基于三角域上V-系统的三维几何模型的正交重构

提出了一种新的对三维几何模型的描述方法.利用三角域上的一类完备正交函数系--V-系统这一数学工具,对三角片构成的几何模型进行正交展开,其展开系数(谱系数)便是该模型的数字描述.由于V-系统所具有的特殊性质,可以对多个分离的三角片,进行整体的表达.这种正交表达,使得把频谱分析的方法引入到对三维网格模型的研究中成为可能.     

基于几何信号频谱分析的网格编辑

提出了一种基于几何信号频谱分析的网格编辑新方法．该方法通过空域中形变编辑和频域中几何信号处理技术的有机结合达到直观交互的目的．为此，通过引入原始网格的一个几何代理，然后构造两者的一致性参数化，并实施频谱分析，在频率域上将几何代理上的形变结果传递到原始网格，达到编辑的目的．其关键创新在于改进了基于径向基函数的参数化网格特征对齐方法，并给出一种崭新的自适应采样方法来更加合理地采样原始模型几何信号．进一步地，将频谱编辑方法进行了推广，将其应用于网格形状混合和几何细节特征迁移，获得了良好的合成效果．     

可控的三维Morphing

提出了一种基于距离场插值的三维Morphing算法.该方法通过解析距离场来实现三维Morphing,使过渡形体的光滑性不依赖于原模型的离散剖分精度.同时,给出了基于约束点对和变形控制体的交互形状过渡算法,用户可由此直观而方便地对变形过程实施有效的控制.多个变形实例证明,该算法能够方便地实现两个任意定向流形模型间的可控三维Morphing.     

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．     

基于细分曲面的泊松网格编辑

针对具有丰富几何细节的三维网格模型,基于直接坐标操纵的传统编辑算法在编辑过程中不可避免地存在细节特征无法得到有效保持的问题.综合基于细分曲面的空间变形方法以及微分域网格编辑二者优势,提出一种基于细分曲面的泊松网格编辑方法.首先建立待变形网格模型的包围网格,以包围网格所决定的细分曲面构造变形控制曲面;然后根据用户变形意图操纵包围网格,将对应细分曲面变化信息转化为对网格模型泊松梯度场的改变;最后根据变化后的梯度场重建网格模型.文中方法交互简单、直观,具有多分辨率编辑的优势,可以有效地保持网格模型的细节特征.丰富的变形实例证明了该方法的有效性和可行性.     

基于细分的网格模型骨架驱动变形技术

针对传统骨架驱动变形方法中模型细节特征不能得到有效保持的问题,提出一种基于细分的骨架驱动网格模型变形方法。首先,对网格模型待变形区域基于截交线进行局部骨架提取和控制网格构建,分别建立骨架与控制网格以及控制网格所对应细分曲面与待变形模型区域之间的关联关系;然后,将基本函数作用下的自由变形方法应用于骨架变形,通过骨架变形驱动控制网格变形,将变形前后控制网格所对应细分曲面的变化信息转为网格模型泊松梯度场的改变;最后,根据改变后梯度场重建网格模型。实例表明,该变形方法针对不同网格模型均可以得到较好的编辑效果,且细节信息在变形后都得到了有效保持。与传统骨架驱动变形方法相比,该方法除具备交互操作简单直观的优势外,同时能够更好保持变形模型几何细节特征,更为适合具有丰富几何细节的复杂模型的变形编辑。     

基于曲率流的四边形主导网格的光顺方法

网格模型是计算机图形学和数字几何处理中运用最为广泛的三维几何表达方式.四边网格(以四边形为主的网格)由于其符合人们对几何形状变化的自然感知,在表示三维几何上有其独有的优势,并且可以更为直接地应用在几何造型、细分曲面、建筑设计等方面.文中针对四边形主导网格含有噪声的情况,设计了一种基于表面微分属性的光顺方法,该方法具有易实现、计算效率高的特点.基于曲率流的几何扩散可以有效地保持原网格的几何特征,同时还针对四边形主导网格的T-顶点进行了特殊处理.     

基于中轴表达的三维模型轮廓提取方法

三维网格模型的轮廓信息在网格检索、网格简化、网格重建中有着广泛应用。现有的轮廓提取方法较为复杂,需要分析和过滤网格模型的几何特征,计算量大且有时无法生成完整的轮廓信息。近年来,三维模型的中轴表达研究趋于成熟,在表达模型几何拓扑关系上有独特的优势。因此,提出了一种基于中轴表达的三维模型轮廓提取方法：首先提取三维模型的中轴表达信息,将中轴角点投影到三维模型表面;然后根据每个区域的拓扑关系选择适合的角点连接关系,将投影点连接形成模型区域轮廓;再针对投影过程中产生的误差进行分析和纠正;最后合并区域轮廓得到三维模型的完整轮廓。通过对多个模型数据库中代表性的三维网格模型进行实验和重建误 差比较,该方法的平均重建质量较现有方法约有 10%的提升,在重建质量和轮廓信息完整度方面优于现有方法。     

面向可展特征的网格模型去噪方法

可展特征是三维网格模型的常见几何特征。为了更好地对具备可展特征的网格模型进行去噪,提出一种面向可展特征的网格模型去噪方法。首先基于变分形状逼近策略分割可展区域,识别出网格模型上可展特征区域,并对分割区域进行基于可展性度量的合并和划分,改进现有 L 0 去噪算法中针对非均匀噪声网格的正则优化表达项,引入三角网格顶点的可展度量项,利用可展特征的曲面法向量 L 0 范数的优化问题求解实现网格模型的去噪。通过对多个模型数据集中的大量模型数据进行处理,验证了该方法的有效性。实验表明,结合模型的可展特性的去噪方法在保持模型的几何特征特别是可展特征上效果优于已有方法。     

全规整重网格化三维模型的压缩

通过保形自适应重采样,可将三维网格模型转化为规则排列的二维几何图像,从而可借鉴成熟的图像压缩技术对其进行压缩.提出了保形自适应采样算法,根据网格模型表面的有效顶点分布密度自适应地调整采样网格,并可最大限度地通过原始网格顶点进行采样.在不增加采样率的前提下,该压缩方法所得解压模型具有更小的失真度.通过大量实例对文中方法进行了验证,并与同类方法进行对比.实验结果表明该方法是切实可行的,且具有更好的压缩效果.     

与视点对应的视图插补

ＩｍａｇｅＭｏｒｐｈｉｎｇ是产生图象之间插补变换一类被广泛使用的技术,所有的Ｍｏｒｐｈｉｎｇ方法奢阳基于两幅图象之间的象素位置和颜色的内插。现行的Ｍｏｒｐｈｉｎｇ技术不能保证所生成图象的真实性。本文提出的视图插 补技术,使得所生成的插 补图象对应于某个视点,且不需要知识源图象所对应的摄像朵矩阵,因此计算简单。     

Feature-based 3D morphing based on geometrically constrained spherical parameterization

Current trends in free form editing motivate the development of a novel editing paradigm for CAD models beyond traditional CAD editing of mechanical parts. To this end, we need robust and efficient 3D mesh deformation techniques such as 3D structural morphing.In this paper, we present a feature-based approach to 3D morphing of arbitrary genus-0 polyhedral objects that is appropriate for CAD editing. The technique is based on a sphere parameterization process built on an optimization technique that uses a target function to maintain the correspondence between the initial polygons and the mapped ones, while preserving topology and connectivity through a system of geometric constraints. Finally, we introduce a fully automated feature-based technique that matches surface areas (feature regions) with similar topological characteristics between the two morphed objects and performs morphing according to this feature correspondence list. Alignment is obtained without user intervention based on pattern matching between the feature graphs of the two morphed objects.     

3D动画技术在移动平台上的研究与实现

本文介绍了移动3D技术的发展,简要介绍了关键帧动画、变形动画、骨骼蒙皮动画三种动画的原理,详细分析了M3G平台上的动画实现原理和实现方法,并给出了M3G平台动画实现的一个例子。     

多特征融合的图像自动变形

目的 图像变形算法中特征基元提取和匹配方式大部分都是采用人机交互的方式进行,并且在遮挡区域变形时出现较多的鬼影和模糊现象,使得针对同一场景图像变形实现繁琐且效果不佳,针对这些问题提出一种基于多特征融合的自动图像变形算法。方法 该算法提取多种图像特征信息（如Surf特征算子、Harris算子、Canny算子等）并进行多特征融合匹配,得到一个分布适当且对应关系正确的三角网格,再结合图像变形,实现自动图像插值。结果 实验结果显示,自动的提取特征基元有效地减少了人工操作,而多特征融合匹配有效地抑制了图像变形时边缘或遮挡区域鬼影的产生。结论 提出的融合匹配方法,将不同的特征信息有效地融合匹配从而改善了图像变形算法。通过对多组实验结果进行问卷调查,91%的参与者认为该算法有效地改进图像变形结果。     

3D动画技术在移动平台上的研究与实现

本文介绍了移动3D技术的发展，简要介绍了关键帧动画、变形动画、骨骼蒙皮动画三种动画的原理，详细分析了M3G平台上的动画实现原理和实现方法，并给出了M3G平台动画实现的一个例子。     

Reconstruction of dynamic 3D scene based on visual hull and view morphing

In this paper, we propose a new method that processes multiple synchronized video sequences and generates 3D rendering of dynamic objects in the video. It exploits an efficient image‐based reconstruction scheme that constructs and shades 3D models of objects from silhouette images by combining image‐based visual hull and view morphing. The proposed hybrid method improves the speed and the quality of the previous visual hull sampling methods. We designed and implemented a system based on this method which is relatively low cost and does not require any special hardware or specific environment. Copyright © 2003 John Wiley & Sons, Ltd.     

真实感人脸模型的细分曲面重建

提出一种利用2张正交照片和细分曲面进行真实感三维人脸建模的方法,并实现了不同模型间的三维变形.为了构造个性化的人脸几何模型,将网格简化、自由曲面变形和细分结合起来,得到多个层次细节下的人脸模型;再经过纹理融合和映射,完成个性化的真实感三维人脸建模;同时利用线性插值实现了同拓扑真实感模型间的光滑变形.实验结果表明：该方法不仅可以进行有效的真实感三维人脸建模,而且变形简单流畅,具有广阔的应用前景.     

Robust Spherical Parameterization of Triangular Meshes

Parameterization of 3D mesh data is important for many graphics and mesh processing applications, in particular for texture mapping, remeshing and morphing. Closed, manifold, genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a 3D triangle mesh onto the 3D sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways.     

Geometric Snakes for Triangular Meshes

Feature detection is important in various mesh processing techniques, such as mesh editing, mesh morphing, mesh compression, and mesh signal processing. In spite of much research in computer vision, automatic feature detection even for images still remains a difficult problem. To avoid this difficulty, semi‐automatic or interactive techniques for image feature detection have been investigated. In this paper, we propose a geometric snake as an interactive tool for feature detection on a 3D triangular mesh. A geometric snake is an extension of an image snake, which is an active contour model that slithers from its initial position specified by the user to a nearby feature while minimizing an energy functional. To constrain the movement of a geometric snake onto the surface of a mesh, we use the parameterization of the surrounding region of a geometric snake. Although the definition of a feature may vary among applications, we use the normal changes of faces to detect features on a mesh. Experimental results demonstrate that geometric snakes can successfully capture nearby features from user‐specified initial positions.     

A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations

A hybrid dynamic grid generation technique for two-dimensional (2D) morphing bodies and a block lower-upper symmetric Gauss-Seidel (BLU-SGS) implicit dual-time-stepping method for unsteady incompressible flows are presented for external bio-fluid simulations. To discretize the complicated computational domain around 2D morphing configurations such as fishes and insect/bird wings, the initial grids are generated by a hybrid grid strategy firstly. Body-fitted quadrilateral (quad) grids are generated first near solid bodies. An adaptive Cartesian mesh is then generated to cover the entire computational domain. Cartesian cells which overlap the quad grids are removed from the computational domain, and a gap is produced between the quad grids and the adaptive Cartesian grid. Finally triangular grids are used to fill this gap. During the unsteady movement of morphing bodies, the dynamic grids are generated by a coupling strategy of the interpolation method based on ‘Delaunay graph’ and local remeshing technique. With the motion of moving/morphing bodies, the grids are deformed according to the motion of morphing body boundaries firstly with the interpolation strategy based on ‘Delaunay graph’ proposed by Liu and Qin. Then the quality of deformed grids is checked. If the grids become too skewed, or even intersect each other, the grids are regenerated locally. After the local remeshing, the flow solution is interpolated from the old to the new grid. Based on the hybrid dynamic grid technique, an efficient implicit finite volume solver is set up also to solve the unsteady incompressible flows for external bio-fluid dynamics. The fully implicit equation is solved using a dual-time-stepping approach, coupling with the artificial compressibility method (ACM) for incompressible flows. In order to accelerate the convergence history in each sub-iteration, a block lower-upper symmetric Gauss-Seidel implicit method is introduced also into the solver. The hybrid dynamic grid generator is tested by a group of cases of morphing bodies, while the implicit unsteady solver is validated by typical unsteady incompressible flow case, and the results demonstrate the accuracy and efficiency of present solver. Finally, some applications for fish swimming and insect wing flapping are carried out to demonstrate the ability for 2D external bio-fluid simulations.