The structure of uniform B-spline curves with parameters

The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions with parameter and the B-spline basis functions. Based on the degree elevation of B-spline, we extend the uniform B-spline basis functions with parameter to ones with multiple parameters. Examples show that the proposed basis functions provide more flexibility for curve design.     

Curve interpolation based on Catmull-Clark subdivision scheme

An efficient algorithm for curve interpolation is proposed. The algorithm can produce a subdivision surface that can interpolate the predefined cubic B-spline curves by applying the Catmull-Clark scheme to a polygonal mesh containing "symmetric zonal meshes", which possesses some special properties. Many kinds of curve interpolation problems can be dealt with by this algorithm, such as interpolating single open curve or closed curve, a mesh of nonintersecting or intersecting curve. The interpolating surface is C2 everywhere excepting at a finite number of points. At the same time, sharp creases can also be modeled on the limit subdivision surface by duplicating the vertices of the tagged edges of initial mesh, i.e. the surface is only C0 along the cubic B-spline curve that is defined by the tagged edges. Because of being simple and easy to implement, this method can be used for product shape design and graphic software development.     

Software Maintainability Prediction with UML Class Diagram

Software system can be classified into many function modules from the perspective of user. Unified modeling language( UML) class diagram of each function module was extracted,and design characteristic metrics which influenced software maintainability were selected based on UML class diagram.Choosing metrics of UML class diagram as predictors,and mean maintenance time of function module was regarded as software maintainability parameter. Software maintainability models were built by using back propagation( BP) neural network and radial basis function( RBF) neural network, respectively and were simulated by MATLAB. In order to evaluate the performance of models,the training results were analyzed and compared with leaveone-out cross-validation and model performance evaluation criterion. The result indicated that RBF arithmetic was superior to BP arithmetic in predicting software maintainability.     

Human Body Modeling and Posture Simulating Based on 3D Surface Scan Data

This paper presents a new approach for modeling the human body by considering the motion state and the shape of whole body. The body model consists of a skeleton kinematic model and a surface model. The former is used to determine the posture of the body, and the latter is used to generate the body shape according to the given posture. The body surface is reconstructed with multi-segment B-spline surfaces based on the 3D scan data from a real human body. Using only a few joints parameters and the original surface scan data, the various body postures and the shape can be generated easily. The model has a strong potential of being used for ergonomic design, garment design, virtual reality environment, as well as creating human animation, etc.     

Reliability Estimations of Control Systems Effected by Several Interference Sources

In order to establish the sufficient and necessary condition that arbitrarily reliable systems can not be constructed with function elements under interference sources, it is very important to expand set of interference sources with the above property. In this paper, the models of two types of interference sources are raised respectively: interference source possessing real input vectors and constant reliable interference source. We study the reliability of the systems effected by the interference sources, and the lower bound of the reliability is presented. The results show that it is impossible that arbitrarily reliable systems can not be constructed with the elements effected by above interference sources.     

Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterizations

Introduction Curves and surfaces can be represented using coefficients and a set of basis functions[1]. In the following, only curves are considered, but all statements apply equally to surfaces. Different representations use different sets of basis functions. These basis functions can be, for example, polynomials for polynomial curves, Bernstein-polynomials for Bézier curves, or B-spline basis functions for B-spline curves. As long as the general representation is of the form: 0( ) ( )ni i…     

A new method for compression-rebuilding of IR spectra

This work presents a new spectral data compression-rebuilding technique to translate the full IR spectral data into compact codes based on the analysis and comprehension encoding approach. This method has been successfully applied to a sample set of 505 IR spectra randomly picked from 100 000 spectra. The results show that the compression ratio reaches 12.7:1 under a very weak curve distortion. The choice of the number and shape of the basis functions is flexible. The IR spectra can be compressed in a fixed data size in fulfilling the distortion criteria. The data after compression have no significance in the sense of 蜶 spectra. To recover the original spectra, a specific algorithm must be applied. So the method can be used as a cryptic tool. Furthermore, the method can be applied to the compression of other complex curve by utilizing some of proper basis functions.     

Woolen Textile Simulation by Synthesis Mapping

This paper proposes a new rapid and efficient method for woolen textile simulation-Cmapping synthesize. This method uses a stochastic function to simulate fuzz on some types of wool textile. The wool yarns are simulated on the basis of Phong illumination model. In order to obtain a visual effect of the wool textile with fuzz, the light intensity of fuzz is synthesized as a color parameter in the Phong illumination model after the yarns have been simulated. The model of woolen textile with fuzz can be built eventually. With synthesis mapping methods, user can choose his favorite fuzz density on the wool by controlling some appropriate parameters.     

Melt Quality Evaluation of Ductile Iron by Pattern Recognition of Thermal Analysis Cooling Curves

The melt quality of ductile iron can be related to the melt's thermal analysis cooling curve. The freezing zone of the thermal analysis cooling curve was found to indicate the melt quality of the ductile iron. A comprehensive difference parameter, Ω, of the thermal analysis cooling curves was found to be related to the properties of ductile iron melts such as composition, temperature, and graphite morphology. As Ω ap- proached O, the thermal analysis cooling curves were found to come together with all the properties indicat- ing melt quality about the same. A database of thermal analysis cooling curves related to the properties of the ductile iron melts was set up as a basis for a method to accurately evaluate the melt quality of ductile iron by pattern recognition of thermal analysis cooling curves. The quality of a ductile iron melt can then be immediately determined by comparing its thermal analysis cooling curve freezing zone shape to those in the database.     

Semi-stationary subdivision operators in geometric modeling

Based on the view of operator, a novel uniform subdivision construction method is proposed for free form curve and surface design. This method can give an appropriate manner of parameter change in the subdivision iteration with fewer parameters and better shape control, such as building local revolving surfaces. The convergent property of order 2 subdivision surface is elegantly analyzed using computing techniques of matrix. This method is promised to be valuable in Computer Aided Design and computer graphics, due to the simplicity both in mathematical theory and practical implementation, the similarity to the B-spline curve and surface, G1 continuity, the affine invariability and local flexible control.     

The structure of uniform B-spline curves with parameters

The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions with parameter and the B-spline basis functions. Based on the degree elevation of B-spline, we extend the uniform B-spline basis functions with parameter to ones with multiple parameters. Examples show that the proposed basis functions provide more flexibility for curve design.     

带形状参数的三角曲线曲面

为了保留B样条曲线的优点,同时克服B样条曲线在控制顶点给定的情况下不具备形状可调性、不能精确表示椭圆(圆)的缺点,定义了一种带形状参数的三角样条曲线.新曲线具有与三次B样条曲线相同的结构与基本性质,但因为引入了形状参数,并采用三角函数作为基底,新曲线还具备了三次B样条曲线不具备的两个性质,即形状可调性和可以精确表示椭圆(圆).另外,新曲线还具有比三次B样条曲线更好的连续性和对控制多边形的逼近性.     

一类带形状参数的三次均匀B样条曲线

利用三次多项式调配函数构造三次均匀B样条基,基于该基函数建立了一类带形状参数的三次均匀B样条曲线,形状参数的值用于调整曲线的形状,描述曲线接近其控制多边形的程度;选取的形状参数不同,得到的连续曲线不同.最后给出曲线设计的实例.     

多形状参数的均匀B样条曲线

利用分段积分的方法并引入多个形状参数,将单形状参数的均匀B样条曲线推广到多形状参数的情形;这类曲线具有标准的均匀B样条曲线及单形状参数的均匀B样条曲线的主要性质,如连续性、凸包性等;根据形状参数的各种不同取值,这类曲线既能整体地又能局部地调控其形状,由此生成的曲线与曲面,作为一种新的几何造型方法,可应用于CAD/CAM领域。     

一类含任意参量的B样条型三次参数曲线

构造了一类含四个参量的B样条型三次参数曲线,它以三次Hermite曲线、Ball曲线、Bezier曲线、Timmer曲线和B样条曲线为其特例。本文还给出了曲线与其特征多边形各边相切的条件。通过调整曲线的四个参量便可改变曲线的形状(包括端点位置、凸向及弯曲程度等)以满足实际需要。     

二次均匀B样条曲线的扩展

该文给出三次和四次多项式调配函数,并将之推广得到高次调配函数,它们是二次B样条函数的进一步扩展。基于给出的调配函数,可建立一种带形状参数的分段多项式曲线;调整形状参数可使三次多项式曲线在二次均匀B样条曲线两侧摆动,而四次多项式曲线在三次多项式曲线两侧摆动;最后给出实例,分别利用它们构造出带局部调节参数的G1和G2连续的曲线。     

多形状参数的双曲多项式均匀B样条

文章利用分段积分的思想并引入多个形状参数,给出了双曲多项式均匀B样条曲线的扩展,该类曲线具有标准的和单形状参数的双曲多项式均匀B样条曲线的主要性质;改变形状参数的值能整体或局部调控其形状,有利于双曲多项式均匀B样条曲线的设计;并给出了多形状参数的均匀B样条曲线,体现了曲线的整体与局部调控.     

基于五次B样条的子区间法

重构细分划了时域,细分划拓展了0次B样条醒的定义,对高次B样条的递推式进行了拓展,获得了细分划拓展的均匀分划的分段式五次B样条函数,因而拓展了展开定理,构造了五次B样条基函数．该基函数与现有的五次B样奈基函数相比,表征的物理概念更清晰和简洁．基于五次B样条基函数,提出和推导了结构动力响应研究中的位移元子区间法和子区间法的嵌套方法递推格式．通过精度比较,得出子区间法的嵌套方法要优越于位移元子区间法．     

一种双正交小波代数构造方法

提出了一种B样条双正交小波的代数构造方法.对同一个尺度函数来说,可通过自由选择参数构造多种不同的对偶尺度函数的系数,从而可以构造不同的B样条双正交小波.在此基础上用同一尺度函数的多种双正交小波分别作了信号消噪和图像的分解与重构实验,取得了小波系数在信号消噪和图像处理中如何按照应用目的选优的相关结论.