基于物理的能量最小法构造融合过渡曲面

提出了用基于物理的能量最小法构造四边域或n边域融合过渡曲面的方法，特别是用于解决四边域管状封闭非周期性曲面和其他曲面间的过渡问题，和任意n边域曲面和其他曲面间的融合问题。所提出的方法，只需给出边界法矢，将要求通过的约束线作为位置约束，即可构造G^1连续的满足工程要求的融合过渡曲面。该融合过渡曲面的过渡区域较易控制，并且能满足一些工程约束。详细讨论了基于物理的能量最小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融合过渡实例。     

过渡曲面的母线构造法

本文用母线法构造叉管的过渡曲面，给出了曲面方程同时得到了具有简单几何意义的ＧＣ＾１条件。     

NURBS曲面的过渡曲面生成

曲面过渡是几何造型的关键技术之一，本文提出的ＮＵＲＢＳ曲面的过渡曲面生成方法，能够处理曲面内具有不同连续性的情况，解决了ＮＵＲＢＳ曲面的等半径，变半径过渡及三面过渡问题，并在超人ＣＡＤ／ＣＡＭ系统中实现。     

Bezier三角组合曲面的局域设计

 在三角组合曲面的设计中，需要根据曲面间的拼接条件，协调求解曲面的内部控制顶点．在分析Bezier三角组合曲面设计方法的基础上，提出了Bezier三角曲面GC 连续局域设计方法． 内部分割点采用九参数三次曲面设计方法估算，由内部分割点将三角曲面分割为3个子曲面片，通过构造曲面边界的跨界过渡切矢，推导得出了3个分割子曲面的内部控制顶点的代数表达式．应用该方法，可以简化三角组合曲面的设计过程，提高三角组合曲面的设计计算速度．     

复合材料弯管曲面的整体造型设计

利用隐式几何造型方法的优点,建立了弯管过渡曲面的方程,改进了弯管现有的过渡方法,且保持其几何造型的特征,由于控制参数的调节作用,增加了过渡曲面造型的自由度。通过对弯管的应力分析得出：在圆环面与小圆柱面接合处、小圆柱面与过渡曲面的接合处、过渡曲面与大圆柱面的接合处这三处的应力突变都很小,表明该弯管的弯曲效应好,验证所建立的弯管过渡曲面是可行的。     

参数Bezier三角曲面G1光滑拼接的相容性

本文对参数Ｂｅｚｉｅｒ三角曲面拼接的相容性问题进行了研究。给出拼接的相容性条件。实现了任意多片参数三角曲面片的一阶几何连续拼接，可对任意复杂形状进行造型。     

NURBS曲面求交及变半径过渡曲面生成

本文探索NURBS曲面求交及构造过渡曲面的方法。基于交线跟踪算法求出NURBS曲面间的交线,算法比较稳定、可靠;采用参数化平面与等距面求交找出两曲面空间等距点,具有自然与变半径过渡曲面的定义相呼应、找点快、准确、稳定的特点;过渡曲面表示为2×3次NURBS曲面,自然、充分地利用了NURBS曲线可精确表示圆弧段的特性,过渡曲面具有表达简单、比较准确、便于采用统一的NURBS曲面处理算法对其进行各种几何处理的优点;实验证明这些方法可行,效果令人满意。     

CAD/CAM中曲面求交技术的研究

提出了用几何特征量来描述二次曲面和相关的边界曲线的方法，并据此研究了求交算法，避免了代数法中频繁的坐标变换，减少了浮点运算误差出现的几率，简化了曲面求交算法，使曲面求交算法更加稳定可靠。     

基于能量法的G2连续的曲面过渡

提出一种基于能量法的G2连续过渡面的构造方法,着重分析过渡曲面能量优化模型的建立,边界约束、法矢方向一致约束以及主曲率相等约束的表达和处理。将过渡曲面的能量优化模型转化为非线性等式约束的二次数学规划问题,并运用Lagrange乘子法求解过渡曲面的能量优化模型。最后给出了应用该方法生成G2连续过渡曲面的几个实例。     

用偏微分方程构造过渡面

用偏微分方程的构造曲面是一种新兴的方法，本文借若干算例说明如何用偏微分方程构造两已知曲面之间的过渡面。论文着重讨论用四阶方程构造一阶连续的过渡面。     

纯粘土边坡稳定性的解析计算

采用解析方法,建立了纯粘土边坡(0=j)圆弧滑裂时安全系数的解析表达式;利用函数取极值的条件,提出了通过求解一代数方程组来确定边坡的临界滑裂面和最小安全系数的方法;并计算了某些边坡的临界滑裂面和最小安全系数。     

Computing Switching Surfaces in Optimal Control Based on Triangular Decomposition

Various algorithms for optimal control require the explicit determination of switching surfaces. However, switching strategies may be very complicated, such that the computation of switching surfaces is quite challenging. General methods are proposed here to compute switching surfaces systematically, based on algebraic computational tools such as triangular decomposition. Our methods are highly complex compared to some widely-used numerical options, but they can be made feasible for real-time applications by moving the computational burden off-line. The tutorial-style presentation is intended to introduce potentially powerful symbolic computation methods to system scientists in particular, and an illustrative example of time-optimal control is given to show the effectiveness and generality of our approach.     

A predictor–corrector-type technique for the approximate parameterization of intersection curves

We describe a method to approximate a segment of the intersection curve of two implicitly defined surfaces by a rational parametric curve. Starting from an initial solution, the method applies predictor and corrector steps in order to obtain the result. Based on a preconditioning of the two given surfaces, the corrector step is formulated as an optimization problem, where the objective function approximates the integral of the squared Euclidean distance of the curve to the intersection curve. An SQP-type method is used to solve the optimization problem numerically. Two different predictor steps, which are based on simple extrapolation and on a differential equation, are formulated. Error bounds are needed in order to certify the accuracy of the result. In the case of the intersection of two algebraic surfaces, we show how to bound the Hausdorff distance between the intersection curve (an algebraic space curve) and its rational approximation.     

An algebraic method for smoothing surface triangulations on a local parametric space

This paper presents a new procedure to improve the quality of triangular meshes defined on surfaces. The improvement is obtained by an iterative process in which each node of the mesh is moved to a new position that minimizes a certain objective function. This objective function is derived from algebraic quality measures of the local mesh (the set of triangles connected to the adjustable or free node). If we allow the free node to move on the surface without imposing any restriction, only guided by the improvement of the quality, the optimization procedure can construct a high‐quality local mesh, but with this node in an unacceptable position. To avoid this problem the optimization is done in the parametric mesh, where the presence of barriers in the objective function maintains the free node inside the feasible region. In this way, the original problem on the surface is transformed into a two‐dimensional one on the parametric space. In our case, the parametric space is a plane, chosen in terms of the local mesh, in such a way that this mesh can be optimally projected performing a valid mesh, that is, without inverted elements. Several examples and applications presented in this work show how this technique is capable of improving the quality of triangular surface meshes. Copyright © 2005 John Wiley & Sons, Ltd.     

基于细分模式与能量优化的曲面混合方法

论述了用Catmull-Clark细分曲面及能量优化法对多张三次B样条曲面进行混合的方法。首先引入一种边界拓扑修改的细分规则，可生成逐段光滑的细分曲面，在此基础上构造多张三次B样条曲面的混合曲面，采用能量优化方法求解控制顶点。与现有方法相比，构造的混合曲面形状易于控制，能满足复杂的边界要求，且整个混合曲面除了在有限奇异点处为C^1连续外均达到C^2连续。     

A monomial-based method for solving systems of non-linear algebraic equations

A monomial-based method for solving systems of algebraic non-linear equations is presented. The method uses the arithmetic-geometric mean inequality to construct a system of monomial equations that approximates the system of non-linear equations. A change of variables transforms the monomial system into a system of linear equations, which is readily solved. Special properties of the monomial method are identified and their significance is discussed. Invariance properties of the monomial method produce a built-in, self-adjusting scaling of the variables and equilibration of the equations of the linear system. Other special properties can lead to useful bounds on, and invariances of, the conditioning of the linear system. An invariance to uniform scaling is responsible for extremely rapid convergence to the equation surfaces in the initial iterations. An invariance to multiplication of the algebraic equations by a certain class of functions leads to a useful insensitivity to form of the algebraic system. Insensitivity of the monomial method to solutions with negative components avoids meaningless solutiuons of the algebraic system that appear as undesirable by-products of the formulation. A practical engineering design problem is solved to demonstrate the special properties of the monomial method.     

构造两个曲面的拼接曲面

给出了当两个待拼接曲面的拼接线具有参数化形式或者可以参数化时,它们之间 G1光滑拼接曲面的构造方法。所得的拼接曲面是由一个空间曲线集定义的,每一条空间曲线由拼接线上的点对确定。并且拼接曲面都是参数曲面,它们的形状可以通过预设的参数很好地调整和控制。作为实例,讨论了两个截口是平面的或非平面的(由两个二次曲面定义)的二次曲面之间的拼接曲面的构造和一般的参数曲面的拼接曲面的构造。     

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

In general, non‐linear continuum mechanics combine global balance equations and local constitutive laws. In this work, frictionless contact between a rigid tool and a thin elastic shell is considered. This class of boundary value problems involves two non‐linear algebraic laws: the first one gives explicitly the stress field as a function of the strain throughout the continuum part, whereas the second one is a non‐linear equation relating the contact forces and the displacement at the boundary.Given the fact that classical computational approaches sometimes require significant effort in implementation of complex non‐linear problems, a computation technique based on automatic differentiation of constitutive laws is presented in this paper. The procedure enables to compute automatically the higher‐order derivatives of these constitutive laws and thereafter to define the Taylor series that are the basis of the continuation technique called asymptotic numerical method. The algorithm is about the same with an explicit or implicit constitutive relation. In the modelling of forming processes, many tool shapes can be encountered. The presented computational technique permits an easy implementation of these complex surfaces, for instance in a finite element code: the user is only required to define the tool geometry and the computer is able to obtain the higher‐order derivatives. Copyright © 2013 John Wiley & Sons, Ltd.     

交叉卷积——一种表面系统推荐算符

近些年来,一些可表征表面特征的参数已经不再适用．自从应用了三维形貌技术,一个表面可由20多种参数来表征．笔者另辟其径从理论上发展了一种算符,它可将2个（或2个以上）的表面联系在一起,以形成一种实用的函数系统．该算符称为“交叉卷积”．运用该新型的技术系统可以产生及表征各种轮廓表面,并能够提供可信的功能．