保形五次几何Hermite插值的构造算法

讨论了计算机辅助几何设计中的GHI问题,GHI曲线需要型值点处的切线和曲率信息,所以GHI曲线比一般的插值曲线更困难.首先将保概念引入到GHI曲线,再用分段五次Bezier曲线构造了GC2保形GHI算法.该曲线的所有Bezier点由型值点及相应的曲率信息直接计算产生,无需求解矢量方程组,因此该曲线计算简单,局部修改方便.最后,两个数值例子被给出。     

基于Bezier算法的采油井管道绘制

Bezier曲线是图形学中最基本、最重要的内容之一,广泛地应用于二维和空间图形中,如何快速、准确地绘制曲线是目前的一个研究方向.油田生产常常利用计算机仿真技术模拟先进采油工艺的实施过程,但地域和客观环境的不同导致油井类型存在较大差异,固定不变的仿真模式已不能满足实际需求,迫切需要寻找更加灵活多变的仿真方法.通过对现有Bezier曲线算法优缺点的比较,提出了一种新的逐点逼近算法,阐述了该算法的原理,并结合在采油井管道绘制中的具体应用,证明了该算法的有效性与实用性.     

基于Bezier曲线求交的曲线裁剪算法

本文研究了三次Ｂｅｚｉｅｒ曲线的裁剪问题。在给出了三次Ｂｅｚｉｅｒ曲线的一种求交算法后，讨论了Ｂｅｚｉｅｒ曲线在一点处的局部性质，给出了三次Ｂｅｚｉｅｒ曲线的裁剪算法。这些算法已被应用到我们自己开发的软件中，取得了良好的效果。     

保形参数四次插值算法

利用四次的Bézier曲线段构造了GC2连续的参数四次插值样条曲线,该样条曲线是保形的和局部的,且计算十分简单,所有的Bézier点由型值点和曲率直接计算产生,避免了求解矢量方程.最后,给出了一个数值实例.     

Modelling and effective modification of smooth boundary geometry in boundary problems using B-spline curves

To create curves in computer graphics, we use, among others, B-splines since they make it possible to effectively produce curves in a continuous way using a small number of de Boor’s control points. The properties of these curves have also been used to define and create boundary geometry in boundary problems solving using parametric integral equations system (PIES). PIES was applied for resolution 2D boundary-value problems described by Laplace’s equation. In this PIES, boundary geometry is theoretically defined in its mathematical formalism, hence the numerical solution of the PIES requires no boundary discretization (such as in BEM) and is simply reduced to the approximation of boundary functions. To solve this PIES a pseudospectral method has been proposed and the results obtained were compared with both exact and numerical solutions.     

Interactive display of large NURBS models

We present algorithms for interactive rendering of large-scale NURBS models. The algorithms convert the NURBS surfaces to Bezier surfaces, tessellate each Bezier surface into triangles, and render them using the triangle-rendering capabilities common to current graphics systems. We present algorithms for computing tight bounds on surface properties in order to generate high quality tessellation of Bezier surfaces. We introduce enhanced visibility determination techniques and present methods to make efficient use of coherence between successive frames. In addition, we also discuss issues in parallelization of these techniques. The algorithm also avoids polygonization anomalies like cracks. Our algorithms work well in practice and, on high-end graphics systems, are able to display models described using thousands of Bezier surfaces at interactive frame rates     

最短Bezier曲线研究

Bezier曲线比较容易计算和稳定，它得到了广泛应用，在分析了Bezier曲线的基础上，提出了最短Bezier曲线问题，并提出了该问题的解法，最后给出了实例。     

A note on the connection between Bezier curves and linear optimal control

We show that Bezier curves can in fact be thought of as the solutions to linear optimal control problems, using results from Hermite interpolation in combination with traditional linear optimal control. This provides us with a computational view of Bezier curves that differs from the standard DeCasteljau Algorithm, and it furthermore points out the close relationship between Bezier curves and interpolating dynamic splines.     

Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves

In this paper vector techniques and elimination methods are combined to help resolve some classical problems in computer aided geometric design. Vector techniques are applied to derive the Bezout resultant for two polynomials in one variable. This resultant is then used to solve the following two geometric problems: Given a planar parametric rational polynomial curve, (a) find the implicit polynomial equation of the curve (implicitization); (b) find the parameter value(s) corresponding to the coordinates of a point known to lie on the curve (inversion). The solutions to these two problems are closed form and, in general, require only the arithmetic operations of addition, subtraction, multiplication, and division. These closed form solutions lead to a simple, non-iterative, analytic algorithm for computing the intersection points of two planar parametric rational polynomial curves. Extensions of these techniques to planar rational Bezier curves are also discussed.     

增量极坐标编码的贝赛尔曲线智能优化算法

针对基于统计的隶属度函数确定方法进行了改进,使用贝塞尔曲线作为隶属度函数的上升或下降沿,使隶属度函数可以经过统计结果规定的任意中间点。使用新的增量极坐标编码对贝塞尔曲线控制点进行表达,解决了传统贝塞尔曲线优化中的控制点约束问题。采用差分进化算法对贝塞尔曲线控制点进行优化,可智能拟合经过任意点的最佳贝塞尔曲线。算法可扩展到任意阶贝塞尔曲线,所得隶属度函数较非贝塞尔曲线方法更为合理。     

隐式二次代数曲线插值

目前,二次参数曲线在曲线曲面造型中应用非常广泛,起着至关重要的作用,因此对二次曲线的性质和应用的研究仍十分有意义。本文首先综述近年来有关二次曲线的研究,对各种方法的优缺点进行了客观的评价。然后根据三次代数曲线的构造方法,提出一种新的二次曲线的构造方法,该方法通过几何量如控制点和切线来控制二次代数曲线的形状。文章在理论上对曲线的一系列性质进行了详细说明。     

Extrapolating Acceleration Algorithms for Finding B-Spline Intersections Using Recursive Subdivision Techniques

The new algorithms for finding B-Spline or Bezier curves and surfaces intersections using recursive subdivision techniques are presented,which use extrapolating acceleration technique,and have convergent precision of order 2.Matrix method is used to subdivide the curves or surfaces which makes the subdivision more concise and intuitive.Dividing depths of Bezier curves and surfaces are used to subdivide the curves or surfaces adaptively.Therefore the convergent precision and the computing efficiency of finding the intersections of curves and surfaces have been improved by the methods proposed in the paper.     

动态调整步长的参数曲线生成算法

本文提出一种在图形显示设备上生成参数曲线的通用算法 ,使生成的曲线精确到象素级 (即以象素逼近曲线上的点 ) .本算法采用在曲线生成过程中动态调整步长的方法 ,调整步长的方法简便 ,无需增加太多的计算量 .应用算法的结果表明 ,生成的曲线既可达到所要求的精确度又可大大地避免点的重复计算 .除了精确到象素级外 ,该算法也适用于其它精确度要求 ,如用折线逼近曲线时 ,相邻两点之间的距离小于给定值等 .而且该算法适用于一切多项式的、有理的或其它形式的参数曲线 ,不受曲线表示形式和曲线次数的限制 .     

基于二次Bezier曲线的无线传感网避障路径规划研究

用固定Sink节点进行无线传感网内数据采集的传统方式会导致热点区域(hot spot)问题,而采用移动Sink节点进行数据采集可以克服这个问题,从而达到均衡网络能量分布与延长网络生命周期的效果.本文针对类车型机器人作为无线传感网中移动数据汇聚节点的应用场景,提出了一种基于Bezier连续曲线的移动Sink节点避障路径规划算法.本文构建了连续分段Bezier曲线为巡航轨迹,采用人工势场中的斥力场理论实现对多个障碍物的智能躲避,动态调节二次Bezier曲线的内部控制点位置,将障碍物排斥在二次Bezier曲线之外.仿真结果验证本文提出的算法可以实现移动Sink节点规划路径的避障功能,同时Bezier曲线规划算法简单,计算量较小.     

基于Hough 变换的三次方Bezier 曲线检测算法研究

类似经典Hough 变换中对直线（段）、圆（弧）、椭圆、抛物线等解析曲 线的检测,论文研究了三次方Bezier 曲线的检测算法,提出了离散Bezier 曲线的特征建模 方法和使用R 函数的Hough 变换曲线检测快速算法。该算法能够根据所给出的待检测目标 点阵图像建立形状参数模型,然后检测该曲线在复杂图像中出现的位置、大小和方向。实验 表明,该法能够有效地检测任意三次方Bezier 曲线,且精确度优于目前广泛用于曲线检测 的广义Hough 变换。     

Bezier曲Bezier曲线修改的一种分割算法线修改的一种分割算法

在图形图像处理过程中,Bezier曲线的应用是非常广的.通过增加控制点对Bezier曲线作修改,为了不改变原有曲线的形状,＂升阶＂是最常用的方法.本文从另一角度出发,提出把Bezier曲线先分割为两段曲线,无需对曲线进行＂升阶＂,只需重新计算控制点,从而也达到对曲线修改的目的,并且以三次Bezier曲线为例,给出了具体的求解过程.实践证明明,这种方法是可行的.     

闭合数字曲线的多项式递归拟合

在数字曲线拟合的各种方法中,常见的用作拟合基元的曲线有B样条、贝塞尔曲线等。与这些曲线相比,二次多项式曲线具有形式简单、计算方便等特点。但二次多项式只能拟合X坐标与Y坐标之间成函数关系的点序列,无法拟合闭合曲线。因此,论文提出了一种基于曲线分解的拟合方法,该方法首先将闭合曲线在X方向和Y方向上进行分解,得到两个一维离散函数,然后用二次多项式分别对这两个离散函数进行递归拟合,直到满足一定的精度要求为止。最后实验表明,该方法与现有拟合算法相比,具有精度高、计算量小等特点。     

Java的发展前景与就业方向探讨

众所周知,21世纪是计算机网络的世纪,而Java语言正是服务于网络编程的。Java是目前发展最快的计算机语言。用它可以很方便地在网上编写应用软件,如数据库、商业、工程计算、网络连接、绘图、设备控制等应用软件。目前最流行的网上商务、网上出版、网上信息交流,甚至网上设备遥控等许多应用软件都是用Java语言编写的。学好java语言对于学生未来的就业非常有帮助。     

Generating Symbolic Interpolants for Scattered Data with Normal Vectors

Algorithms to generate a triangular or a quadrilateral interpolant with G1-continuity are given in this paper for arbitrary scattered data with associated normal vectors over a prescribed triangular or quadrilateral decomposition. The interpolants are constructed with a general method to generate surfaces from moving Bezier curves under geometric constraints. With the algorithm, we may obtain interpolants in complete symbolic parametric forms, leading to a fast computation of the interpolant. A dynamic interpolation solid modelling software package DISM is implemented based on the algorithm which can be used to generate and manipulate solid objects in an interactive way.     

Evolutionary composition of QoS-aware web services: A many-objective perspective

Web service based applications often invoke services provided by third-parties in their workflow. The Quality of Service (QoS) provided by the invoked supplier can be expressed in terms of the Service Level Agreement specifying the values contracted for particular aspects like cost or throughput, among others. In this scenario, intelligent systems can support the engineer to scrutinise the service market in order to select those candidates that best fit with the expected composition focusing on different QoS aspects. This search problem, also known as QoS-aware web service composition, is characterised by the presence of many diverse QoS properties to be simultaneously optimised from a multi-objective perspective. Nevertheless, as the number of QoS properties considered during the design phase increases and a larger number of decision factors come into play, it becomes more difficult to find the most suitable candidate solutions, so more sophisticated techniques are required to explore and return diverse, competitive alternatives. With this aim, this paper explores the suitability of many-objective evolutionary algorithms for addressing the binding problem of web services on the basis of a real-world benchmark with 9 QoS properties. A complete comparative study demonstrates that these techniques, never before applied to this problem, can achieve a better trade-off between all the QoS properties, or even promote specific QoS properties while keeping high values for the rest. In addition, this search process can be performed within a reasonable computational cost, enabling its adoption by intelligent and decision-support systems in the field of service oriented computation.