标网格空洞周围领域;最后使用Laplacian光顺并基于网格曲率及法向进行ICP迭代配准,使源网格与目标网格光滑拼接融合。结果 该方法能够有效修补网格空洞缺失的细节特征,并且拼接处光滑连续。 结论 环驱动球坐标配准避免了网格变形的包围网格笼子构造,再通过ICP迭代精确配准网格,和以往的网格修补方法相比,该方法能够很好地修补网格空洞处细节特征。     

球面坐标下的凸组合球面参数化

球面参数化是一种应用价值很广的几何参数化方法.对于封闭且亏格为零的三角形网格,该文提出了一种新的球面参数化方法.通过引入多个球面坐标覆盖,在球面坐标系下,用凸组合方法,得到了接近线性的球面参数化求解方法.与已有的直角坐标系下的凸组合参数化方法相比,该文所提出的方法大大降低了求解方程组的非线性程度,因此求解时间大幅度降低.此外,还避免了直角坐标系下求解的多种退化情况.最后,给出了实验结果,并对凸组合球面参数化中存在的几个问题进行了讨论.     

Geometry seam carving

We present a novel approach to feature-aware mesh deformation. Previous mesh editing methods are based on an elastic deformation model and thus tend to uniformly distribute the distortion in a least-squares sense over the entire deformation region. Recent results from image resizing, however, show that discrete local modifications such as deleting or adding connected seams of image pixels in regions with low saliency lead to far superior preservation of local features compared to uniform scaling — the image retargeting analog to least-squares mesh deformation. Hence, we propose a discrete mesh editing scheme that combines elastic as well as plastic deformation (in regions with little geometric detail) by transferring the concept of seam carving from image retargeting to the mesh deformation scenario. A geometry seam consists of a connected strip of triangles within the mesh’s deformation region. By collapsing or splitting the interior edges of this strip, we perform a deletion or insertion operation that is equivalent to image seam carving and can be interpreted as a local plastic deformation. We use a feature measure to rate the geometric saliency of each triangle in the mesh and a well-adjusted distortion measure to determine where the current mesh distortion asks for plastic deformations, i.e., for deletion or insertion of geometry seams. Precomputing a fixed set of low-saliency seams in the deformation region allows us to perform fast seam deletion and insertion operations in a predetermined order such that the local mesh modifications are properly restored when a mesh editing operation is (partially) undone. Geometry seam carving hence enables the deformation of a given mesh in a way that causes stronger distortion in homogeneous mesh regions while salient features are preserved much better.     

Modeling smooth shape using subdivision on differential coordinates

Traditional subdivision schemes are applied on Euclidean coordinates (the spatial geometry of the control mesh). Although the subdivision limit surfaces are almost everywhere C² continuous, their mean-curvature normals are only C⁰. In order to generate higher quality surfaces with better-distributed mean-curvature normals, we propose a novel framework to apply subdivision for shape modeling, which combines subdivision with differential shape processing. Our framework contains two parts: subdivision on differential coordinates (a kind of differential geometry of the control mesh), and mutual conversions between Euclidean coordinates and differential coordinates. Further discussions about various strategies in both parts include a special subdivision method for mean-curvature normals, additional surface editing options, and a version of our framework for curve design. Finally, we demonstrate the improvement on surface quality by comparing the results between our framework and traditional subdivision methods.     

Differential Representations for Mesh Processing

Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. This framework is based on linear operators defined on polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. The core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator.     

凸组合球面参数化

针对具有单边界的三角网格或与球面同胚的零亏格封闭网格，提出一种基于球面向量线性凸组合的三维网格球面参数化方法．把参数域从平面凸区域扩展到球面凸区域，并把具有凸性的重心坐标纳入到参数化框架中，使得参数化具有保形性质且变形小，同时证明了该参数化方法的存在性和惟一性．整个算法简单可靠．