Constrained multi-degree reduction of rational Bezier curves using reparametenzation

Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bezier curves to the algorithms of constrained multi-degree reduction for rational Bezier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bezier curves, which are used to make uniform the weights of the rational Bezier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of ＂cancelling the best linear common divisor＂ and ＂shifted Chebyshev polynomial＂, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.     

A quadratic programming method for optimal degree reduction of Bézier curves with G~1-continuity

This paper presents a quadratic programming method for optimal multi-degree reduction of Bézier curves with G1-continuity. The L2 and l2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applica- tions of degree reduction of Bézier curves with their parameterizations close to arc-length parameterizations are also discussed.     

A quadratic programming method for optimal degree reduction of Bezier curves with G^1-continuity

This paper presents a quadratic programming method for optimal multi-degree reduction of Bézier curves with G1-continuity. The L2 and l2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applica     

Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer

We decompose the problem of the optimal multi-degree reduction of Bezier curves with comers constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of ＇divide and conquer＇ has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm.     

An Approach to Representing Heterogeneous Non-Uniform Rational B-Spline Objects

The representation method of heterogeneous material information is one of the key technologies of het-erogeneous object modeling, but almost all the existing methods cannot represent non-uniform rational B-spline (NURBS) entity. According to the characteristics of NURBS, a novel data structure, named NURBS material data structure, is proposed, in which the geometrical coordinates, weights and material coordinates of NURBS heterogeneous objects can be represented simultaneously. Based on this data structure, both direct representation method and inverse construction method of heterogeneous NURBS objects are introduced. In the direct representation method, three forms of NURBS heterogeneous objects are introduced by giving the geometry and material information of control points, among which the homogeneous coordinates form is employed for its brevity and easy programming. In the inverse construction method, continuous heterogeneous curves and surfaces can be obtained by interpolating discrete points and curves with specified material information. Some examples are given to show the effectiveness of the proposed methods.     

A family of quasi-cubic blended splines and applications

INTRODUCTION Bézier curves and uniform B-spline curves are powerful tools for constructing free form curves and surfaces (FFC/FFS). But they cannot represent the arcs, hyperbola, sphere, cylinders and other transcendental curves and surfaces exactly. In order to avoid the in- conveniences, many bases are presented in other new spaces (Zhang, 1996; Pe?a, 1997; Walz, 1997; Sánchez-Reyes, 1998; Mainar et al., 2001). Note that, these existing methods can deal with both polynomial curve…     

The Mastery of Listening Skills for College Students

Aiming at solving the problems of lacking listening skills practices in English class. The paper is written for two purposes. Firstly, it intends to drive the attention of present obstacles in English listening teaching. Most children in China have their English classes at schools, however, they don’t learn too much English they just learn about English. After years of learning the problems come up: the college students who have passed CET4(College English Test) and CET6 are unable to speak or listen to native speakers. Secondly, it tries to introduce the listening skills and the methods of teaching it. Language is not a knowledge but a skill, to learn language does not mean to know as many rules and information about it, but is to practice from the first day your learn it and do practice as much as possible.     

Estimation of vegetation biophysical parameters by remote sensing using radial basis function neural network

Hyperspectral reflectance (350~2500 nm) data were recorded at two different sites of rice in two experiment fields including two cultivars, and three levels of nitrogen (N) application. Twenty-five Vegetation Indices (VIs) were used to predict the rice agronomic parameters including Leaf Area Index (LAI, m2 green leaf/m2 soil) and Green Leaf Chlorophyll Density (GLCD, mg chlorophyll/m2 soil) by the traditional regression models and Radial Basis Function Neural Network (RBF). RBF emerged as a variant of Artificial Neural Networks (ANNs) in the late 1980’s. A large variety of training algorithms has been tested for training RBF networks. In this study, Original RBF (ORBF), Gradient Descent RBF (GDRBF), and Generalized Regression Neural Network (GRNN) were employed. Results showed that green waveband Normalized Difference Vegetation Index (NDVIgreen) and TCARI/OSAVI have the best prediction power for LAI by exponent model and ORBF respectively, and that TCARI/OSAVI has the best prediction power for GLCD by exponent model and GDRBF. The best performances of RBF are compared with the traditional models, showing that the relationship between VIs and agronomic variables are further improved when RBF is used. Compared with the best traditional models, ORBF using TCARI/OSAVI improves the prediction power for LAI by lowering the Root Mean Square Error (RMSE) for 0.1119, and GDRBF using TCARI/OSAVI improves the prediction power for GLCD by lowering the RMSE for 26.7853. It is concluded that RBF provides a useful exploratory and predictive tool when applied to the sensitive VIs.     

超级成语SHOW

1.one's line of country爱好范围;熟悉范围 　　A What do you like best? 　　B:Music and movie are my line of country. 　　A Oh… 　　B:I have learned the piano for ten years,and I like to go to the cinema by myself;especially the classics never too boring to see. 　　……     

A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter

We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.     

Get Attention with a Balanced Resume Objective

When it conies right down to it, employers considering candidates for a job really only want to know two things: What do you offer in the way of education, experience and skills? What sort of job are you looking for? Do your career goals match the job that's available?One of the best ways to answer these questions is with an objective statement at the beginning of your resume. Simply put, an objective concisely tells prospective employers what you want in a job and what you can bring to an organization. You may have heard that some employers don't want to see an objective on your resume. It's true. But for every hiring manager who says something like this:     

危险的高跟鞋

Directions:Read the following passage.The passage is followed by several questions or unfinished statements.For each of them there are four choices marked A,B,C and D.Choose the one that fits best according to the information given in the passage. Healthy knees aren’t the main consideration in choosing high heels,but new research says chunky heels are just as bad for the knees as spindly stilettos(细高跟鞋)."It takes a long time to feel the effects of knee osteoarthritis(骨关节炎)—and once you do it,it is too late,"said Dr.Casey Kerrigan,leading researcher of the study and associate professor at Harvard     

主流形和非线性维数化简的切向空间校正

We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized da-ta points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approxi-mation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data pointswith respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can bequite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimension-al Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.     

Analysis and Evaluation of the Learners’ESL in Terms of Developmental Acquisition Stage

This essay aims at utilizing the acquisition criterion developed by researchers to analyze the data collected from the two learners of English in Australia. Drawn from the Processability theory and the theory of Second Language Acquisition, the findings in both quantitative and qualitative forms will be presented to draw a conclusion that the two students have reached at which developmental stage their L2 learning is.     

阿拉斯加非凡之旅

This is Alaska,which might as well have been a different country. Seeing the Alaskan Wildlife for the First Time Early morning is the best time to see the brown and black bears.They usually come here to fish for 1)salmon. There were a surprising number of people at the 2)walkway.We sat down by the bridge,looking at the salmon as they 3)raced.In fact,salmon could be found almost anywhere in Alaska,and for a bargain price.I turned my attention to wondering about this miracle of nature.     

An Initial Study of Improving English Reading Efficiency

Reading,as an important medium for human beings to gain knowledge,also plays a major part in the teaching and learning of English.Nevertheless,in practical teaching,we find that the students are quite at a loss at what to do.This article will probe into how to improve the reading efficiency from two aspects:linguistic factors and non-linguistic factors.     

单机最小化加权总完工时间的产品加工问题

In this paper,a fabrication scheduling problem concerning the production of components at a single manufacturing facility was studied,in which the manufactured components are subsequently assembled into a finite number of end products. Each product was assumed to comprise a common component to all jobs and a unique component to itself.Common operations were processed in batches and each batch required a setup time.A product is completed when both its two operations have been processed and are available.The optimality criterion considered was the minimization of weighted flow time.For this scheduling problem,the optimal schedules were described in a weignted shortest processing time first(WSPT)order and two algorithms were constructed corresponding to the batch availability and item availability,respectively.     

NURBS curve blending using extension

Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that comer are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G^1- or G^2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth： （1） The parameterization of the original shapes does not change; （2） No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.     

一种切触有理插值在线性系统模型简化中的应用

A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation.On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems.Some numerical examples were given to explain the result in this paper.     

Layer-layout-based heuristics for loading homogeneous items into a single container

The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxes into a single container. Both algorithms adopt the concept of building layers on one face of the container, but the first heuristic determines the layer face once for all, while the second treats the remaining container space as a reduced-sized container after one layer is loaded and, hence, selects the layer face dynamically. To handle the layout design problem at a layer's level, a block-based 2D packing procedure is also developed. Numerical studies demonstrate the efficiency of the heuristics.