基于STL文件的Laplacian网格优化算法

针对直接重构得到且以STL文件格式存储的网格模型质量不高的问题, 提出了一种基于Laplacian坐标的网格模型全局优化算法。该算法在提高三角面片质量的同时可以很好地保持原网格模型的局部几何特征, 其核心思想是通过在最小二乘意义下求解由权重控制的包含顶点位置和拉普拉斯坐标双重约束的线性系统来对网格顶点进行重新定位。从实验结果可以看出, 该算法较以往的Lapacian优化算法在对网格细节特征的保持上有一定优势。     

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.     

保细节的网格刚性变形算法

提出了一种新的保细节的变形算法,可以使网格模型进行尽量刚性的变形,以减少变形中几何细节的扭曲.首先根据网格曲面局部细节的丰富程度,对原始网格进行聚类生成其简化网格;然后对简化网格进行变形,根据其相邻面片变形的相似性,对简化网格作进一步的合并,生成新的变形结果,将该变形传递给原始网格作为初始变形结果.由于对属于同一个类的网格顶点进行相同的刚性变形,可在变形中较好地保持该区域的表面细节,但分属不同类的顶点之间会出现变形的不连续.为此,通过迭代优化一个二次能量函数,对每个网格顶点的变形进行调整来得到最终变形结果.实验结果显示,该算法简单高效,结果令人满意.     

基于STL文件的Laplacian网格优化算法

针对三角网格模型优化算法对模型几何细节描述不够精确的问题,提出一种基于Laplacian坐标的网格模型全局优化算法。模型几何细节描述方面,采用网格顶点Laplacian坐标。网拓扑结构不变的前提下,可精确描述网格曲面局部几何特性。顶点重新定位方面,采用在最小二乘意义下求解由权重控制的包含顶点位置,以及Laplacian坐标双重约束的线性系统最优解的方法。实验结果表明,该算法在优化提高模型三角面片质量的同时,可较好地保留原始模型的几何细节。     

保特征的加权最小二乘三角网格光顺算法

在逆向工程和计算机图形学中,由扫描得到的数据多存在噪声,为了对其进行光顺处理,提出一种基于加权最小二乘思想的保特征网格光顺算法.首先提出一个关于光顺后网格顶点或者法向的离散二次能量函数,该能量一方面满足光顺后的网格在除特征点外的地方处处光滑的同时,还满足光顺后网格与原噪声网格尽可能相似;然后对此能量函数关于每个顶点求偏导数并使其为0,得到一个线性方程组,求解该方程组得到光顺后的网格.实验结果表明,该算法是线性的,复杂度低,且无需人工交互就可以很好地保持网格的尖锐特征,还能避免发生收缩现象.     

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。     

基于四面体控制网格的模型变形算法

提出一种鲁棒的保体积保表面细节的模型变形算法.首先将输入模型嵌入到一个稀疏的四面体控制网格中,并且通过一种改进的重心坐标来建立两者的对应关系;然后通过用户的交互,对控制网格建立一个二次非线性能量函数对其进行变形,而输入模型的变形结果则可以通过插值来直接获得.由于能量函数的优化是在控制网格上进行的,从而大大提高了算法的效率.与此同时,提出一种新的能量--Laplacian能量,可以使四面体控制网格进行尽量刚性的变形,从而有效地防止了大尺度编辑过程中模型形状的退化现象.文中算法还具有通用性,可支持多种模型的表示方式,如三角网格模型、点模型等.实验结果表明,该算法可以有效地保持输入模型的几何细节、防止明显的体积变化,得到了令人满意的结果.     

一种基于物理的实时细节保持变形算法

实时变形是计算机图形学研究的热点问题之一,复杂物体的实时变形至今仍未得到很好的解决.从物理变形方法和多分辨率网格编辑技术的优点出发,提出了一种适合于复杂弹性物体的实时变形算法.在预处理阶段,将原始精细网格模型进行简化以建立其基网格表示,基于基网格对模型的局部细节特征进行编码;在实时绘制阶段,在基网格上进行物理变形操作,并通过变形后的基网格和细节编码重构出变形后的精细网格.以上过程充分利用图形硬件的并行处理能力,利用像素处理器进行大部分计算操作.实验结果表明,该算法在变形过程中较好地保持了物体的局部特征,适合于表面细节复杂物体的实时变形应用.     

基于面法向量谱变换的网格光顺算法

微分坐标是刻画网格模型几何细节特征的有力工具,面法向量作为网格模型的一阶微分量,计算简单、不易受噪声影响,能真实反映网格模型的细节特征。基于此,提出一种改进的网格光顺去噪算法,使用信号处理技术中的谱网格处理方法,通过分解面法向量的拉普拉斯矩阵,将网格模型的面法向量变换到频谱域中,利用低频滤波器去除高频噪声得到连续的面法向量信号,基于三角面片重心约束条件重建网格顶点坐标,得到光顺的网格模型。实验结果表明,该算法使用的面法向量不易受到噪声影响,比顶点法向量更鲁棒,大幅提高了谱分解的效率,并且能克服光顺过程中产生的体积收缩、变形和过光滑等现象。     

勾画式泊松网格编辑

结合勾画式自由变形方法简单直观易用的优点和基于微分方程的网格变形方法能够保持形变物体几何细节的性质,提出一种勾画式的泊松网格编辑方法.通过允许目标勾画线和参照勾画线不必位于相同的相机平面,把原有的二维勾画变形推广至三维,并提出了一组完整的变形操作.这些变形操作根据参照勾画线与目标勾画线决定了一系列的局部变换,并由这些局部变换产生出用户希望的梯度场,最终根据用户需要的梯度场重建出变形后的三维模型.丰富的编辑实例表明了该方法具有直观便捷的交互特点.     

Skeleton-based Variational Mesh Deformations

In this paper, a new free-form shape deformation approach is proposed. We combine a skeleton-based mesh deformation technique with discrete differential coordinates in order to create natural-looking global shape deformations. Given a triangle mesh, we first extract a skeletal mesh, a two-sided Voronoibased approximation of the medial axis. Next the skeletal mesh is modified by free-form deformations. Then a desired global shape deformation is obtained by reconstructing the shape corresponding to the deformed skeletal mesh. The reconstruction is based on using discrete differential coordinates. Our method preserves fine geometric details and original shape thickness because of using discrete differential coordinates and skeleton-based deformations. We also develop a new mesh evolution technique which allow us to eliminate possible global and local self-intersections of the deformed mesh while preserving fine geometric details. Finally, we present a multi-resolution version of our approach in order to simplify and accelerate the deformation process. In addition, interesting links between the proposed free-form shape deformation technique and classical and modern results in the differential geometry of sphere congruences are established and discussed.     

LSM: A layer subdivision method for deformable object matching

A deformation technique is a method to deform any part of, or an entire object, into a desired shape. Existing deformation methods take a lot of computational cost to represent smoothness correctly due to the constraints caused by differential coefficients of high degree. Thus, it is very difficult to find a general solution. In this paper we propose a LSM (layered subdivision method) that integrates a controlling mechanism, surface deformation, and mesh refinement processing 3D modeling and free-form deformable object matching. The proposed method is considerably more efficient and robust when compared to the existing method of free-form surface, because of the computation of the reference points of deformation edge using geometry of free-form surface. This approach can be applied to automatic inspection of NURBS models and object recognition.     

基于多不动点约束的网格模型局部编辑

传统的自由变形方法通过计算控制晶格来变形,不适用于精确变形的情况。针对此问题,提出一种基于多不动点约束的网格模型局部编辑算法,该算法通过多个不动点的合理配置设定多种复杂的约束条件,实现网格模型的局部编辑,进而精确的变形模型。实验表明算法计算代价低,可实现精确变形。     

A non-parametric free-form optimization method for shell structures

This paper presents a numerical shape optimization method for the optimum free-form design of shell structures. It is assumed that the shell is varied in the out-of-plane direction to the surface to determine the optimal free-form. A compliance minimization problem subject to a volume constraint is treated here as an example of free-form design problem of shell structures. This problem is formulated as a distributed-parameter, or non-parametric, shape optimization problem. The shape gradient function and the optimality conditions are theoretically derived using the material derivative formulae, the Lagrange multiplier method and the adjoint variable method. The negative shape gradient function is applied to the shell surface as a fictitious distributed traction force to vary the shell. Mathematically, this method is a gradient method with a Laplacian smoother in the Hilbert space. Therefore, this shape variation makes it possible both to reduce the objective functional and to maintain the mesh regularity simultaneously. With this method, the optimal smooth curvature distribution of a shell structure can be determined without shape parameterization. The calculated results show the effectiveness of the proposed method for the optimum free-form design of shell structures.     

Parametric free-form shape design with PDE models and reduced basis method

We present a coupling of the reduced basis methods and free-form deformations for shape optimization and design of systems modelled by elliptic PDEs. The free-form deformations give a parameterization of the shape that is independent of the mesh, the initial geometry, and the underlying PDE model. The resulting parametric PDEs are solved by reduced basis methods. An important role in our implementation is played by the recently proposed empirical interpolation method, which allows approximating the non-affinely parameterized deformations with affinely parameterized ones. These ingredients together give rise to an efficient online computational procedure for a repeated evaluation design environment like the one for shape optimization. The proposed approach is demonstrated on an airfoil inverse design problem.     

基于任意骨架的隐式曲面造型技术

给出了一个新的基于任意多面体网格骨架的构造性自由曲面造型算法.算法首先由每个给定骨架构造出一个距离场,然后利用隐函数光滑过渡技术和CSG(constructive solid geometry)表示技术将所构造的隐式曲面自由地两两粘合成一张光滑曲面.隐式曲面的多边形化算法则用来生成最终曲面网格.以任意骨架作为基本体素,突破了传统隐式曲面以点为基本骨架的限制.而且,距离曲面很好地逼近了原骨架形状,使用户可直观地对复杂曲面进行交互设计.而形变函数的引入,则极大地丰富了此方法的造型能力.实验结果表明,基于该算法的原型系统能够方便、直观地构造复杂的自由曲面.     

多边形物体的精确B-样条自由变形*

在计算机动画与几何造型中,自由变形是一种重要的几何形状修改方法.该文从移位算子和函数复合的观点探讨一种方法,即当被变形物体用三角片表示、变形工具为B-样条参数体时,变形后的物体可以精确地表示为一组三角Bzier曲面片,其次数为B-样条参数体3个方向的次数之和.此方法的核心在于自由变形是作用在三角片上,而不是顶点上,所以解决了多边形物体B-样条自由变形的点采样问题.     

A New Approach for Direct Manipulation of Free-Form Curve

There is an increasing demand for more intuitive methods for creating and modifying free-form curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters, such as control points, knots, and weights, but also on the user's specified constraints and shapes. This paper presents a new approach for directly manipulating the shape of a free-form curve, leading to a better control of the curve deformation and a more intuitive CAD modeling interface. The user's intended deformation of a curve is automatically converted into the modification of the corresponding NURBS control points and knot sequence of the curve. The algorithm for this approach includes curve elevation, knot refinement, control point repositioning, and knot removal. Several examples shown in this paper demonstrate that the proposed method can be used to deform a NURBS curve into the desired shape. Currently, the algorithm concentrates on the purely geometric consideration. Further work will include the effect of material properties.     

插值Doo-Sabin表面形状调节

修改了插值的Doo-Sabin细分表面的初始控制网格，在第一次细分的同时加入了表面调节参数。这个方案具有以下特征：1）满足插值所有顶点或某些顶点的同时可以由参数调节极限表面；增加了对极限表面的调节自由度。2）整个的计算复杂度为O(k),其中k是顶点的数量。在最后也对结果表面的形状处理进行了讨论。     

A sketching interface for feature curve recovery of free-form surfaces

In this paper, we present a semi-automatic approach to efficiently and robustly recover the characteristic feature curves of a given free-form surface where we do not have to assume that the input is a proper manifold. The technique supports a sketch-based interface where the user just has to roughly sketch the location of a feature by drawing a stroke directly on the input mesh. The system then snaps this initial curve to the correct position based on a graph-cut optimization scheme that takes various surface properties into account. Additional position constraints can be placed and modified manually which allows for an interactive feature curve editing functionality. We demonstrate the usefulness of our technique by applying it to two practical scenarios. At first, feature curves can be used as handles for surface deformation, since they describe the main characteristics of an object. Our system allows the user to manipulate a curve while the underlying non-manifold surface adopts itself to the deformed feature. Secondly, we apply our technique to a practical problem scenario in reverse engineering. Here, we consider the problem of generating a statistical (PCA) shape model for car bodies. The crucial step is to establish proper feature correspondences between a large number of input models. Due to the significant shape variation, fully automatic techniques are doomed to failure. With our simple and effective feature curve recovery tool, we can quickly sketch a set of characteristic features on each input model which establishes the correspondence to a pre-defined template mesh and thus allows us to generate the shape model. Finally, we can use the feature curves and the shape model to implement an intuitive modeling metaphor to explore the shape space spanned by the input models.