曲线的一类非线性多分辨率算法及其收敛性

在曲线的多分辨率分析基础上,构造了一种新的非线性三分多分辨率算法.并研究这个正则三分多分辨率算法的收敛性和稳定性,进一步,证明了小波参数的收敛性精密地依靠这个基本的多分辨率细分算法的收敛性.     

Shape controlled interpolatory ternary subdivision

Ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same (or higher) smoothness but smaller support.In this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements. We show that both these features can be included in a unique interpolating 4-point subdivision method by means of non-stationary insertion rules that do not affect the improved smoothness and locality of ternary schemes. This is realized by exploiting local shape parameters associated with the initial polyline edges.     

A unified three point approximating subdivision scheme

In this paper,we propose a three point approximating subdivision scheme,with three shape parameters,that unifies three different existing three point approximating schemes.Some sufficient conditions for subdivision curve C0 to C3 continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed.The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.     

绝对编码光栅的相位细分及其在位移测量中的应用

提出通过光栅条纹相位的精密测量,获取光栅高精度位移信息的方法。具体方法是对光栅图像采用多码道设计,用CCD二维图像传感器获取测量段光栅图像多码道信息。对最低码道图形的周期函数序列进行傅里叶变换、基频滤波和逆傅里叶变换获得光栅截断相位分布,其余码道信息提供相位展开的级次,以此获得测量段光栅的绝对相位分布。用光刻的手段制作了实用的绝对编码光栅,基元码道的尺寸是:27.36μm用于明条纹,27.36μm用于暗条纹,最小基元码道空间周期为54.72μm,光栅长度为14008.32μm。在步长近似3μm的位移测试中,与比对的标准仪器记录值比较,标准偏差为0.2057μm,精度在亚微米量级。重复性实验表明,位置测试的稳定性为0.09μm(标准差),得到600倍以上细分的分辨力。     

线-板式脉冲电晕放电反应器的发射光谱研究

以发射光谱法为基础,检测了常压状态线-板式脉冲电晕放电过程OH自由基在反应器内的空间分布;研究了线电极直径,线线间距以及线板间距对生成OH自由基的影响;从而明确脉冲电晕放电反应器的性能。结果显示:OH自由基浓度沿线电极X轴方向逐渐降低,活化区域半径20mm左右,沿Y轴方向先升高后降低,活化区域半径大于30mm;线电极的直径小于2mm时,OH自由基的光谱强度基本不变,线电极直径继续增大,发射光谱强度随之迅速下降。线线间距逐渐增大,OH自由基的发射光谱强度随之增强。OH自由基的发射光谱强度随着线板间距的增大而降低。     

若干冠图的邻点可区别V-全染色

应用构造染色函数法研究了冠图C_m·C_n、C_m·C_n的邻点可区别V-全染色.通过对P_m·C_n的邻点可区别V-全染色的研究巧妙给出了C_m·C_n邻点可区别V-全染色,并得到了这些图的邻点可区别V-全色数,从而验证了图的邻点可区别V-全染色猜想.     

Modified form of binary and ternary 3-point subdivision schemes

Binary 3-point scheme, developed by Hormann and Sabin [Hormann, K. and Sabin, Malcolm A., 2008, A family of subdivision schemes with cubic precision, Computer Aided Geometric Design, 25, 41-52], has been modified by introducing a tension parameter which generates a family of C¹ limiting curves for certain range of tension parameter. Ternary 3-point scheme, introduced by Siddiqi and Rehan [Siddiqi, Shahid S. and Rehan, K., 2009, A ternary three point scheme for curve designing, International Journal of Computer Mathematics, In Press, DOI: 10.1080/00207160802428220], has also been modified by introducing a tension parameter which generates family of C¹ and C² limiting curves for certain range of tension parameter. Laurent polynomial method is used to investigate the continuity of the subdivision schemes. The performance of modified schemes has been demonstrated by considering different examples along with its comparison with the established subdivision schemes.     

一种基于正则参数化的降维细分算法(英文)

In our previous work, we have given an algorithm for segmenting a simplex in the n-dimensional space into rt n＋ 1 polyhedrons and provided map F which maps the n-dimensional unit cube to these polyhedrons. In this paper, we prove that the map F is a one to one correspondence at least in lower dimensional spaces （n _〈 3）. Moreover, we propose the approximating subdivision and the interpolatory subdivision schemes and the estimation of computational complexity for triangular Bézier patches on a 2-dimensional space. Finally, we compare our schemes with Goldman＇s in computational complexity and speed.     

激光衍射测量中应用插值细分的可行性分析

激光衍射测微的精度关键在于衍射图样暗纹间距的精确测量，暗纹间距的测量目前主要采用高位数、小中心距的固体图象传感器线阵，为此，提出了一种硬件插值细分的方法。介绍了激光衍射的测量原理，分析了图像传感器的功能，根据采样和恢复定理，对输出的视频信号进行间距插值细分的可行性进行了论证，给出了插值细分的电路框图。分析表明其测量精度不受器件中心距大小的限制，为低位数、大中心距的固体图象传感器线阵的应用提供了方便。     

双圈拟阵

Sim■es Pereira于1992年提出双圈拟阵.本文讨论了(i)双圈拟阵及其秩函数;(ii)次模函数在双圈拟阵中的应用;(iii)双圈拟阵B(G)的横贯拟阵.主要结果:1°由圈矩阵Bf=[I,Bf12]和圈秩的概念,推出M(f0)为双圈拟阵;2°证明了双圈拟阵B(G)等于由子集族{Av∶v∈V(G)},e与v在G中相关联}所确定的横贯拟阵;3°用不同于Matthews(1977)的方法证明了(iii).