基于单位圆弧段逼近的Bezier曲线等距线生成算法

提出一种用四次Bezier曲线逼近单位圆弧段（Unit Circular Arcs）的方法及其详细误差函数分析。使用这种方法,给出一种使用同阶Bezier曲线逼近给定Bezier曲线等距线的算法。在Matlab7．0上实现了该算法,试验表明,新算法比Lee和Ahn所提出的算法有更高的精度和计算效率。由于B样条和NURBS曲线可以认为由多段Bezier曲线组成,因此,新算法为B样条和NURBS曲线等距线的求解提供了一种新的途径。     

基于单位圆弧段逼近的Bézier曲线等距线生成算法

提出一种用四次Bézier曲线逼近单位圆弧段(Unit Circular Arcs)的方法及其详细误差函数分析.使用这种方法,给出一种使用同阶Bézier曲线逼近给定Bézier曲线等距线的算法.在Matlab7.0上实现了该算法,试验表明,新算法比Lee和Ahn所提出的算法有更高的精度和计算效率.由于B样条和NURBS曲线可以认为由多段Bézier曲线组成,因此,新算法为B样条和NURBS曲线等距线的求解提供了一种新的途径.     

用参数优化整体逼近方法构造NURBS曲线等距线

从原始ＮＵＲＢＳ曲线求得一组精确等距点后用最小二乘法拟合等距线。用参数优化方法提高等距线的逼近精度。优化目标函数为各精确等距点至拟合曲线的距离平方和取极小值。     

代数曲线的"种子点"有理Bézier插值

基于代数曲线的合理分割,提出了曲线段的"种子点"有理Bézier插值方法.详细地讨论了代数曲线的分段有理二次、三次Bézier插值算法,同时给出了任意次数的Bézier插值曲线的计算方案.定义了一种便于计算的新型误差,在新型误差概念之下,结合数值实验说明了插值算法的逼近精度高于已有的逼近算法.同时,插值曲线保持了原始曲线的凹凸性和G1连续性等重要几何性质.     

B样条曲线的等距算法及应用

等距曲线的拓扑结构是等距算法中的核心因素之一。该文以B样条曲线为例,给出了一种基于关键点的等距算法。它应用了自适应离散等手段并给出了关键点的求解方法,同时利用关键点确定等距线各个分段的取舍,从而有效地去除自交的情况,使得计算出的等距曲线有着正确的拓扑结构。该文的算法已应用于商业软件OpenCAD中。     

代数曲线的“种子点”有理Bézier插值

基于代数曲线的合理分割,提出了曲线段的“种子点”有理Bézier插值方法。详细地讨论了代数曲线的分段有理二次、三次Bézier插值算法,同时给出了任意次数的Bézier插值曲线的计算方案。定义了一种便于计算的新型误差,在新型误差概念之下,结合数值实验说明了插值算法的逼近精度高于已有的逼近算法。同时,插值曲线保持了原始曲线的凹凸性和G1连续性等重要几何性质。     

平面二次代数曲线的最优参数化

在CAGD和CG中,代数曲线上指定曲线段的最优参数化是热点问题,而不是整条曲线。以最接近于弧长的参数化为最优的参数化评判标准,得到了二次代数曲线上的任意指定曲线段的最优或逼近最优的有理参数化公式,具有较强的自适应性。最后,通过实例对该方法与传统方法得到的参数化结果进行了对比。     

有理Bézier光顺样条曲线

本文给出一种用低次有理Bézier样条曲线光顺逼近任意次Bézier曲线及其等距线的方法,本文还应用了非线性优化技术。     

基于一元对称幂基的等距曲面有理逼近算法

给出了基于一元对称幂基的等距曲面蒙面逼近新算法。利用一元对称幂基逼近张量积Bézier曲面u向曲线的等距曲线,得到一组等距逼近曲线,取固定的v值,得到一组数据点,用反算控制顶点的方法得到过这组数据点的v向曲线。对这两组曲线用蒙面算法得到逼近的有理等距曲面。该算法计算简单,将二元等距曲面有理逼近转化为一元曲线有理逼近,同时方便地解决了整体误差问题,随着对称幂基阶数的升高,可以得到较理想的逼近效果。     

代数双曲空间中拟Legendre基的应用

鉴于Legendre基等正交基在代数多项式空间中的广泛应用,论文在深入研究代数双曲空间的拟Legendre基性质的基础上,给出了其在反函数逼近和等距曲线逼近上的应用。利用多项式和双曲函数的混合多项式序列来逼近反函数,并通过实例证明给出方法的有效性;对基曲线的法矢曲线进行逼近,构造H-Bézier曲线的等距曲线的最佳逼近,这种方法直接求得逼近曲线的控制顶点,计算简单,截断误差小。     

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。     

The roller-coaster curve is in

This is the second part of a three-part article under the general heading of ‘Off the bathtub onto the roller-coaster curve’, a short version¹ of which was presented at the 1988 Annual Reliability and Maintainability Symposium in the U.S.A. The first part was entitled ‘The bathtub does not hold water any more’,² and the last part, to be published in a later issue of this journal, is entitled ‘Physical basis for the roller-coaster hazard rate curve’. This three-part article provides detailed discussions of the findings leading to the conclusions on the roller-coaster characteristics for the hazard rate curve for electronics. Part 1 discussed problems with the bathtub curve. This part explores the shape of the failure rate curve in view of some recent observations. For more than twenty years investigators studying semiconducting device burn-in have subscribed to the concept of freak failures, which manifest themselves as a hump on the hazard rate curve. In addition to semiconducting device data several sets of screening data, as well as operational data dating all the way back to 1961, also showed that indeed one can expect electronic systems to have generally decreasing failure rate curves with failure humps on them. The author of this paper calls these curves the roller-coaster curves.     

Computing a hyperelliptic integral using arithmetic in the Jacobian of the curve

In this paper, we describe an efficient algorithm for computing an elementary antiderivative of an algebraic function defined on a hyperelliptic curve. Our algorithm combines B. M. Trager's integration algorithm and a technique for computing in the Jacobian of a hyperelliptic curve introduced by D. G. Cantor. Our method has been implemented and successfully compared to Trager's general algorithm.Work partially made at Departement Informatik ETH ZurichUnité de Recherche Associée au CNRS 1586     

Improved security in the genetic algorithm-based image steganography scheme using Hilbert space-filling curve

This paper presents the security analysis of a recently proposed data hiding scheme by Kanan and Nazeri [A novel image steganography scheme with high embedding capacity and tunable visual image quality based on a genetic algorithm. Expert Syst Appl. 2014;41(14):6123–6130]. Security of the scheme depends upon a secret key\chromosome constructed using a genetic algorithm. The key specifies offsets and patterns for data embedding. By performing the key-sensitivity analysis and exploiting image pixel correlation, it is shown in the present paper that the secret data can be easily revealed. Simulation results demonstrate that just 11 bits out of the 27-bit secret key are sufficient to reveal the data. To overcome the problem, an improvement is suggested in the data embedding pattern that demonstrates high data security. Bitwise analysis of the secret key used in the modified approach exhibits high sensitivity to change in the key.     

The innovation and performance effects of well-designed environmental regulation: evidence from Sweden

This paper provides novel empirical insights into the Porter hypothesis (PH) and its dynamic nature. The PH posits that well-designed environmental regulations induce eco-innovations at polluting firms that improve both their environmental and business performance via ‘innovation offsets.’ We conduct an econometric test of this proposition, using Swedish pulp and paper plants as empirical application. Swedish environmental regulation of polluting industries provides an interesting case because it has been praised, due to containing elements of ‘well-designed’ regulations, for being conducive to accomplishing the ‘win-win’ situation of mutual environmental and economic benefits. The empirical results indicate that flexible and dynamic command-and-control regulation and economic incentive instruments have induced innovation offsets through improved energy efficiency. Our study bears important implications: empirical tests of the PH that do not account for its dynamic nature, and that do not measure ‘well-designed’ regulations, might provide misleading conclusions as to its validity.     

球面插值PH曲线

本文讨论球面上PH曲线的C1Hermite插值问题。基于球极投影保持PH性质这一特性,通过球极投影把球面数据投影到平面上,构造一条平面PH曲线。然后,逆投影回球面得到一条球面有理插值PH曲线。球面PH曲线对球面数据达到C1插值,拓宽了PH曲线在机器人路径的设计、数控加工的计算等方面的应用范围。     

杆系结构自由振动精确求解的理论和算法

杆系结构的自由振动特性对结构的抗震设计至关重要。与常规有限元方法采用近似形函数将原问题化为线性特征值问题不同,本文的精确方法从杆件精确的形函数出发获得精确的动力刚度,将原问题化为非线性特征值问题。已有的Wittrick-Willliams算法很好地解决了该问题的频率求解。在此基础上,进一步提出了求解该非线性问题的导护型Newton法格式,并优化了各个算法环节。该法能同时求出频率和振型,求解结果精确可靠且具有二阶收敛速度,是一种快速精确、可靠实用的工程计算方法。     

重采样和曲面拟合的图像匹配方法

模式识别中的目标匹配和定位是一个传统问题,但是大多数经典算法其定位精度都是象素级的.图像的亚象元匹配算法,可以突破物理分辨率的限制,把匹配和定位精度从象素级提高到亚象元级,从而满足大规模集成电路制造、摄影测量、工业检测和目标检测等应用对精度的要求.将重采样方法和曲面拟合法有机结合的图像亚象元匹配方法,既有重采样方法精度高的优势,同时通过曲面拟合法加快了计算速度,减少了所需时间.实验结果证明了这种基于重采样和曲面拟合的图像亚象元匹配算法的有效性.     

Polynomial parametrization of nonsingular complete intersection curves

In this paper we give a new method to compute a polynomial parametrization, in case it exists, of an affine nonsingular complete intersection curve. Our method is based on the study of vector fields on nonsingular algebraic curves. In contrast to the existing methods, our algorithm does not use any projection, and no sample point on the curve is needed. It is also important to stress the fact that the algorithm produces a parametrization with coefficients in the ground field.