基于laplacian坐标修正的(√3)细分法

根据原始网格对细分极限曲面的影响分析,提出了基于laplacian坐标修正的(√3)插值网格细分方法.通过插值出面片中心点的laplacian坐标,来对动态生成的中心点进行修正,达到保持原始网格细节的目的.在非封闭网格的边界面片细分方面,指出了原始(√3)细分法的不足,提出了一种新的边界统一细分模式,它可以很好地控制边界面片的增长,而且具有稳定性和易于操作性.实验结果表明,该方法不仅能够让原始网格的细节在极限曲面上得到表达,而且可以得到一个连续光滑的曲面网格.     

基于二次误差的三角网格自适应细分算法研究

提出一种基于二次误差的三角网格自适应细分算法,该算法采用二次误差描述三角网格的曲率变化情况,只对二次误差大于阈值的三角面片进行细分,避免了在较平坦区域再进行细分,以较少的三角面片表达了模型的特征,实现三角网格的自适应细分.与全局细分相比,自适应细分既可增加模型光顺性,又可减少模型的数据处理量,提高细分效率.     

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.     

基于laplacian坐标修正的sqrt(3)细分法

根据原始网格对细分极限曲面的影响分析,提出了基于laplacian坐标修正的sqrt(3)插值网格细分方法。通过插值出面片中心点的laplacian坐标,来对动态生成的中心点进行修正,达到保持原始网格细节的目的。在非封闭网格的边界面片细分方面,指出了原始3细分法的不足,提出了一种新的边界统一细分模式,它可以很好地控制边界面片的增长,而且具有稳定性和易于操作性。实验结果表明,该方法不仅能够让原始网格的细节在极限曲面上得到表达,而且可以得到一个连续光滑的曲面网格。     

基于laplacian坐标修正的3~(1/2)细分法

根据原始网格对细分极限曲面的影响分析,提出了基于laplacian坐标修正的3~(1/2)插值网格细分方法。通过插值出面片中心点的laplacian坐标,来对动态生成的中心点进行修正,达到保持原始网格细节的目的。在非封闭网格的边界面片细分方面,指出了原始3~(1/2)细分法的不足,提出了一种新的边界统一细分模式,它可以很好地控制边界面片的增长,而且具有稳定性和易于操作性。实验结果表明,该方法不仅能够让原始网格的细节在极限曲面上得到表达,而且可以得到一个连续光滑的曲面网格。     

网格曲面特征的稀疏性优化检测算法

针对现有的特征检测算法大多数基于微分几何量,对噪声比较敏感、运行速度比较慢、对于过渡特征处理得不够理想的问题,提出一种基于稀疏性优化的网格特征检测算法.该算法主要包括3个过程:首先利用带l1范数稀疏性约束项和l2范数误差项的Laplacian能量函数对网格进行光顺,得到光顺后网格顶点的移动距离;然后根据顶点的移动距离提取初始特征点;最后对提取的特征点进行后处理,使得特征点更为完整.其中,l1范数稀疏性约束项用来约束发生移动点的数目;l2范数的误差约束项用来控制光顺后模型的退化程度.该算法易于实现,能够处理尖锐特征、弱特征和过渡特征.与基于微分几何量的特征提取方法相比,文中算法不仅简单有效、运行时间短,而且提取的特征线也更好.     

非均匀B样条曲面顶点及法向插值

本文以非均匀Catmull-Clark细分模式下的轮廓删除法为基础,通过在细分网格中定义模板并调整细分网格的顶点位置,为非均匀B样条曲面顶点及法向插值给出了一个有效的方法．该细分网格由待插顶点形成的网格细分少数几次而获得．细分网格的顶点被分为模板内的顶点和自由顶点．各个模板内的顶点通过构造优化模型并求解进行调整,自由顶点用能量优化法确定．这一方法不仅避免了求解线性方程组得到控制顶点的过程,而且在调整顶点的同时也兼顾了曲面的光顺性．     

误差可控的细分曲面图像矢量化

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.     

基于C-C细分的四边形网格上插值光滑Bézier曲面的生成

在任意拓扑的四边形网格上构造光滑的曲面是计算机辅助几何设计中的一个重要问题.基于C-C细分,提出一种从四边形网格上生成插值网格顶点的光滑Bézier曲面片的算法.将输入四边形网格作为C-C细分的初始控制网格,在四边形网格的每张面上对应得到一张Bézier曲面,使Bézier曲面片逼近C-C细分极限曲面.曲面片在与奇异顶点相连的边界上G1连续,其他地方C2连续.为解决C-C细分的收缩问题,给出了基于误差控制的迭代扩张初始控制网格的方法,使从扩张后网格上生成的曲面插值于初始控制网格的顶点.实验结果表明,该算法效率高,生成的曲面具有较好的连续性,适用于对四边化后的网格模型上重建光滑的曲面.     

Catmull-Clark细分网格数据点拾取

针对将OpenGL选择拾取机制直接作用于Catmull-Clark细分网格数据点的拾取,可能会因细分网格数据量过大而导致名字堆栈溢出的问题,借鉴细分曲面求交的思想,提出一种新的细分网格数据点拾取方法.该方法通过提取拾取对象的邻域网格并进行局部细分,将对细分任意层次上网格数据点的拾取转化为对初始控制网格以及在达到细分层次要求以前每一次局部细分网格点、边、面的拾取和对最后一次局部细分网格数据点的拾取.采用多个拾取算例进行对比分析实验,当细分网格顶点数量较多时,所给拾取方法的拾取命名对象总量和拾取时间都远小于传统OpenGL选择拾取方法.实验结果表明,所给拾取方法能快速准确实现细分网格数据点的拾取,尤其适用于数据量较大的复杂细分模型,可有效避免因拾取名字堆栈溢出而导致的拾取错误.     

A cascadic geometric filtering approach to subdivision

A new approach to subdivision based on the evolution of surfaces under curvature motion is presented. Such an evolution can be understood as a natural geometric filter process where time corresponds to the filter width. Thus, subdivision can be interpreted as the application of a geometric filter on an initial surface. The concrete scheme is a model of such a filtering based on a successively improved spatial approximation starting with some initial coarse mesh and leading to a smooth limit surface.

In every subdivision step the underlying grid is refined by some regular refinement rule and a linear finite element problem is either solved exactly or, especially on fine grid levels, one confines to a small number of smoothing steps within the corresponding iterative linear solver. The approach closely connects subdivision to surface fairing concerning the geometric smoothing and to cascadic multigrid methods with respect to the actual numerical procedure. The derived method does not distinguish between different valences of nodes nor between different mesh refinement types. Furthermore, the method comes along with a new approach for the theoretical treatment of subdivision.     

Optimization methods for scattered data approximation with subdivision surfaces

We present a method for scattered data approximation with subdivision surfaces which actually uses the true representation of the limit surface as a linear combination of smooth basis functions associated with the control vertices. A robust and fast algorithm for exact closest point search on Loop surfaces which combines Newton iteration and non-linear minimization is used for parameterizing the samples. Based on this we perform unconditionally convergent parameter correction to optimize the approximation with respect to the L² metric, and thus we make a well-established scattered data fitting technique which has been available before only for B-spline surfaces, applicable to subdivision surfaces. We also adapt the recently discovered local second order squared distance function approximant to the parameter correction setup. Further we exploit the fact that the control mesh of a subdivision surface can have arbitrary connectivity to reduce the L^∞ error up to a certain user-defined tolerance by adaptively restructuring the control mesh. Combining the presented algorithms we describe a complete procedure which is able to produce high-quality approximations of complex, detailed models.     

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.     

加权Catmull-Clark曲面

文中给出一种加权的 Catm ull- Clark剖分方法 .算法首先对初始多边形网格作一次不同于 Catmull- Clark方法的带权因子的剖分 ,再对生成网格实施 Catmull- Clark剖分 ,从而得到可控形状的 C1光滑曲面 .通过对第 1步中的权因子赋不同的值 ,能方便地控制生成曲面与其原始控制网格的逼近精度 .实验表明 ,本算法非常简洁 ,比传统 Catm ull- Clark方法具有更多的自由度 .     

Direct Reconstruction of a Displaced Subdivision Surface from Unorganized Points

In this paper we describe the generation of a displaced subdivision surface directly from a set of unorganized points. The displaced subdivision surface is an efficient mesh representation that defines a detailed mesh with a displacement map over a smooth domain surface and has many benefits including compression, rendering, and animation, which overcome limitations of an irregular mesh produced by an ordinary mesh reconstruction scheme. Unlike previous displaced subdivision surface reconstruction methods, our method does not rely on a highly detailed reconstructed mesh. Instead, we efficiently create a coarse base mesh, which is used to sample displacements directly from unorganized points, and this results in a simple process and fast calculation. We suggest a shrink-wrapping-like shape approximation and a point-based mesh simplification method that uses the distance between a set of points and a mesh as an error metric to generate a domain surface that optimally approximates the given points. We avoid time-consuming energy minimization by employing a local subdivision surface fitting scheme. Finally, we show several reconstruction results that demonstrate the usability of our algorithm.     

任意拓扑网的细分改进

在改进任意拓扑网构造光滑表面时,初始控制网格确定的情况下,生成的曲面形状惟一确定,最终的物体造型也随之确定,不具有可调性,因而在曲面细分过程中引入了控制参数和摄动。通过引入控制参数,调节一个参数值,使得所得的细分曲面的表达度可控,可以得到一系列的细分曲面。引入摄动是为了改进了空间位置,允许局部地调控约束曲面的形状。最后给出了曲面设计的实例,表明这种算法简单、有效。     

细分曲面拟合的局部渐进插值方法

逼近型细分方法生成的细分曲面其品质要优于插值型细分方法生成的细分曲面.然而,逼近型细分方法生成的细分曲面不能插值于初始控制网格顶点.为使逼近型细分曲面具有插值能力,一般通过求解全局线性方程组,使其插值于网格顶点.当网格顶点较多时,求解线性方程组的计算量很大,因此,难以处理稠密网格.与此不同,在不直接求解线性方程组的情况下,渐进插值方法通过迭代调整控制网格顶点,最终达到插值的效果.渐进插值方法可以处理稠密的任意拓扑网格,生成插值于初始网格顶点的光滑细分曲面.并且经证明,逼近型细分曲面渐进插值具有局部性质,也就是迭代调整初始网格的若干控制顶点,且保持剩余顶点不变,最终生成的极限细分曲面仍插值于初始网格中被调整的那些顶点.这种局部渐进插值性质给形状控制带来了更多的灵活性,并且使得自适应拟合成为可能.实验结果验证了局部渐进插值的形状控制以及自适应拟合能力.     

光顺B-spline曲面片的一种实用方法

重构曲面的光顺处理是逆向工程中的关键步骤，如何快速、简便、正确地光顺曲面，是曲面光顺处理问题研究的核心。本文针对B-spline方法重构曲面提出了一种光顺方法。并描述了其基本原理和光顺准则。实例表明，本文所提出的光顺方法快速、简便，是一种较为实用的光顺方法。     

Dynamic Catmull-Clark subdivision surfaces

Recursive subdivision schemes have been extensively used in computer graphics, computer-aided geometric design, and scientific visualization for modeling smooth surfaces of arbitrary topology. Recursive subdivision generates a visually pleasing smooth surface in the limit from an initial user-specified polygonal mesh through the repeated application of a fixed set of subdivision rules. We present a new dynamic surface model based on the Catmull-Clark subdivision scheme, a popular technique for modeling complicated objects of arbitrary genus. Our new dynamic surface model inherits the attractive properties of the Catmull-Clark subdivision scheme, as well as those of the physics-based models. This new model provides a direct and intuitive means of manipulating geometric shapes, and an efficient hierarchical approach for recovering complex shapes from large range and volume data sets using very few degrees of freedom (control vertices). We provide an analytic formulation and introduce the “physical” quantities required to develop the dynamic subdivision surface model which can be interactively deformed by applying synthesized forces. The governing dynamic differential equation is derived using Lagrangian mechanics and the finite element method. Our experiments demonstrate that this new dynamic model has a promising future in computer graphics, geometric shape design, and scientific visualization     

基于任意三角网格的ternary插值细分曲面造型及其分析

针对任意三角网格,提出一种简单有效且局部性更好的带参数的ternary插值曲面细分法,给出并证明了细分法收敛与G1连续的充分条件.在任意给定三角控制网格的条件下,可通过对形状参数的适当选择来实现对插值细分曲面形状的调整.