参数曲面导矢界估计及其在曲面绘制中的应用

目的是改进参数曲面的绘制效率。采用的方法是在参数曲线导矢界的基础上，进一步提出了3次参数曲面导矢界的公式。基于这些公式，能够较好地解决了参数曲面绘制算法过程中出现的重复绘制的问题和不连续的问题，进一步提高了曲面绘制的效果和效率。     

A bound on the distance between Loop subdivision surface and its control mesh

By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions,we obtain a bound on the distance between Loop subdivision surface patch and its control mesh.The bound can be used to compute the numbers of subdivision for a given tolerance.Finally,two examples are listed in this paper to demonstrate the applications of the bound.     

平面NURBS曲线及其Offset的双圆弧逼近

除直线、圆弧、速端曲线等少数几种曲线外,平面参数曲线的offset曲线通常不能表示成有 理参数形式,因此在实际应用中,为了方便造型系统中数据结构和几何算法的统一表示,offse t曲线通常用低次曲线逼近来表示.通过用双圆弧逼近表示NURBS(non-uniform rational B -spline)曲线及其offset,并利用双圆弧逼近的特有性质,把offset的双圆弧逼近转化为原 曲线的双圆弧逼近,简化了问题的求解.同时考虑了双圆弧逼近算法中分割点的选取、公切点 的确定以及误差估计等主要问题.具体算     

一种新的二元有理插值及其性质

构造了一种带参数的仅基于函数值的分子为双四次、分母为双二次的二元有理插值样条函数,插值函数具有简洁的显式表示。插值函数中含有4个参数,当这些参数满足一定条件时,插值曲面在插值区域上C1光滑。由于插值函数中含有参数,这样可以在插值数据不变的情况下通过对参数的选择进行插值曲面的局部修改。最后讨论了插值函数的一些性质。     

五次Hermite曲线在电缆路径设计中的应用研究

利用五次Hermite曲线建立了满足电缆路径曲线段边界约束的数学模型,通过最小化Hermite曲线的近似应变能,保证了生成的路径曲线具有较佳光顺性,尽可能避免了多余的环圈和尖点等奇异现象,推导了计算路径曲线段最优参数的解析公式。进一步分析计算了路径曲线段的最小曲率半径,为电缆的最大直径阀值估算提供理论依据。     

The intersection of a bicubic Bézier patch and a plane

Let S be an arbitrarily given bicubic Bézier patch and P an arbitrarily given plane. In this paper, a necessary and sufficient condition for S ∩ P to be non-empty is given, and some properties of S ∩ P, if non-empty, are included. Furthermore an efficient and robust algorithm for finding S ∩ P is described, and many interesting examples are shown.     

三次Hermite插值曲线的细化优化

在给定端点及其切矢方向的条件下,通过在相邻两节点之间插入一个中间节点,研究三次Hermite插值曲线的优化问题．如果以与曲率有关的二阶导数为目标,证明插入节点与不插入节点的情形是一样的,体现三次Hermite插值曲线的一种特性．如果以与挠率有关的三阶导数为目标,给出优化三次Hermite曲线的计算公式,从而提出一种新的曲线构造方法．实例表明了方法的有效性．     

特征设计中有向约束机制及算法研究

几何约束求解是基于特征设计系统的核心算法之一,由于目前沿用的是非特征设计环境下的约束机制,采用的约束方法没有充分利用特征设计的特点,约束难于管理,所得约束解往往背离设计初衷,约束算法复杂度高,文中提出一种基于自由度分析的有向约束实现机制及相关算法,算法时间复杂度低,提高了三维参数化设计系统的交互性能。     

交互更新模式的量子遗传算法的几何约束求解

目的针对传统量子遗传算法无法充分利用种群中未成熟个体信息的不足,提出了基于交互更新模式的量子遗传算法(IUMQGA)并应用于几何约束求解中。方法几何约束问题的约束方程组可转化为优化模型,因此约束求解问题可以转化为优化问题。采用将遗传算法与量子理论相结合的量子遗传算法,使用双串量子染色体结构,使用交互更新策略将遗传算法中的交叉操作利用量子门变换来实现,根据不同情况采用不同的交互更新策略。这里的交互,指的是两个个体进行信息交换的过程,该过程用以产生新的个体。这不仅增加了个体间信息的交换而且充分利用了种群中未成熟个体的信息,提高了算法的收敛速度。结果通过非线性方程实例和几何约束实例测试并与其他方法比较表明,基于交互更新模式的量子遗传算法求解几何约束问题具有更好的求解精度和求解速率。双圆外公切线问题实例中,IUMQGA算法比QGA算法稳定;单圆填充问题和双圆外公切线问题实例中,通过实验求得各变量的最优值与其相应的精确值的误差在1E-2以下。结论采用交互更新模式的量子遗传算法可以很好地求解几何约束问题。     

旋转圆锥网格及其在玻璃/钢结构中的应用

圆锥网格是计算机辅助建筑设计中一类新的平面四边形网格,具有良好的等距性质,非常适用于玻璃/钢结构,而旋转曲面是建筑设计中的常用形状.通过引入旋转圆锥网格的概念,并利用圆锥网格的定义,给出了构造旋转圆锥网格的简单方法.证明了只在旋转曲面r(u,v)=(f(u)cosv,f(u)sinv,g(u))的v参数方向进行均匀分割,而在U参数方向进行任意分割,则所产生的平面四边形网格为圆锥网格;并研究了旋转曲面为圆锥曲面和圆柱曲面的特殊情况;最后给出了基于旋转圆锥网格的玻璃结构造型实例.该方法简单易行,对计算机辅助建筑设计中的玻璃/钢结构造型有一定的实际应用价值.     

An upper bound for the distance between a zero and a critical point of a solution of a second order linear differential equation

This paper presents an upper bound for the distance between a zero and a critical point of a solution of the second order linear differential equation (p(x)y^′)^′+q(x)y(x)=0, with p(x),q(x)>0. It also compares it with previous results.     

On the interpolation of a function on a bounded domain by its traces on parametric hypersurfaces

We consider the problem of interpolating a multivariable function defined on a bounded domain using its traces on parametric hypersurfaces. Our approach is based on the theory of operator polynomial interpolation. We construct the corresponding operator interpolation polynomial for a given function and analyse in detail particular two- and three-dimensional cases. Numerical examples presented in the paper show the flexibility of the proposed approach.     

Hand tool handle size and shape determination based on hand measurements using a contour gauge

The purpose of this study is to provide a novel approach to tool handle design and development based on measurements of hand shape using a contour gauge. In general, traditional design techniques, designing based on anthropometric data, and derived mathematical models do not incorporate enough subject data to design a customized product. First, anthropometric measurements on the right hand of 60 participants were collected with a contour gauge to manufacture matching handles. A curved handle fitting the human hand was constructed with common computer‐aided design software, and cylindrical handles and elliptical handles were added for comparison. All of the handles were used to record the participants' grip force to evaluate the operating efficiency of the handles. Finally, the participants completed a comfort‐rating questionnaire. The results show that contours based on the hand provided the highest operating performance and the best overall comfort‐rating compared to cylindrical handles and elliptical cylindrical handles. The newly developed handles in the grip force tasks have the highest push performance and the best comfort ratings compared to traditional cylindrical and elliptical handles. The developed handles could provide the hand tool industry information on developing and manufacturing many other similar handle designs (such as those for saws and electric screwdrivers).     

基于Lupas q-模拟Bernstein 算子的广义Bézier 曲线

提出了一种全新的广义Bézier 曲线。首先,从Lupas q-模拟Bernstein 算 子出发,得到了一组有理函数,该函数带有一个形状参数,是经典Bernstein 基函数的自然 推广。然后,构造了相应的广义Bézier 曲线,本文称之为Lupas q-Bézier 曲线,并研究了 其基本性质。Lupas q-Bézier 曲线具有与经典Bézier 曲线相类似的升阶公式和de Casteljau 算法。     

The Implementation Methods for Computer Aided Design and Analysis on Color-Woven Fabrics

Methods for computer aided design and analysis on color-woven fabrics are presented. The relation of color pattern, colored warp, colored weft and the model for regular weave texture are given based on their formative principle. Some efficient algorithms are developed to determine the color order of warp and weft threads which yields a given color pattern and regular weave texture. Finally, the design system structure and data process flowing are introduced.     

Tight upper bound on the number of edges in a bipartite K3,3-free or K5-free graph with an application

We show that an n-vertex bipartite K_3,3-free graph with n?3 has at most 2n−4 edges and that an n-vertex bipartite K₅-free graph with n?5 has at most 3n−9 edges. These bounds are also tight. We then use the bound on the number of edges in a K_3,3-free graph to extend two known NC algorithms for planar graphs to K_3,3-free graphs.     

球谐函数在蛋白质分子匹配和对接中的应用

本文将球谐函数应用在分子表面模拟上,以解决生物大分子(蛋白质)与生物大分子(蛋白质)之间的对接(dock),为药物分子设计的研究奠定理论基础。     

计算机辅助设计在工业设计的应用状况及发展前景

在工业设计进行的流程中,计算机辅助设计悄然的穿插在每一个相对独立的主题活动之中.从一个完整的设计流程审视,计算机辅助设计的作用显而易见.它在设计流程数据管理,产品效果表现以及计算机辅助模型制作等广泛应用,发挥了工具化的作用.在应用过程中,促进了其自身的发展和工业设计的发展.     

A methodology for brand feature establishment based on the decomposition and reconstruction of a feature curve

For creative products, maintaining original brand elements and features in a new product is an important issue in the design process as brand features are conceived and generated for longevity. However, current methods rely on designers’ abilities, and the size of forms is easily affected when shape morphing is applied, causing limitations in computer-aided design. In order to focus on design while preserving key features, a systematic method for presenting brand features is proposed in this article. In this method, the feature curves of the brand features of a company are decomposed with defined feature parameters, which were then used to reconstruct the feature curve of the designed product in the design stage by using a residual modified gray prediction model. A classic vehicle configuration design is taken as an example to show the implementation procedure of the proposed method. With residual modification, this method can also assimilate other forms from the original form database, and generate new forms based on gray prediction. The results show that brand features can be retained in the newly designed product based on the proposed method. Though vehicle design is taken as the example, this method can also be used to develop designs for many other the brand features. For classic products with historical value, this method can generate new forms that maintain original brand features, thereby satisfying customers’ needs for brand authenticity.     

连续反应动力学的计算及过程的计算机模拟

在连续反应中,速率系数的比值很大程度上决定了中间产物浓度的走向,并由此引出了一个重要的方法：稳态近似法。微软公司推出的可视化编程语言Visual Basic提供了强大的计算与绘图功能,作者利用它研制了一级连续反应动力学的模拟程序。该程序能够计算出参与反应的各个物质的浓度,并且能够生动和直观地演示出各个物质的浓度随着反应的进行而发生的变化,从而使初学者进一步深刻理解一级连续反应和掌握稳态近似法的理论来源。