基于四边形网格的可调细分曲面造型方法

提出了一种基于四边形网格的可调细分曲面造型方法。该方法不仅适合闭域拓扑结构，且对初始网格是开域的也能进行处理。细分算法中引入了可调参数，增加了曲面造型的灵活性。在给定初始数据的条件下，曲面造型时可以通过调节参数来控制极限曲面的形状。该方法可以生成C1连续的细分曲面。试验表明该方法生成光滑曲面是有效的。     

曲面三参数binary细分法

在经典四点细分法的基础上,通过在曲线细分过程中引入三个参数,给出一种改进的细分曲线构造的算法,利用生成多项式等方法对细分法的一致收敛性、Ck连续性进行了分析。并把该方法扩展到曲面上,进而提出了曲面三参数binary细分法。在给定初始控制数据的条件下,可以通过对形状参数的适当选择来实现对细分极限曲面形状的调控。数值实验表明该算法较容易控制曲面形状,可方便地应用于工程实际,解决曲线、曲面位置调整和控制问题。     

基于双参数四点细分法的曲面造型

将双参数四点细分曲线方法进行推广，提出了基于双参数四点细分法的曲面造型方法，并对其收敛性进行了分析。该方法通过对两个参数的适当调节能够较容易地控制极限曲面的形状，极限曲面能够达到C4连续，可以应用到对曲面的连续性要求较高的曲面造型中去。在给定初始数据的条件下，可通过对形状参数的适当选择来实现对极限曲面的形状调整和控制，试验表明该算法生成光滑曲面是有效的。     

可调表面上的曲线插值

提出一个带有多特征的曲线插值可调表面算法。引入形状相似形参数,拓扑地修改初始控制网格。这样使得满足曲线插值的同时,结果表面与初始控制网格有不同的相似性;引入双边控制调节参数,更新插值曲线两边位置,调节插值曲线的弯曲程度;形成求解满足控制曲率的公式。实验结果表明此算法使得曲线插值在可调表面上可行,能够表现出多样性。     

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。     

基于任意拓扑网的细分可控表达方法

在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.通过在曲面细分过程中引入一个参数,给出一种新的细分曲面构造的算法,使得所得的细分曲面的表达度可控.调节一个参数值,可以得到一系列的细分曲面.最后给出了曲面设计的实例,表明这种算法简单、有效.     

Physics-Based Loop Surface Modeling

Strongly inspired by the research on physics-based dynamic models for surfaces, we propose a new method for precisely evaluating the dynamic parameters (mass, damping and stiffness matrices, and dynamic forces) for Loop surfaces without recursive subdivision regardless of regular or irregular faces. It is shown that the thin-plate-energy of Loop surfaces can be evaluated precisely and efficiently, even though there are extraordinary points in the initial meshes, unlike the previous dynamic Loop surface scheme. Hence, the new method presented for Loop surfaces is much more efficient than the previous schemes.     

An approximating non-stationary subdivision scheme

We present a 3-point C² approximating non-stationary subdivision scheme for designing curves. The weights of the masks of the scheme are defined in terms of some values of trigonometric B-spline basis functions. The scheme has some interesting properties and it is compared with the 2-point and 3-point schemes generating uniform trigonometric spline curves of order 3 and 5. The comparison and the performance of the scheme are demonstrated by examples.     

约束自适应Loop曲面细分

自适应细分已经被广泛应用于曲面细分领域以减少不需要的细分次数和细分面数。但是目前自适应细分都存在不同细分层次之间的裂缝拟合问题,造成了不同细分层次之间的曲面无法光滑连接,对此提出一种基于中分面的约束应细分方法。该方法的主要思想是通过对深度较高区域的1邻域三角形平分,根据产生裂缝的个数,将插入点与其1邻域的网格相连,从而降低高细分区域与低细分区域的深度差,达到不同细分程度光滑过度的细分效果。     

Surface modeling with ternary interpolating subdivision

In this paper, a new interpolatory subdivision scheme, called ternary interpolating subdivision, for quadrilateral meshes with arbitrary topology is presented. It can be used to deal with not only extraordinary faces but also extraordinary vertices in polyhedral meshes of arbitrary topologies. It is shown that the ternary interpolating subdivision can generate a C¹-continuous interpolatory surface. Some applications with open boundaries and curves to be interpolated are also discussed.     

双参数五点插值细分法

提出包含两个参数的五点ternary插值细分法。利用生成多项式等方法对细分法的一致收敛性,C K连续性进行了分析。讨论了参数对细分法的收敛性及连续性的影响,同时给出了细分法C0到C2连续的充分条件和数值算例。     

三参数binary细分法

通过在曲线细分过程中引入三个参数,给出一种新的细分曲线构造的算法,并利用生成多项式等方法对细分法的一致收敛性、Ck连续性进行了分析.在给定初始控制数据的条件下,可以通过对形状参数的适当选择来实现对细分极限曲线形状的调控.该方法可以生成C4连续的细分曲线,增加了曲线造型的灵活性.数值试验表明这种算法是有效的.     

渐进插值的LOOP曲面细分*

目前很多细分方法都存在不能用同一种方法处理封闭网格和开放网格的问题。对此,一种新的基于插值技术的LOOP曲面细分方法,其主要思想就是给定一个初始三角网格M,反复生成新的顶点,新顶点是通过其相邻顶点的约束求解得到的,从而构造一个新的控制网格M,在取极限的情况下,可以证明插值过程是收敛的;因为生成新顶点使用的是与其相连顶点的约束求解得到的,本质上是一种局部方法,所以,该方法很容易定义。它在本地方法和全局方法中都有优势,能处理任意顶点数量和任意拓扑结构的网格,从而产生一个光滑的曲面并忠实于给定曲面的形状,其控制     

Construction of minimal subdivision surface with a given boundary

The fascinating characters of minimal surface make it to be widely used in shape design. While the flexibility and high quality of subdivision surface make it a powerful mathematical tool for shape representation. In this paper, we construct minimal subdivision surfaces with given boundaries using the mean curvature flow, a second order geometric partial differential equation. This equation is solved by a finite element method where the finite element space is spanned by the limit functions of an extended Loop’s subdivision scheme proposed by Biermann et al. Using this extended Loop’s subdivision scheme we can treat a surface with boundary, thereby construct the perfect minimal subdivision surfaces with any topology of the control mesh and any shaped boundaries.     

基于逆细分的自由曲线分解与重建*

针对自由曲线的多分辨率表示,选取了双参数Chaikin细分法,基于几何逆向思想提出了相应的逆细分算法,建立了双参数可控的自由曲线渐近分解规则,通过分析双参数对曲线分解的影响,寻找出最优分解参数值,实现了自由曲线的最优分解,通过渐近分解时建立的误差向量,最终实现了自由曲线的完全重建。该算法比以往方法构造过程简单,几何意义明显,易于推广到其他细分模式上。     

表面细分的最优方法的分析与设计

基于模型上采集的非组织的样本点数据,给出了一个非线性至少平方的表面细分的完整框架。通过研究和分析三个几何上最优的表面细分的方法：点距离最小、切线距离最小、平方距离最小,来揭示它们的相交性与稳定性,以及非线性约束最优化的内部联系。对于点距离最小方法的分析,它是切线下降的变体,因此,只有线性相交。对于切线距离最小方法,它是接近二次相交零余留的问题,也有可能没有相交。平方距离最小方法,可以通过牛顿公式得到,并且是三种方法中相对最优的。通过对这三种方法的研究,来保证表面细分稳定地相交,且解决了对最优方法的争议。     

A novel method for sculptured surface subdivision

In this work,a novel method for sculptured surface subdivision to improve the machinery’s ability and efficiency in 5-axis CNC machining complex surface is introduced.The method subdivides automatically a monolithic convex or concave or simultaneously complex sculptured surface into a number of surface patches and achieves the goal of similar normal directions and small difference between the curvatures in every patch by using weight fuzzy cluster algorithm which takes the curvatures and normal vectors of the sculptured surface into account simultaneously.The inclination angle variation between every two Cutter Contact Points (CC Points) is decreased in every patch to avoid large-angle rotation of tool to save machining time when a flat-end mill is used.This work contributes to automating 5-axis CNC tool path generation for sculptured part machining and forming a foundation for further research.     

Composite freeform surface reconstruction using recursive interpolating subdivision scheme

Composite freeform surface reconstruction from 3D scanned data of a physical model has become a more and more important topic in the field of CAD/CAE/CAM. By repeated application of a fixed set of recursive interpolation subdivision schemes on the initial mesh of the 3D sparse scanned data of a physical model, a polygonal model of composite freeform surface can be constructed. In the paper, the algorithm for constructing the initial triangular mesh from 3D sparse scanned data is presented. The unified recursive interpolating subdivision scheme for triangular mesh is proposed. A special quad-tree data structure is suggested to store all the necessary information of the vertices and elements of the polygonal model. Examples of composite surface reconstruction are provided to explain the distinguished superiority of subdivision scheme for reconstructing the arbitrary topological complex surface.