共查询到20条相似文献，搜索用时 31 毫秒
1.
Cubic algebraic hyperbolic （AH） Bezier curves and AH spline curves are defined with a positive parameter a in the space spanned by {1, t, sinht, cosht}. Modifying the value of a yields a family ofAH Bezier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called ＂path of AH curve＂ （AH Bezier and AH spline curves） when a changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point. 相似文献
2.
A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter 总被引：1，自引：1，他引：0
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. 相似文献
3.
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. 相似文献
4.
Vanishing torsion of parametric curves 总被引：1，自引：0，他引：1
JUHASZ Imre 《浙江大学学报(A卷英文版)》2007,8(4):593-595
We consider the class of parametric curves that can be represented by combination of control points and basis func- tions. A control point is let vary while the rest is held fixed. It’s shown that the locus of the moving control point that yields points of zero torsion is the osculating plane of the corresponding discriminant curve at its point of the same parameter value. The special case is studied when the basis functions sum to one. 相似文献
5.
CAI Hong-jie WANG Guo-jin 《浙江大学学报(A卷英文版)》2007,8(10):1650-1656
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. 相似文献
6.
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. 相似文献
7.
CAO Juan WANG Guo-zhao 《浙江大学学报(A卷英文版)》2007,8(10):1663-1670
As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterization of the curve when the fourth point is in each region. This partitioned plane is called a "characterization diagram". By moving one of the control points but fixing the rest, one can induce different characterization diagrams. In this paper, we investigate the relation among all different characterization diagrams of cubic C-curves based on the singularity conditions proposed by Yang and Wang (2004). We conclude that, no matter what the C-curve type is or which control point varies, the characterization diagrams can be obtained by cutting a common 3D characterization space with a corresponding plane. 相似文献
8.
LU Li-zheng WANG Guo-zhao 《浙江大学学报(A卷英文版)》2007,8(10):1657-1662
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 相似文献
9.
任伯帜 《重庆大学学报(英文版)》2003,2(2)
1. Introduction In drawing up the rainstorm intensity formula of a modern town to obtain the datum relation between the rainfall intensity and the rainfall time-recurrence period from original data of rainstorm intensity at different rainfall time, there are two methods: 1) the method of theoretical frequency, 2) adjusting original data with some theories or an empirical frequency curve. The second method is usually adopted based on a great quantity of project practices done by predecessors. … 相似文献
10.
In fringe projection profilometry, the nonlinear intensity response caused by the γ effect of a digital projector results in periodic phase error and therefore measurement error. Previous error correction methods are largely based on the calibration of single γ value. However, in practice, it is difficult to accurately model the full range of the intensity response with a one-parameter γ function. In this paper, a compensated intensity response curve is generated and fitted with the constrained cubic spline. With the compensated curve, the full range of the nonlinear intensity response can be corrected and the periodic phase errors can be removed significantly. Experimental results on a flat board confirm the average root mean square （RMS） of the phase error which can be reduced to at least 0.0049 rad. 相似文献
11.
PAN Yong-juan WANG Guo-jin 《浙江大学学报(A卷英文版)》2007,8(8):1199-1209
In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable. 相似文献
12.
CHENG Si-yuan ZHANG Xiang-wei HUANG Man-hui 《重庆大学学报(英文版)》2005,4(4):185-188
1 Introduction a Planar curve approximation is a crucial issue in many applications of computer graphics, computer vision, CAD/CAM, image processing, etc., and there have been many reports in the literature on solving the curve approximation problem by using the B-splines. However, most of the existing methods required parameterization of data points on the target curve. It is a difficult task to estimate these parameters and different parameter choices may largely affect the approximation … 相似文献
13.
We have investigated the feedback control of the cooperative dynamics of two coupled electrochemical oscillators that is induced merely by external noise. The interacting electrochemical cells are modeled with parameter values at which no autonomous oscillations occur, and each unit is forced by its own source of random fluctuations. Application of delayed feedback to only one of two subsystems is shown to be able to change the coherence and time scales of noise-induced oscillations either in the given subsystem or globally. It can also induce or suppress stochastic resonance under the certain conditions. 相似文献
14.
In order to deal with torque pulsation problem caused by traditional control method for brushless DC （BLDC） motor and to achieve high precision and good stability, a novel control strategy is proposed. Compared with the traditional control scheme, by using phase voltage as a control objective and making waveform of phase current approximately quasi-sinusoidal, torque ripple of BLDC motor is reduced from the original 14% to 3.4%, while toque is increased by 3.8%. Furthermore, by detecting zero-crossings of back electromotive force （BEMF） with non-conducting phases, sensorless control is realized. The new control strategy is simple. It can minimize torque ripple, increase torque, and realize sensorless control for BLDC motor. Simulation and experiments show good performance of BLDC motor by using the new control method. 相似文献
15.
主流形和非线性维数化简的切向空间校正 总被引：8，自引：0，他引：8
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. 相似文献
16.
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. 相似文献
17.
Improving the Fatigue Performance of the Welded Joints of Ultra-Fine Grain Steel by Ultrasonic Peening 总被引：2，自引：0，他引：2
Contrast tests were carried out to study the fatigue performance of the butt joints treated by ultrasonic peening, aiming at the improvement of ultrasonic peening treatment(UPT) on welded joints of a new material. The material is a new generation of fine grain and high purity SS400 steel that has the same ingredients as the traditional low carbon steel. The specimens are in two different states:welded and ultrasonic peening conditions. The corresponding fatigue testing data were analyzed according to the regulation of the statistical method for fatigue life of the welded joints established by International Institute of Welding(IIW). Welding residual stress was considered in two different ways: the constant stress ratio R = 0.5 and the Ohta method. The nominalstress-number (σ-N) curves were corrected because of the different plate thickness compared to the standard and because there was no mismatch or angular deformation. The results indicated that: 1 ) Compared with the welded specimens, when the stress range was 200 MPa, the fatigue life of the SS400 steel specimens treated by ultrasonic peening is prolonged by over 58 times, and the fatigue strength FAT corresponding to 106 cycles is increased by about 66％; 2) As for the SS400 butt joint ( single side welding double sides molding) , after being treated by UPT, the nominal S-N curve (m = 10) of FAT 100 MPa(R =0.5) should be used for fatigue design. The standard S-N curves of FAT 100 MPa (R = 0.5, m = 10) could be used for fatigue design of the SS400 steel butt joints treated by ultrasonic peening. 相似文献
18.
WANG Yuan-jun CAO Yuan 《浙江大学学报(A卷英文版)》2006,7(9):1572-1577
INTRODUCTION In Computer Aided Design, fairness is one of the basic requirements for designing curves. If the curves are not fair, the design will be unsatisfactory and the producing process will be discommodious. In practice, there are all kinds of errors such as modelling error and measuring error. It means that the information on the data points may not be accurate. In order to obtain fair curves by interpolating these data points, we should fair the data points first. This is the so… 相似文献
19.
Two kinds of B-basis of the algebraic hyperbolic space 总被引：15，自引：2，他引：15
In this paper, two new kinds of B-basis functions called algebraic hyperbolic (AH) Bezier basis and AH B-Spline basis are presented in the space (?)k=span{1,t,...,tk-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bezier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms: AH B-Spline surface and AH T-Spline surface. 相似文献
20.
This thesis is mainly concerned with the two translation strategies of domesticating translation and foreignizing translation.The former is to make readers understand original works easier;the latter is to make readers understand original works clearer.It is necessary to take into consideration the necessity of using these two kinds of strategies,the affecting factors of using these two strategies to translate fic tions and the ways of using these two strategies. 相似文献