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．     

基于骨架的三维网格局部编辑

复杂网格的编辑是三维动画设计的关键技术,已经出现了多种比较成功的方案和算法。在研究了三维网格的骨架生成及其优化方法的基础上,提出了一种基于骨架的局部网格编辑算法。先由用户确定编辑区域,绘出与变形后的骨架相对应的编辑曲线,再根据网格顶点与骨架曲线及编辑曲线之间的对应关系,实现网格结点的平移和旋转等编辑操作。实验证明,该算法的实现具有编辑直观、易于控制等特点,能够很好地应用于网格的局部特征编辑。     

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。     

保持细节的网格曲面局部变形算法

针对直接控制自由变形算法(DFFD)在对大规模网格模型实施局部变形时细节保持性差的问题,以网格曲面上的离散泊松方程和微分算子为理论基础,提出一种完全自动化的网格模型局部变形算法。基本思想是依据用户对模型上控制顶点的移动及网格的表面几何特征,由算法自动判断得到变形区域,继而将用户对控制顶点的编辑操作映射为对变形区域梯度场地操作,最后通过泊松重建得到变形后的网格。优点是在使模型表面的局部几何细节得到保持的基础上省略了人为划定变形区域的步骤。     

一种基于约束特征的网格编辑技术

为了改进自由变形技术在用户交互和编辑灵活性的不足,提出了一种直观的交互式网格模型编辑技术,该技术可以根据不同的约束变形特征、封闭的变形边界以及编辑参考曲线来完成网格模型的编辑,并且为了模型的平滑和自然,采用了自适应细分策略。实验证明,该方法简便直观,有良好的交互性,并能得到很好的编辑结果。此技术可以方便地应用于CAD/CAM和计算机动画系统中。     

鲁棒的网格实时几何编辑算法

目的 本文提出一种网格实时编辑方法,能够实现精确的参数化区域选择来对网格进行复制粘贴操作。方法 首先通过提供给用户的笔刷在网格上选择感兴趣区域,通过半边结构遍历和种子填充算法精确指定参数化区域;在遍历过程中加入一个距离场限制,然后使用平面中值坐标方法对被复制区域进行变形处理;最后将被复制区域和目标网格进行无缝融合,恢复三维形状。结果 实验表明本文提出的方法能够对高曲率和凸长网格进行有效编辑,复制得到的模型能够符合需求,并且鲁棒稳定。结论 泊松方程结合平面中值坐标的网格实时编辑方法,能够实现精确的参数化区域选择对网格进行复制粘贴操作。通过与已有的网格克隆方法相比较,该方法具有很好的鲁棒性并且效果良好。     

等距cage生成

广义重心坐标已被广泛应用于三维网格模型的编辑与变形中,而cage是广义重心坐标编辑的重要载体.为此提出一种全自动的cage生成方法.首先对给定三维网格模型做适当简化,然后建立简化网格的距离场,再抽取指定距离值的offset网格,最后根据指定顶点数或误差阈值简化offset网格,从而得到该网格模型的等距cage.其中,最耗时的距离场生成过程可以通过GPU加速使得算法接近实时.实验结果表明,文中方法生成的等距cage能很好地应用于广义重心坐标的网格编辑中.     

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.     

人脸识别中表情弱化处理研究

针对表情对人脸识别准确率的影响问题,提出了基于向导的局部表情弱化模型,其利用网格变形技术来减少表情人脸的塑性变形。首先在表情区域按三角面片变换,采用梯度算子计算出变形后梯度场,实现基于向导微分梯度场的变换;然后代入泊松方程完成离散三角形拼接和变形模型的重建。找到脸部表情不变的刚性区域,得到类内的平均人脸差异,从而产生约束条件并将之加入变形过程来保持类间的差异和类内的相似度。与其它算法比较,其识别准确率有明显提高,证明了算法的有效性。     

A shape design system using volumetric implicit PDEs

Solid modeling based on partial differential equations (PDEs) can potentially unify both geometric constraints and functional requirements within a single design framework to model real-world objects via its explicit, direct integration with parametric geometry. In contrast, implicit functions indirectly define geometric objects as the level-set of underlying scalar fields. To maximize the modeling potential of PDE-based methodology, in this paper we tightly couple PDEs with volumetric implicit functions in order to achieve interactive, intuitive shape representation, manipulation, and deformation. In particular, the unified approach can reconstruct the PDE geometry of arbitrary topology from scattered data points or a set of sketch curves. We make use of elliptic PDEs for boundary value problems to define the volumetric implicit function. The proposed implicit PDE model has the capability to reconstruct a complete solid model from partial information and facilitates the direct manipulation of underlying volumetric datasets via sketch curves and iso-surface sculpting, deformation of arbitrary interior regions, as well as a set of CSG operations inside the working space. The prototype system that we have developed allows designers to interactively sketch the curve outlines of the object, define intensity values and gradient directions, and specify interpolatory points in the 3D working space. The governing implicit PDE treats these constraints as generalized boundary conditions to determine the unknown scalar intensity values over the entire working space. The implicit shape is reconstructed with specified intensity value accordingly and can be deformed using a set of sculpting toolkits. We use the finite-difference discretization and variational interpolating approach with the localized iterative solver for the numerical integration of our PDEs in order to accommodate the diversity of generalized boundary and additional constraints.     

A Revisit of Shape Editing Techniques:From the Geometric to the Neural Viewpoint

3D shape editing is widely used in a range of applications such as movie production,computer games and computer aided design.It is also a popular research topic in computer graphics and computer vision.In past decades,researchers have developed a series of editing methods to make the editing process faster,more robust,and more reliable.Traditionally,the deformed shape is determined by the optimal transformation and weights for an energy formulation.With increasing availability of 3D shapes on the Internet,data-driven methods were proposed to improve the editing results.More recently as the deep neural networks became popular,many deep learning based editing methods have been developed in this field,which are naturally data-driven.We mainly survey recent research studies from the geometric viewpoint to those emerging neural deformation techniques and categorize them into organic shape editing methods and man-made model editing methods.Both traditional methods and recent neural network based methods are reviewed.     

Sketch-based 3D model retrieval by incorporating 2D-3D alignment

Sketch-based 3D model retrieval is very important for applications such as 3D modeling and recognition. In this paper, a sketch-based retrieval algorithm is proposed based on a 3D model feature named View Context and 2D relative shape context matching. To enhance the accuracy of 2D sketch-3D model correspondence as well as the retrieval performance, we propose to align a 3D model with a query 2D sketch before measuring their distance. First, we efficiently select some candidate views from a set of densely sampled views of the 3D model to align the sketch and the model based on their View Context similarities. Then, we compute the more accurate relative shape context distance between the sketch and every candidate view, and regard the minimum one as the sketch-model distance. To speed up retrieval, we precompute the View Context and relative shape context features of the sample views of all the 3D models in the database. Comparative and evaluative experiments based on hand-drawn and standard line drawing sketches demonstrate the effectiveness and robustness of our approach and it significantly outperforms several latest sketch-based retrieval algorithms.     

Spectral Affine‐Kernel Embeddings

In this paper, we propose a controllable embedding method for high‐ and low‐dimensional geometry processing through sparse matrix eigenanalysis. Our approach is equally suitable to perform non‐linear dimensionality reduction on big data, or to offer non‐linear shape editing of 3D meshes and pointsets. At the core of our approach is the construction of a multi‐Laplacian quadratic form that is assembled from local operators whose kernels only contain locally‐affine functions. Minimizing this quadratic form provides an embedding that best preserves all relative coordinates of points within their local neighborhoods. We demonstrate the improvements that our approach brings over existing nonlinear dimensionality reduction methods on a number of datasets, and formulate the first eigen‐based as‐rigid‐as‐possible shape deformation technique by applying our affine‐kernel embedding approach to 3D data augmented with user‐imposed constraints on select vertices.     

Sketching MLS Image Deformations On the GPU

In this paper, we present an image editing tool that allows the user to deform images using a sketch‐based interface. The user simply sketches a set of source curves in the input image, and also some target curves that the source curves should be deformed to. Then the moving least squares (MLS) deformation technique [ [SMW06] ] is adapted to produce realistic deformations while satisfying the curves' positional constraints. We also propose a scheme to reduce image fold‐overs in MLS deformations. Our system has a very intuitive user interface, generates physically plausible deformations, and can be easily implemented on the GPU for real‐time performance.     

Modeling Surperspective Projection of Landscapes for Geographical Guide-Map Generation

It is still challenging to generate hand-drawn pictures because they differ from ordinary photographs in that they are often drawn as seen from multiple viewpoints. This paper presents a new approach for modeling such surperspective projection based on shape deformation techniques. Specifically, surperspective landscape images for guide-maps are generated from 3D geographical elevation data. Our method first partitions a target geographical surface into feature areas to provide designers with landmarks suitable for editing. The system takes as input 2D visual effects, which are converted to 3D geometric constraints for geographical surface deformation. Using ordinary perspective projection, the deformed shape is then transformed into a target guide-map image where each landmark enjoys its own vista points. An algorithm for calculating such 2D visual effects semi-automatically from the geographical shape features is also considered.     

A procedural method to exchange editable 3D data from a free-hand 2D sketch modeling system into 3D mechanical CAD systems

In the concept development phase, a designer wants to rapidly create a product’s overall shape and user interfaces by making simple sketches, known as ‘thumbnail sketches’, to evaluate ideas and possibilities. Free-hand 2D sketch systems are regarded as a computerized tool for making thumbnail sketches. After the concept development phase, subsequent editing of the 3D data reconstructed from a free-hand 2D sketch with a 3D mechanical CAD system in the detail design phase is indispensable because inaccurate dimensions are inherent in a free-hand 2D sketch. For this reason, we present a new method to translate 3D data reconstructed from a free-hand 2D sketch into an editable form that reflects design intent so that the translated data can be directly used in 3D mechanical CAD systems. The feasibility of the proposed method has been demonstrated through experiments with prototype systems.     

Customizing 3D garments based on volumetric deformation

Improving the reusability of design results is very important for garment design industry, since designing an elegant garment is usually labor-intensive and time-consuming. In this paper, we present a new approach for customizing 3D garment models. Our approach can transfer garment models initially dressed on a reference human model onto a target human model. To achieve this goal, firstly a spatial mapping between the two human models is established with the shape constraints of cross-sections. Secondly, the space around the clothed reference human model is tetrahedralized into five tetrahedral meshes each of which either can be worked dependently with its adjacent ones or can be worked independently. The clothed reference human model is parametrically encoded in the tetrahedral meshes. Thirdly, these tetrahedral meshes are deformed by fitting the reference human model onto the target human model by using constrained volumetric graph Laplacian deformation. The updated garment models are finally decoded from the deformed tetrahedral meshes. As a result, the updated garment models are fitted onto the target human model. Experiments show that our approach performs very well and has the potential to be used in the garment design industry.     

网格图形编辑的样条方法

提出基于样条的网格图形编辑方法,首先在网格表面附近构建近似的样条曲面,同时预计算网格顶点在样条上的对应点处局部标架下的坐标表示,并作为不变量在变形中进行保持;然后编辑样条的位置和形状,利用局部标架和细节坐标重建变形后的网格,同时进行网格光滑和网格细分,改善变形效果,以实现复杂模型简单快捷的编辑/变形.方法在保细节的同时允许对网格在多个尺度下编辑.实验结果表明,融合了样条的三角网格方法较传统的样条编辑方法可避免产生过多的控制点,大大地简化了操作.