带尖锐特征的Loop细分曲面拟合系统

实现了一个基于带尖锐特征的Loop细分曲面的三角网格拟合系统,其基本原理来自文献,但在系统设计层面对原算法作了相当大的补充和完善．整个系统框架包括尖锐特征提取、保持尖锐特征的三角网格简化、保持尖锐特征的网格平滑和拓扑优化、基于最近点策略的重采样和线性拟合系统求解．所得到的拟合曲面质量较原来的结果有了显著提高。     

散乱数据点的细分曲面重建算法及实现

提出一种对海量散乱数据根据给定精度拟合出无需裁剪和拼接的、反映细节特征的、分片光滑的细分曲面算法．该算法的核心是基于细分的局部特性，通过对有特征的细分控制网格极限位置分析，按照拟合曲面与数据点的距离误差最小原则，对细分曲面控制网格循环进行调整、优化、特征识别、白适应细分等过程，使得细分曲面不断地逼近原始数据．实例表明：该算法不仅具有高效性、稳定性，同时构造出的细分曲面还较好地反映了原始数据的细节特征。     

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.     

误差可控的细分曲面图像矢量化EI北大核心CSCD

为了提高矢量化图像的重构质量,提出一种基于细分曲面的误差可控矢量化算法.首先提取图像特征,构建特征约束的初始网格,并利用二次误差度量方法简化初始网格,得到特征保持的基网格;然后利用带尖锐特征的Loop细分曲面拟合图像颜色,得到控制网格;最后计算重构图像的误差,对控制网格进行自适应细分,直至重构误差达到用户需求.实验结果表明,该算法能够大幅度提高初始重构结果的质量,并在一定程度上做到误差可控.     

混合网格的可调细分算法

论文主要研究混合网格的曲面细分问题,提出了一种带有可调参数的细分算法。该算法适用于多边形网格、三角形网格,以及两者的混合网格情形,且对开的和闭的拓扑结构都能进行处理。由于在算法中引入了可调参数,这样既可产生光滑曲面,也可产生具有尖锐特征的曲面,且通过调整参数还可产生标准的Catmull-Clark细分和Loop细分。另外,实现该算法不需要复杂的数据结构。     

具有特殊效果的混合细分方法

提出了基于三角形和四边形的混合控制网格的细分曲面尖锐特征、半尖锐特征生成和控制方法,避免了已有方法仅局限于初始控制网格为单一的三角形或单一的四边形网格的缺陷.通过局部修改混合细分规则,在光滑混合曲面上产生了刺、尖、折痕、角的尖锐特征效果,并对尖锐特征处局部细分矩阵进行了详细的特征分析,讨论了极限曲面的收敛性及光滑性.同时,用特征处的离散曲率来控制特征处的尖锐程度,实现了半尖锐的特征效果,并通过自适应细分方法,把尖锐特征、半尖锐特征的生成统一起来.该方法具有多分辨率表示能力强、局部性好、简单易操作的特点.实验结果表明,该算法效果好,成功地解决了混合曲面特殊效果生成问题.     

Loop细分小波对网格模型的多分辨率分析

高分辨率网格模型因其数据量庞大,对其在网络中很难进行实时处理,因此,根据Loop细分模板,将边点作为小波的细节信息构造出了Loop细分小波,用于对网络模型进行多分辨率分析.该方法未涉及曲面几何拓扑关系,因而不受曲面拓扑特征的影响,具有很强的适应性.利用其对三维网格模型进行多分辨率分析,得到的低分辨率模型轮廓逼真,面片数量大幅度减少.由于该方法对细节信息取舍尺度还不能用统一的公式确定下来,因此只适合对模型做一些简单的处理.     

面向三角网格的自适应细分

细分曲面存在的一个问题是随着细分次数的增多，网格的面片数迅速增长，巨大的数据量使得细分后的模难以进行其它处理。针对这个问题，该文利用控制点的局部信息提出了一种基于Loop模式的自适应细分算法，利用该算法可避免在相对光滑处再细分，与正常细分相比，既大大减少了数据量，提高了模型的处理速度，又达到了对模型进行细分的目的。     

一种散乱数据点的多分辨率曲面重构方法

给出一种基于细分曲面技术实现散乱数据点的多分辨率曲面重构的方法。在曲面重构过程中,依据灰度图像边缘检测思想分析散乱数据特征值,将这些特征值生成纹理特征曲线进行曲面细分,从而形成了多分辨率网格模型结构。经过测试,该方法不仅重构曲面时间短,同时构造出的细分曲面能较好地反映原始数据的细节特征。     

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。     

A direct approach for subdivision surface fitting from a dense triangle mesh

This article presents a new and direct approach for fitting a subdivision surface from an irregular and dense triangle mesh of arbitrary topological type. All feature edges and feature vertices of the original mesh model are first identified. A topology- and feature-preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision surface with exactly the same topological structure and sharp features as that of the simplified mesh is finally fitted from a subset of vertices of the original dense mesh. During the fitting process, both the position masks and subdivision rules are used for setting up the fitting equation. Some examples are provided to demonstrate the proposed approach.     

Fitting Sharp Features with Loop Subdivision Surfaces

Various methods have been proposed for fitting subdivision surfaces to different forms of shape data (e.g., dense meshes or point clouds), but none of these methods effectively deals with shapes with sharp features, that is, creases, darts and corners. We present an effective method for fitting a Loop subdivision surface to a dense triangle mesh with sharp features. Our contribution is a new exact evaluation scheme for the Loop subdivision with all types of sharp features, which enables us to compute a fitting Loop subdivision surface for shapes with sharp features in an optimization framework. With an initial control mesh obtained from simplifying the input dense mesh using QEM, our fitting algorithm employs an iterative method to solve a nonlinear least squares problem based on the squared distances from the input mesh vertices to the fitting subdivision surface. This optimization framework depends critically on the ability to express these distances as quadratic functions of control mesh vertices using our exact evaluation scheme near sharp features. Experimental results are presented to demonstrate the effectiveness of the method.     

Non-Uniform Subdivision Surfaces with Sharp Features

Sharp features are important characteristics in surface modelling. However, it is still a significantly difficult task to create complex sharp features for Non-Uniform Rational B-Splines compatible subdivision surfaces. Current non-uniform subdivision methods produce sharp features generally by setting zero knot intervals, and these sharp features may have unpleasant visual effects. In this paper, we construct a non-uniform subdivision scheme to create complex sharp features by extending the eigen-polyhedron technique. The new scheme allows arbitrarily specifying sharp edges in the initial mesh and generates non-uniform cubic B-spline curves to represent the sharp features. Experimental results demonstrate that the present method can generate visually more pleasant sharp features than other existing approaches.     

Conjugate-Gradient Progressive-Iterative Approximation for Loop and Catmull-Clark Subdivision Surface Interpolation

Loop and Catmull-Clark are the most famous approximation subdivision schemes, but their limit surfaces do not interpolate the vertices of the given mesh. Progressive-iterative approximation (PIA) is an efficient method for data interpolation and has a wide range of applications in many fields such as subdivision surface fitting, parametric curve and surface fitting among others. However, the convergence rate of classical PIA is slow. In this paper, we present a new and fast PIA format for constructing interpolation subdivision surface that interpolates the vertices of a mesh with arbitrary topology. The proposed method, named Conjugate-Gradient Progressive-Iterative Approximation (CG-PIA), is based on the Conjugate-Gradient Iterative algorithm and the Progressive Iterative Approximation (PIA) algorithm. The method is presented using Loop and Catmull-Clark subdivision surfaces. CG-PIA preserves the features of the classical PIA method, such as the advantages of both the local and global scheme and resemblance with the given mesh. Moreover, CG-PIA has the following features. 1) It has a faster convergence rate compared with the classical PIA and W-PIA. 2) CG-PIA avoids the selection of weights compared with W-PIA. 3) CG-PIA does not need to modify the subdivision schemes compared with other methods with fairness measure. Numerous examples for Loop and Catmull-Clark subdivision surfaces are provided in this paper to demonstrate the efficiency and effectiveness of CG-PIA.     

Surface interpolation of meshes by geometric subdivision

Subdivision surfaces are generated by repeated approximation or interpolation from initial control meshes. In this paper, two new non-linear subdivision schemes, face based subdivision scheme and normal based subdivision scheme, are introduced for surface interpolation of triangular meshes. With a given coarse mesh more and more details will be added to the surface when the triangles have been split and refined. Because every intermediate mesh is a piecewise linear approximation to the final surface, the first type of subdivision scheme computes each new vertex as the solution to a least square fitting problem of selected old vertices and their neighboring triangles. Consequently, sharp features as well as smooth regions are generated automatically. For the second type of subdivision, the displacement for every new vertex is computed as a combination of normals at old vertices. By computing the vertex normals adaptively, the limit surface is G¹ smooth. The fairness of the interpolating surface can be improved further by using the neighboring faces. Because the new vertices by either of these two schemes depend on the local geometry, but not the vertex valences, the interpolating surface inherits the shape of the initial control mesh more fairly and naturally. Several examples are also presented to show the efficiency of the new algorithms.     

保持尖锐特征的混合细分曲面生成

基于混合细分模式,提出了细分曲面尖锐特征生成方法,通过对初始混合控制网格上要生成的各种尖锐特征的顶点和边分别作标记,然后局部修改细分规则进行迭代细分,实现了光滑混合曲面上产生折痕、角点、刺点、尖点的尖锐特征效果,并对尖锐特征处的局部细分矩阵进行了详细的特征分析。实验结果表明,该文算法效果好,能很好地保持模型的尖锐特征。     

用逼近型√3细分方法构造闭三角网格的插值曲面

为了避免用逼近型3~(1/2)细分方法构造插值曲面过程中出现的烦琐运算,利用3细分方法极限点计算公式,提出一种用逼近型3~(1/2)细分方法构造闭三角网格插值曲面的方法.给定待插值的闭三角网格,先用一个新的几何规则与原3~(1/2)细分方法的拓扑规则细分一次得到一个初始网格,用3~(1/2)细分方法细分该初始网格得到插值曲面;新几何规则根据极限点公式确定,保证了初始网格的极限曲面插值待插值的三角网格.由于初始网格的顶点仅与待插值顶点2邻域内的点相关,所以插值曲面具有良好的局部性,即改变一个待插值点的位置时,只影响插值曲面在其附近的形状.该方法中只有确定初始网格顶点的几何规则与原3细分方法不同,故易于整合到原有的细分系统中.实验结果表明,该方法具有计算简单、有充分的自由度调整插值曲面的形状等特点,使得利用3~(1/2)细分方法构造三角网格的插值曲面变得极其简单.     

带尖锐特征的细分曲线参数化及曲线拟合

快速精确地估计曲线曲面参数具有广泛的应用。在前人研究的基础上,通过对细分过程及三次B样条细分矩阵的特征结构进行分析,将细分模式转换到其特征空间,给出了带尖锐特征的B样条细分曲线的参数化形式。并用于处理带尖锐特征的光滑曲线拟合问题。以曲率极大点作为初始拟合点。利用推导的参数化公式构造曲线的尖锐部分并方便误差估计。拟合点为曲线段端点,误差估计时不仅优化计算速度,而且在曲线分支距离过近或自交情况下避免错误匹配。