均匀二重混合双曲多项式B样条曲线

为扩展B样条曲线,提出1种均匀二重混合双曲多项式B样条曲线. 该样条曲线在span{sinh t,cosh t,tsinh t,tcosh t,1,t,…,tk-6,tk-5}空间上均匀产生,其中k是大于等于5的整数. 证明k阶二重混合双曲多项式B样条基的性质和二重混合双曲多项式B样条曲线的性质. 二重混合双曲多项式B样条曲线精确地包含双曲多项式B样条曲线. 给出这种新样条曲线的细分公式并证明其有变差缩减性质和细分控制多边形逼近性质. 该性质使得通过递归细分得到曲线成为可能.     

基于折半运算的快速双基数标量乘算法

为了提高椭圆曲线标量乘法效率,对二元域上椭圆曲线的基于双基数的标量乘法进行改进。在底层域推导出直接计算3^kP的快速算法,该算法只需一次求逆;新设计的以1/2和3为基的双基数编码可结合高效的直接计算3^kP和折半运算,基于该双基数编码的标量乘算法只涉及到点加运算、折半运算、三倍点和直接计算3^kP,底层域运算复杂性得到降低,在NIST推荐的椭圆曲线上比Dimitrov算法效率提高70%以上,比Wong方法提高10%以上。     

Conference key agreement protocol with non-interactive fault-tolerance over broadcast network

Most conventional conference key agreement protocols have not been concerned with a practical situation. There may exist some malicious conferees who attempt to block conference initiation for some purposes, e.g. commercial, political or military benefit. Instances where conference must be launched immediately due to emergency, efficient detection of malicious behavior would be needed. Recently, Tzeng (IEEE Trans. Comput. 51(4):373–379, 2002) proposed a fault-tolerant conference key agreement protocol to address the issue where a conference key can be established among conferees even though malicious conferees exist. However, his protocol might be complex and inefficient during fault-detection. In the case where a malicious conferee exists and a fault-tolerant mechanism is launched, complicated interactions between conferees will be required. In this paper, we introduce a novel strategy, where any malicious conferee may be identified and removed from the conferee list without any interaction. With such a non-interactive fault-tolerance, conferences could be established and started efficiently. A complete example of our protocol will be given to describe the fascinating fault-tolerance. We analyse the security of our protocol regarding four aspects, i.e. correctness, fault-tolerance, active attack and passive attack. The comparisons of performance between our protocol and that of Tzeng are also shown. As a whole, the advantage of our protocol is superior to that of Tzeng under the situation where malicious conferees exist.

Efficient processing of spatial joins with DOT-based indexing

A spatial join is a query that searches for a set of object pairs satisfying a given spatial relationship from a database. It is one of the most costly queries, and thus requires an efficient processing algorithm that fully exploits the features of the underlying spatial indexes. In our earlier work, we devised a fairly effective algorithm for processing spatial joins with double transformation (DOT) indexing, which is one of several spatial indexing schemes. However, the algorithm is restricted to only the one-dimensional cases. In this paper, we extend the algorithm for the two-dimensional cases, which are general in Geographic Information Systems (GIS) applications. We first extend DOT to two-dimensional original space. Next, we propose an efficient algorithm for processing range queries using extended DOT. This algorithm employs the quarter division technique and the tri-quarter division technique devised by analyzing the regularity of the space-filling curve used in DOT. This greatly reduces the number of space transformation operations. We then propose a novel spatial join algorithm based on this range query processing algorithm. In processing a spatial join, we determine the access order of disk pages so that we can minimize the number of disk accesses. We show the superiority of the proposed method by extensive experiments using data sets of various distributions and sizes. The experimental results reveal that the proposed method improves the performance of spatial join processing up to three times in comparison with the widely-used R-tree-based spatial join method.     

A Complex View of Barycentric Mappings

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two‐dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real‐valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real‐valued barycentric coordinates from a given weight function can be applied to generating complex‐valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex‐weighted combination of edge‐to‐edge similarity transformations, allowing the design of “home‐made” barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.     

计算两参数对称音叉式分岐曲线扩张系统的构造

构造了计算两参数分岐线的扩张系统，讨论了扩张系统的正则性。     

加速基因方法在最大流量频率曲线参数估计中的应用

基因方法是基于自然选择和自然基因机制的并行随机自适应工程模型参数全局优化估计的通用数值方法。它不限制模型结构、优化准则、被估参数的数目、约束条件等，已开始广泛用于各种工程模型的优化设计之中。文中对它的原理、步骤、特点进行初步探讨，并针对基因方法的弱点，作者提出予以改进的加速基因方法，后者在最大流量频率曲线参数估计中得到成功应用     

平面四点确定一条抛物线及其在参数插值中的应用

本文讨论了用平面有序四点确定一条抛物线及其在参数插值中的应用。提出了有用四点确定一条抛物线的算法，讨论了确定抛物线的四点相互间要满足的位置。对平面给定的一组数据点，提出了构造参数插值曲线的新方法。所构造的插值曲线是ＧＣ＾１连续的分片三次参数曲线，其插值精度为二次参数多项式。本文还以计算实例对新方法与其它方法的插值精度进行了比较。     

空间曲线拟合算法的研究

在数控加工中，通常需要将空间曲线用合适的样条拟合出来，以方便加工．B样条概念于20世纪40年代由Sehoenberg提出后，已广泛应用于曲线、曲面的造型中．该文以变直径、变螺距的转向蜗杆的空间曲线为例，介绍了用B样条拟合空间曲线的方法，具体讨论了空间曲线反求控制点的计算方法，通过模拟仿真，该方法所拟合的曲线比较平整光滑、误差较小．用此方法拟合出的曲线可以直接用API得出加工程序．     

渐开线齿轮点蚀位置的确定及其计算综合曲率半径的误差修正

依据赫兹强度理论 ,指出一对标准渐开线直齿齿轮啮合时 ,最大接触应力位于齿轮单啮合区靠近小齿轮处单双啮合区的分界线上。小齿轮点蚀发生在分度圆与齿根圆之间 ,大齿轮点蚀发生在分度圆与齿顶圆之间。并列举实例 ,证明目前传统设计方法计算点蚀处齿轮综合曲率半径误差较大 ,绘制出精确计算值与传统计算值的比值曲线 ,并给出结论 :传统设计方法得到的结果不安全 ,有误差 ;误差与齿轮模数无关 ,误差随着小齿轮齿数的增加渐小 ,误差随着齿轮齿数比的增大先渐大后渐小