用分片代数曲面构造管道曲面的过渡曲面

借助围绕一个顶点处代数曲面的光滑拼接条件,提出并研究了用分片代数曲面构造三通管道的过渡曲面问题。首先对空间区域进行适当的剖分以确定分片代数曲面的定义区域。然后,通过求解一个线性方程组来构造出光滑拼接的分片代数曲面,同时还了在代数曲面片的Ｂ－Ｂ表示下,Ｂｅｚｉｅｒ纵标对过渡曲面的形状的局部控制问题。结果表明,用分片代数曲面构造过渡曲面不仅可以降低曲面的次数,而且更有利于曲面形状的控制。     

注塑模CAD系统中过渡曲面的生成

介绍一种实用化的多面体过渡曲面的生成方法,过渡曲面达到Ｇ＾１连续,可以处理等半径、变半径及三面过渡的问题,也可以处理不规则多面体的过渡问题,该方法是在线框模型的基础上建立表面模型。     

基于物理的能量曲面造型方法构造过渡曲面

讨论了过渡曲面的生成问题,指出了半径过渡和PDE方法构造过渡面的局限性,提出了用基于物理的能量曲面造型方法构造过渡曲面的方法,特别是用于解决管状封闭非周期性曲面和其他曲面间的过渡问题。该文详细讨论了基于物理的能量曲面造型方法构造过渡曲面的原理及求解方法,并给出了飞行器的翼身过渡和三通过渡的实例。     

B样条曲面间G1连续条件及局部格式构造问题

研究了内部单节点张量积B样条曲面间G1连续的条件.通过选择特殊类型的拼接函数,打破了公共边界必须是整体多项式曲线的限制,给出了以内部单节点双四次B样条曲面为工具、使用局部格式构造G1连续曲面的算法.最后给出了计算实例.     

多项式混合曲线曲面方法构造

针对混合曲线表示及其求导和求积困难的问题,通过计算构造出一种多项式混合曲线曲面形式.当待混合曲线是多项式时,混合曲线也为多项式形式.该多项式混合公式可以推广得到任意参数连续C(n)和几何连续G(n)的混合曲线曲面.另外,在得到的混合曲线曲面族中构造出了新的更优能量光顺方程,通过设置参数可得到合适的混合曲线曲面.实验结果表明,文中提出的混合曲线曲面造型方法稳定、有效.     

基于Helmholtz 方程的过渡曲面设计

阐述了二阶和四阶Helmholtz 方程的一类周期边界问题的差分解法及其在 过渡曲面设计中的应用。这类方法不同于传统的PDE 方法中的二阶和四阶的偏微分方程, 比传统的二阶和四阶偏微分方程有了更多的自由项,因此,在曲面设计的时候,就有更多的 形状控制参数可进行调整,文中重点讨论了方程中的系数对曲面形状的影响,并研究了边界 切矢条件对曲面形状的影响及其在曲面形状设计中的应用。设计者只需给出边界曲线和边界 切矢,并通过对它们的控制就可构造和修改曲面形状。     

基于C1连续的NURBS边界Gregory曲面片实现曲面拼接

该文通过使用C1连续的NUR BS边界Gregory(N BG)曲面片进行插值,实现曲面拼接,使得在曲面连接处达到G1连续。实现了插值曲面的高阶连续,解决了用平滑的NUR BS曲面对曲线网格区域进行插值这一难以实现的问题,使用户在设计曲线网格时,只需考虑形状设计而不必关心曲线的类型及插值到曲线网格区域的曲面方程。     

构造G^1曲面的变分优化方法

给出一个克服曲面Ｇ＾１拼接中出现的扭曲现象的方法。扭曲现象是由于Ｇ＾１连续条件对曲面控制顶点的约束和曲面的自由交互输入之间的矛盾造成的，为了解决这个矛盾，我们采用多步线性变分优化的方法，逐步自动调整原输入曲面片上的角点、扭矢、边控制顶点、边附近控制顶点和内部控制顶点的多余自由度，使曲面片间达到Ｇ＾１连续的同时，也具备光顺性。     

三角网格上的代数曲面重建

提出一种用分片代数曲面构造三角曲面片的方法,利用具有公共边的2个三角形区域的4个顶点的函数值以及公共边2个端点的外法向量来构造一个二次曲面V(g)和一个截面V(h),其交V(g,h)即为2个三角曲面片的公共边界曲线.对每个已确定了边界条件的三角片内部进一步划分成3部分,每部分各自定义一个三次代数曲面.这3个三次代数曲面不仅在其交线处光滑拼接,而且分别沿三角形的边界与V(g)光滑拼接,从而构成一个具有GC1连续性的分片代数曲面.对于只属于一个三角片的边界留有一个自由度,可对曲面形状加以控制.     

三角网格上五次齐次代数曲面的重构

提出三角网格上重建代数曲面的一种方法,利用三次控制曲面来构造五次具有"齐次"形式的GC<'1>光滑曲面,所构造的代数曲面具有2次精度、局部性好、计算量低、自由参数几何意义明确的优点;而且这个五次代数曲面在与一簇特殊的平面相交时,交线为一个四次代数曲线和一条直线,从而化简了这类曲面参数化的计算量.     

用有理双三次Bezier曲面片混合二次曲面

提出一种二次曲面混合方法，混合曲面由2张有理双三次B6zier曲面片构成，它们之间保持G^2连续，混合曲面与二次曲面间保持G^1连续．给出了混合曲面片控制顶点的显式表示，通过修改2类混合参数可以直观地调节混合方向及混合曲面的形状．另外，混合5个圆锥曲面的例子表明，该方法为多个二次曲面的混合问题提供了有效途径．     

Ensuring compatibility of G-continuous surface patches around a nodepoint

The problem of ensuring compatibility of mixed partial derivative vectors of surface patches joining G²-continuously around a common nodepoint is essential in modelling G²-continuous n-sided surfaces. Although the compatibility constraints can be removed by using C² Gregory patches, these patches have singularities at their corner points. This paper presents conditions for ensuring the compatibility of the mixed partial derivative vectors of surface patches joining G²-continuously around a common nodepoint. After investigating the solvability of these compatibility conditions, a new solution method exploiting G³-continuity of surface patches at a common nodepoint is given. Example surfaces based on this solution method are also provided.     

异度隐函数样条曲线曲面

隐式曲线曲面被广泛应用于曲线曲面插值、逼近与拼接. 通过添加辅助曲线曲面,提出异度隐函数样条曲线曲面方法,并对其插值性、凸性与正则性进行分析. 具体实例表明,异度隐函数样条提供了次数低、构造简单、灵活性好的曲线曲面插值与拼接方法.     

Approximate G continuous interpolation of a rectangular network of rational cubic curves

The problem of spanning a rectangular network of rational cubic curves with a smooth surface is discussed in this paper. Provided the network is compatible with a smooth surface, then algorithms for patch construction, optimization and subdivision are developed to construct an ‘approximately smooth’ surface, that is, G¹ continuous to within some tolerance, composed of rational bicubic patches. The algorithms have been applied in the die and mould industry. The toolmaker constructs a wireframe model of an EDM (electro-discharge machining) electrode and the algorithms automatically construct the surface model. For toolmaking companies, this simplifies the surface modelling process making a highly-specialized and time-consuming task virtually automatic.     

Non-four-sided patch expressions with control points

This paper introduces new mathematical expressions which describe surface patches with three, five or six sides. Each side of a patch is given as a space curve expressed in Bézier type of second or third degree. Patch shape is modified predictably by moving its control points in the same way as with a four-sided patch. Distribution of cross tangent vectors along a patch boundary is also expressed in the same form with a few control vectors belonging to the boundary concerned. Therefore it can be connected with its surrounding four-sided patches smoothly. A general method of derivation of these equations is explained for further applications.     

Optimal approximate conversion of spline surfaces

The paper introduces an effective method for approximate conversion of spline surfaces. The method uses mainly geometric continuity conditions, parameter transformations and nonlinear optimization techniques. Degree reduction to bicubic and biquintic surfaces is introduced, curvature oriented segmentation is developed. The method can be extended to merging spline surfaces and to spline approximation of offset surfaces.     

PDE blending surfaces with C continuity

In this paper, we propose to use a general sixth-order partial differential equation (PDE) to solve the problem of C² continuous surface blending. Good accuracy and high efficiency are obtained by constructing a compound solution function, which is able to both satisfy the boundary conditions exactly and minimise the error of the PDE. This method can cope with much more complex surface-blending problems than other published analytical PDE methods. Comparison with the existing methods indicates that our method is capable of generating blending surfaces almost as fast and accurately as the closed-form method and it is more efficient and accurate than other extant PDE-based methods.     

Filling n-sided regions with NURBS patches

n -sided region with G ^ɛ continuous NURBS patches that interpolate boundary curves and approximate given cross-boundary derivatives. The NURBS surfaces joining along inner or boundary curves have normal vectors that do not deviate more than the user-specified angular tolerance ɛ. The method is general in that there are no restrictions on the number of boundary curves, and the cross-boundary derivatives can be specified independently. To satisfy all conditions, only one degree elevation is needed.