四边形上一种线性双有理映射构造方法

作为一种特殊的有理映射,双有理映射可应用于图像变形、等几何分析中区域参 数化中。针对文献[1]通过几何方法构造四边形上的双有理映射,需要先确定权值再构造的问题, 提出一种基于动直线的方法,可直接构造四边形上的双有理映射。此外,通过选择不同的参数, 可以得到四边形上不同的双有理映射。验证可知,该方法满足文献[1]提出的权值比例关系,并 通过实例说明了其有效性。     

构造正六面体表面混沌吸引子的平面迭代映射

为了实现用二维迭代映射构造三维球面图形,提出用平面正方形格子上的迭代映射构造三维正六面体表面上连续排列的混沌吸引子的方法.首先提出用于构造正六面体上连续排列混沌吸引子的平面迭代映射在正方形格子上应满足的边界条件;其次用截断的傅里叶三角级数构造出满足边界条件的3个平面排列迭代映射;最后找到了2个基本绘图窗口,利用3个迭代映射在2个正方形格子边界上的对称特性完成混沌吸引子在平面上和正六面体上的连续排列图形的构造.实验结果表明,文中提出的基于正方形格子的二维平面排列迭代映射可以用于大量的自动生成三维正六面体上的连续混沌吸引子图形.     

一种二元有理插值样条函数的凸性

通过研究一种基于函数值的(3,2)¹阶二元有理插值样条函数中诸如边界插值、极限、解析和正则等性质,指出极限曲面是双曲抛物面,揭示了参数对这种插值曲面的影响.首先引入双8次矩阵表示的凸性判别函数,推导了判定插值曲面凸性的充要条件;然后根据该条件给出数值实例,展示如何适当选取参数实现有理插值样条曲面的局部保凸性.特别发现了这种插值曲面凸性在某些点处即使型值是凸的数据也是相对刚性的,并提出了插值曲面局部保凸的必要条件.最后还讨论了文献(Zhang Y,Duan Q,Twizell E H.Convexity control of a bivariate rational interpolating spline surfaces.Computers&Graphics,2007,31(5):679-687)中存在的部分计算问题.     

基于Jacobian椭圆有理映射的组密钥管理方案

提出了一种新的基于Jacobian椭圆有理映射的组密钥管理方案.该方案与现有的组密钥管理方案相比,具有较少的密钥更新信息量和计算量,并能够支持前向保密、后向保密以及能抵御同谋攻击的优点.分析证明,在中度规模和较小规模的组播环境中,该方案具有较高的效率.     

直觉模糊映射的凸分析

介绍了直觉模糊数和直觉模糊映射的凸性、凹性、拟凸性、拟凹性上半连续性、下半连续性和正齐次性的定义.通过引入一种新的偏序关系来研究凸直觉模糊映射性质,对凸直觉模糊映射和凹直觉模糊映射分别建立了两个刻画定理.讨论了直觉模糊映射的凸性与拟凸性的关系,证明了一个凸直觉模糊映射必是一个拟凸直觉模糊映射和一个凹直觉模糊映射必是一个拟凹直觉模糊映射.考虑了直觉模糊映射的凸性与半连续性的关系,获得了直觉模糊映射的凸性与上半连续性(下半连续性)等价的条件.在直觉模糊算子方面,给出了正齐次直觉模糊映射是凸直觉模糊映射的充要条件及直觉模糊算子是凸直觉模糊映射的判别定理.拓展了经典集合上的凸函数和凸模糊映射的相关理论,使之成为直觉模糊理论的有益补充.     

有理C-Bezier曲线的形状分析

对有理C—Bezier曲线进行了形状分析，得出曲线上含有奇点、拐点和曲线为局部凸或全局凸的、用控制多边形边向量相对位置表示的充分必要条件，并讨论了权因子变化对曲线形状图的影响．     

双n次曲面凸性的判别

矩形域上双n次曲面片的一般表达式为 z=[x~n,…,x,1]A[y~n…y 1],0≤x,y≤1,(1.1)其中A=[α_(i,j)]_(1≤i,j≤n 1)为n 1阶的实矩阵。在计算机辅助几何设计中所使用的曲面常常是由这样的一些曲面依一定的连接条件拼接而成的。对n为3的特殊情形,文献[1]给出了这类曲面凸性的几个充分条件。本文试图将该文结论作一推广,同时尝试将多项式理论中的Budan-Fourier定理以及Descarte的符号规则用于对曲面片(1.1)的凸性     

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．     

Positive Gordon–Wixom coordinates

We introduce a new construction of transfinite barycentric coordinates for arbitrary closed sets in two dimensions. Our method extends weighted Gordon–Wixom interpolation to non-convex shapes and produces coordinates that are positive everywhere in the interior of the domain and that are smooth for shapes with smooth boundaries. We achieve these properties by using the distance to lines tangent to the boundary curve to define a weight function that is positive and smooth. We derive closed-form expressions for arbitrary polygons in two dimensions and compare the basis functions of our coordinates with several other types of barycentric coordinates.     

A unified, integral construction for coordinates over closed curves

We propose a simple generalization of Shephard's interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A third instance of this family yields a previously unknown generalization of discrete harmonic coordinates to smooth curves. For closed, piecewise linear curves, we prove that our interpolant reproduces a general family of barycentric coordinates considered by Floater, Hormann and Kós that includes Wachspress coordinates, mean value coordinates and discrete harmonic coordinates.     

Perimeter discovery in wireless sensor networks

In this paper, we focus on the perimeter detection problem using wireless sensor networks, as perimeter detection has a wide range of uses in several areas. We present a decentralized localized algorithm where sensor nodes determine if they are located along the perimeter of a wireless sensor network. Our proposed algorithm uses the location neighborhood information in conjunction with the Barycentric technique to determine if the sensor node enclosed by neighboring nodes, and consequently, if it is located within the interior of the wireless sensor network. We define performance metrics to analyze the performance of our approach and the simulation shows that the algorithm gives fairly accurate results.     

A framework based on barycentric coordinates for localization in wireless sensor networks

Localization is a fundamental and vital problem in wireless sensor networks. This paper presents an optimizing framework for localization based on barycentric coordinates. The framework consists of two components. The first component retains the structure revealed by the distances between pairs of nodes; the second component constrains the boundary nodes to maintain the distance with their neighbor nodes. A hybrid localization algorithm is derived on top of the optimizing framework. A part of the computation is performed collaboratively by nodes, whereas the rest is executed on the sink node. Experimental results show that the proposed localization algorithm obtains lower location errors without higher communication costs.     

Convex Subspace Routing (CSR): Routing via anchor-based convex virtual subspaces in sensor networks

Convex Subspace Routing (CSR) is a novel approach for routing in sensor networks using anchor-based virtual coordinates. Unlike geographical routing schemes that require physical location information of nodes, obtaining which is often difficult, error-prone and costly, the Virtual Coordinate (VC) based schemes simply characterize each node by a vector of shortest hop distances to a selected subset of nodes known as anchors. Even though VC based routing (VCR) schemes benefits from having connectivity information implicitly embedded within the VCs, VCs lack the directional information available with physical coordinates. The major issues affecting routing using VCs are addressed. Due to local minima problem in the virtual space, the VCR schemes rely on backtracking or hill climbing techniques to overcome the local minima. Convex Subspace Routing, in contrast, avoids using anchors that cause local minima. It dynamically selects subsets of anchors that define subspaces to provide convex distance functions from source to destination. Consequently, it is less sensitive to anchor placement and over anchoring, and does not require tracking route history for backtracking, resulting in shorter packet lengths and energy efficient operation. Three techniques for selection of convex subspaces are proposed and evaluated. Performance evaluation for several different network topologies indicates that CSR significantly outperforms the existing VCR scheme, Logical Coordinate Routing (LCR), while being competitive with geographic coordinate based Greedy Perimeter Stateless Routing (GPSR), even though latter makes use of node location information.     

Semistrictly preinvex fuzzy mappings

In this paper, we introduce the concepts of a strictly preinvex fuzzy mapping, a semistrictly preinvex fuzzy mapping, a strictly prequasi-invex fuzzy mapping and a semistrictly prequasi-invex fuzzy mapping. Some properties of these mappings and relations among them are studied. A few interesting theorems are proved, including that: (1) a strictly prequasi-invex fuzzy mapping has at most one global minimum point; (2) the solution set is invex if the fuzzy mapping is prequasi-invex and (3) prequasi-invex fuzzy mappings satisfy most of the basic properties of the preinvex fuzzy mappings.     

逐像素偏移纹理坐标的视差映射改进方法

视差映射技术可以通过沿着视点方向平移纹理坐标来实现纹理图像的真实感绘制, 然而不正确的纹理坐标偏移量将导致纹理图像的滑动现象.根据视差映射技术原理, 通过定义纹理坐标值与高度值之间的映射函数得到偏移量与当前视点坐标的对应关系;利用GPU技术计算得到正确的纹理坐标偏移量, 使得在视点动态变换时纹理图像的绘制不会产生滑动现象.实验结果表明, 与传统视差映射方法及现有GPU技术校正纹理坐标偏移量方法相比, 在没有增加算法复杂度的前提下, 采用文中方法可改善纹理图像真实感绘制的效果.     

Windows图形编程中的坐标系与GDI映射方式

本文从GDI映射方式入手，对基于设备坐标的视口和基于逻辑坐标的窗口的概念、内涵及其相互关系进行了分析介绍。在此基础上，文章详述了怎样建立不同原点、单位和正方向的逻辑坐标系。对坐标系的构建原理进行了深入剖析。