细分蒙皮曲面

对细分曲面在曲面造型中的应用进行了研究,并着重于蒙皮曲面造型技术．所提方法在传统的蒙皮曲面构造过程中引入细分方法,有效地避免了因截面曲线的相容性处理而产生的数据量激增的问题;最后生成的蒙皮曲面能够精确插值预先设计的截面曲线,并且可以在指定的截面曲线处产生折痕效果．     

Least Squares Subdivision Surfaces

The usual approach to design subdivision schemes for curves and surfaces basically consists in combining proper rules for regular configurations, with some specific heuristics to handle extraordinary vertices. In this paper, we introduce an alternative approach, called Least Squares Subdivision Surfaces (LS), where the key idea is to iteratively project each vertex onto a local approximation of the current polygonal mesh. While the resulting procedure haves the same complexity as simpler subdivision schemes, our method offers much higher visual quality, especially in the vicinity of extraordinary vertices. Moreover, we show it can be easily generalized to support boundaries and creases. The fitting procedure allows for a local control of the surface from the normals, making LS³ very well suited for interactive freeform modeling applications. We demonstrate our approach on diadic triangular and quadrangular refinement schemes, though it can be applied to any splitting strategies.     

Loop细分曲面的等距曲面的逼近

提出了一种生成Loop细分曲面的等距曲面的逼近方法．通过让生成的等距曲面在对应于其控制网格顶点的地方是精确的等距,作者将等距曲面的逼近问题转化为求解一个线性方程组．文中提出了一个用于快速求解该线性方程组的改进的Gauss—Jacobi迭代法．另外,该文还考虑了逼近的误差控制和等距曲面的自交问题．     

Pseudo‐Spline Subdivision Surfaces

Pseudo‐splines provide a rich family of subdivision schemes with a wide range of choices that meet various demands for balancing the approximation power, the length of the support, and the regularity of the limit functions. Special cases of pseudo‐splines include uniform odd‐degree B‐splines and the interpolatory 2n‐point subdivision schemes, and the other pseudo‐splines fill the gap between these two families. In this paper we show how the refinement step of a pseudo‐spline subdivision scheme can be implemented efficiently using repeated local operations, which require only the data in the direct neighbourhood of each vertex, and how to generalize this concept to quadrilateral meshes with arbitrary topology. The resulting pseudo‐spline surfaces can be arbitrarily smooth in regular mesh regions and C¹ at extraordinary vertices as our numerical analysis reveals.     

Hierarchical Functional Maps between Subdivision Surfaces

We propose a novel approach for computing correspondences between subdivision surfaces with different control polygons. Our main observation is that the multi‐resolution spectral basis functions that are open used for computing a functional correspondence can be compactly represented on subdivision surfaces, and therefore can be efficiently computed. Furthermore, the reconstruction of a pointwise map from a functional correspondence also greatly benefits from the subdivision structure. Leveraging these observations, we suggest a hierarchical pipeline for functional map inference, allowing us to compute correspondences between surfaces at fine subdivision levels, with hundreds of thousands of polygons, an order of magnitude faster than existing correspondence methods. We demonstrate the applicability of our results by transferring high‐resolution sculpting displacement maps and textures between subdivision models.     

Loop细分曲面精确求值新公式

利用控制网格拓扑结构的对称性,通过将奇异点周围1-环和2-环的控制顶点进行离散Fourier变换(DFT)得到分块对角阵,将其进行特征分解及排序之后,再通过离散Fourier逆变换(IDFT)和截断等操作得到细分矩阵的高次幂的表达式,从而得到Loop细分曲面新的精确参数化公式.     

常平均曲率细分曲面的构造

常平均曲率曲面经常作为界面出现在许多物理问题当中,是物理膜泡的一种数学抽象,而细分曲面的灵活性及其高质量的特性使得它成为一种强有力的曲面设计工具.通过给定边界,使用由一个二阶能量范函导出的四阶几何偏微分方程和一个二阶几何偏微分方程来构造常平均曲率细分曲面,这2个方程采用有限元方法求解;由于扩展的Loop细分规则能处理带...     

A Blend of Subdivision Surfaces and NURBS

In present paper, the contour deletion method is developed both to blend surfaces and to fill N-sided holes, which is used for subdividing the NURBS surface. First, according to the non-uniform Catmull-Clark subdivision principle, surfaces are blended. The non-uniform Catmull-Clark subdivision method is constructed, which build the surface through interpolating corner vertices and boundary curves. Then the contour deletion method is adapted to remove the controlling mesh boundary contour in the process of segmentation iteration. Last, N sided-hole is filled to generate a integral smooth continuous surface. This method not only guarantee that the blending surface and base surface patches have C2 continuity at the boundary, but also greatly improve the smoothness of the N-side hole filling surface. The results show that, this method simplifies the specific computer-implemented process, broads the scope of application of subdivision surfaces, and solves the incompatible problem between the subdivision surface and classical spline. The resulting surface has both advantages of the subdivision surface and classical spline, and also has better filling effect.     

位移蝶形细分面片的渐进传输

随着三维激光扫描和建模技术的不断进步,三维网格模型的数据量越来越大．与此同时,无处不在的智能计算要求数据必须能够在网络上进行快速的传输,现有的三维网格渐进传输技术无论是基于任意拓扑结构网格的渐进网格技术,还是基于参数化细分面片的渐进传输技术,都存在着传输数据量大、渐进显示效果差的问题,针对这些缺点,提出了首先利用位移蝶形细分面片重建原来的网格模型,然后对于重建后的位移蝶形细分面片设计了一种新的数据简化方法,进而构造了一种渐进传输算法,该算法在减少传输数据总量的同时,提高了渐进传输的视觉效果。     

Improving the Parameterization of Approximate Subdivision Surfaces

We provide a method for improving the parameterization of patching schemes that approximate Catmull‐Clark subdivision surfaces, such that the new parameterization conforms better to that of the original subdivision surface. We create this reparameterization in real‐time using a method that only depends on the topology of the surface and is independent of the surface's geometry. Our method can handle patches with more than one extraordinary vertex and avoids the combinatorial increase in both complexity and storage associated with multiple extraordinary vertices. Moreover, the reparameterization function is easy to implement and fast.     

一种对称非均匀细分曲面算法

为了得到能更好应用于CAD系统的细分曲面造型方法,提出一种基于B-样条的对称非均匀细分算法,其中的思想和均匀Lane-Riesenfeld节点插入算法相似。基于B-样条的节点插入算法,以Blossoming为工具,计算出细分后的新控制顶点。细分后得到的极限曲面由张量积样条曲面组成,在奇异点达到2C连续。与传统的细分曲面算法相比,该细分曲面算法具有良好的局部支撑性,大大降低了算法的复杂度,而且该算法是对称的,不用考虑定向问题。     

Filling N-Sided Regions by Quad Meshes for Subdivision Surfaces

Given an n-sided region bounded by a loop of n polylines, we present a general algorithm to fill such a region by a quad mesh suitable for a subdivision scheme. Typically, the approach consists of two phases: the topological phase and the geometrical phase. In the first part, the connectivity of the mesh is based on determining a partitioning of the region into rectangular subregions across which regular grid could be constructed. The geometrical phase generalizes discrete Coon's patches to position the vertices in the 3D space. The generated mesh could be taken as input to any quad-based subdivision scheme, such as that of Catmull–Clark or Doo–Sabin to generate the corresponding limit surface. The goal of the algorithm is to generate smooth meshes with minimum number and less valence of extraordinary vertices deemed undesirable in such subdivision schemes.     

NURBS曲线与曲面的细分算法

本文讨论了 NU RBS曲线、曲面的细分算法 ,给出了 NU RBS基的加细方程。对于均匀的 NU BRS曲线 ,我们还得到了加细方程系数的生成函数。算法是单侧逼近 ,是保凸的 ,可以融入现行的 CAGD系统。     

曲面三参数四点造型

文章是对经典的四点细分格式进行推广,提出了可通过对形状参数的适当选择来实现对极限曲线形状调整和控制的四参数四点细分曲线造型方法,并把该方法扩展到曲面上;对其收敛性进行了分析,同时给出了曲线曲面C0到C2连续的充分条件。     

Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces

The volume of a solid enclosed by a recursive subdivision surface can be approximated based on the closed-form representation of regular parts of the subdivision surface and a tight estimate of the local convex hull near extraordinary points. The approach presented is efficient, i.e. non-exponential, and robust in that it yields rapidly contracting error bounding boxes. An extension to measuring higher-order moments is sketched.     

Evolutions of Polygons in the Study of Subdivision Surfaces

We employ the theory of evolving n-gons in the study of subdivision surfaces. We show that for subdivision schemes with small stencils the eigenanalysis of an evolving polygon, corresponding either to a face or to the 1-ring neighborhood of a vertex, complements in a geometrically intuitive way the eigenanalysis of the subdivision matrix. In the applications we study the types of singularities that may appear on a subdivision surface, and we find properties of the subdivision surface that depend on the initial control polyhedron only.     

Catmull-Clark细分曲面的纹理映射技术

提出了一种在细分曲面的过程中应用纹理映射的方法,即在控制网格逐步加细的过程中,纹理图像由无损压缩变换矩阵M进行变换并映射到相应的细分曲面上.这种方法既有效的避免了纹理接缝问题,又保证了纹理图像的完整性.该技术已经在Catmull-Clark细分曲面上得以实现,也可以用于其他任何面分裂型的细分曲面.     

基于C-B样条的Catmull-Clark细分曲面造型系统的开发

论文针对工程应用,根据C-B样条和Catmull-Clark细分曲面的特点可调因子使得生成曲面形状可调和一次细分操作以后所有的网格面片都为四边域,构造合理的数据结构,采用有效的实时交互式的用户界面,开发了基于C-B样条的Catmull-Clark细分曲面的造型系统.为细分曲面的形状调整提供了简单、实时而且直观的人机交互方法.该系统能处理任意拓扑结构,能够精确地表示二次曲面,所生成的曲面光滑可调.可以以软件包或插件的形式加入到现有的CAD系统中.