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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.
In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given. 相似文献
3.
Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduc- tion for polynomial Bézier curves to the algorithms of constrained multi-degree reduction for rational Bézier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bézier curves, which are used to make uniform the weights of the rational Bézier 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
4.
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
5.
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
6.
OROZCO Rubén 《浙江大学学报(A卷英文版)》2006,7(10):1748-1756
INTRODUCTION Deconvolution of ultrasonic signals is defined as the solution of the inverse problem of convolving an input signal, known as the system function h(n), with a medium reflectivity function x(n) and can be rep- resented by y(n)=h(n)*x(n) η(n), (1) where y(n) is the measured signal, * denotes the convolution operation and η(n) is the additive noise. Recovering x(n) from the observation y(n) leads to improving the appearance and the axial resolution of the RF-signals by removin… 相似文献
7.
在正规线性空间上讨论微分方程系统X′(t)=F(t,x,y)X′(t)=ε.G(t,x,y),这里参数ε很小。证明了如果F和G满足Lipschitz条件,F(t,x,y)对y的小的值是指数稳定的,系统在x和y对1/ε阶时间周期的持久扰动是稳定的。考虑扰动系统X′(t)=F(t,x,y) J(t),X′(t)=ε.G(t,x,y) K(t),这里J(t)和K(t)从S到S 1的积分值很小。从而得到存在仅依赖于F和G的常数A,B,C和λ,使对σ≤λ,如果初始值和持久扰动比σ小,且ε≤σ,则解X(t)和Y(t)对一切时间t有界σAeBtε,使得σeBtε≤C。 相似文献
8.
The failure mode and adhesion of thermal barrier coating (TBC) 8YSZ (ZrO2+8% (w/w) Y2O3) deposited on NiCoCrAlTaY bond coat by atmospheric plasma spraying were investigated. A grooved modified three-point bending specimen that can generate a single interface crack to facilitate the control of crack growth was adopted for testing, which was conducted at the ambient temperature of 100 °C. The morphology and composition of fractured surfaces were examined by means of a scanning electron microscopy (SEM) and an energy disperse spectroscopy (EDS). Images and spectrum show that cracks are initiated and propagated exclusively within YSZ layer adjacent to top/bond coat interface. The load-displacement curves obtained exhibit similar shapes that indicate two distinct stages in crack initiation and stable crack growth. Finite element analyses were performed to extract the adhesion strength of the TBCs. The delamination toughness of the plasma-sprayed 8YSZ coatings at 100 °C, in terms of critical strain energy release rate Gc, can be reliably obtained from an analytical solution. 相似文献
9.
Cun-jian MIAO Jin-yang ZHENG Xiao-zhe GAO Ze HUANG A-bin GUO Du-yi YE Li MA 《浙江大学学报(A卷英文版)》2013,14(1):31-37
Cold-stretched pressure vessels from austenitic stainless steels(ASS) are widely used for storage and transportation of liquefied gases,and have such advantages as thin wall and light weight.Fatigue is an important concern in these pressure vessels,which are subjected to alternative loads.Even though several codes and standards have guidelines on these pressure vessels,there are no relevant design methods on fatigue failure.To understand the fatigue properties of ASS 1.4301(equivalents include UNS S30400 and AISI 304) in solution-annealed(SA) and cold-stretched conditions(9% strain level) and the response of fatigue properties to cold stretching(CS),low-cycle fatigue(LCF) tests were performed at room temperature,with total strain amplitudes ranging from -.4% to -.8%.Martensite transformations were measured during the tests.Comparisons on cyclic stress response,cyclic stress-strain behavior,and fatigue life were carried out between SA and CS materials.Results show that CS reduces the initial hardening stage,but prolongs the softening period in the cyclic stress response.Martensite transformation helps form a stable regime and subsequent secondary hardening.The stresses of monotonic and cyclic stress-strain curves are improved by CS,which leads to a lower plastic strain and a much higher elastic strain.The fatigue resistance of the CS material is better than that of the SA material,which is approximately 1?03 to 2?04 cycles.The S-N curve of the ASME standard for ASS is compared with the fatigue data and is justified to be suitable for the fatigue design of cold-stretched pressure vessels.However,considering the CS material has a better fatigue resistance,the S-N curve will be more conservative.The present study would be helpful in making full use of the advantages of CS to develop a new S-N curve for fatigue design of cold-stretched pressure vessels. 相似文献
10.
INTRODUCTION Computing the visible portions of parameteriz surfaces is a fundamental problem for Comput Graphics, Computer Aided Design, Computer Visio and so on. Generally, a common solution to getti the visible region of the parameterized surfaces is use discrete methods including Z-Buffer (Greene al., 1993), Hierarchical Occlusion Map (HOM (Zhang et al., 1997), Ray-Tracing (Toth, 1985), an tessellating the surface with its u and v isoparametr curves (Maghrabi and Griffiths, 198… 相似文献
11.
非线性守恒律的高阶谱粘性方法 总被引：2，自引：0，他引：2
1IntroductionIn this paper,we consider the following2π-periodicnonlinear conservationlaw tu(x,t) xf(u(x,t))=0,00(1)withu(x,0)=u0(x).The problem(1)may deve-lopshock discontinuities even for smoothu0andf[1].Ingeneral,we must consider the weak notion of solu-tion.To guarantee the uniqueness of the weak solu-tion,one of the various equivalent entropy conditions,such as[1,2],withF(u)≡∫uU′(ω)f′(ω)dω,tU(u) xF(u)≤0,Uconvex(2)is i mposed.The spatialL2norm of the entropy solu-tion d… 相似文献
12.
An efficient method for tracing planar implicit curves 总被引：1，自引：0，他引：1
YU Zheng-sheng CAI Yao-zhi OH Min-jae KIM Tae-wan PENG Qun-sheng 《浙江大学学报(A卷英文版)》2006,7(7):1115-1123
INTRODUCTION Tracing a planar implicit curve f(x, y)=0 on a rectangular region [xl, xr]×[yb, yt] is of great interest in Computer-Aided Design and Computer Graphics. While parametric curves are easy to plot, plotting implicit curves is a challenging problem. Planar im- plicit curve plotting method can be classified into two categories (Shou et al., 2005; Martin et al., 2002; Lopes et al., 2002). In the first category are subdivi- sion methods (Shou et al., 2005; Martin et al., 2002) … 相似文献
13.
二阶泛函微分方程属于L.S或L.C的判定 总被引：1，自引：0，他引：1
孟东沅 《黄冈师范学院学报》2006,26(3):4-7,41
通过构造一类泛函,借助于两个重要不等式,讨论了方程(r(t)x′(t)) ′p(t)x(′t) q1(t)x(t) q2(t)x(h(t))=f(t),建立了其属于L.C或L.C∩L.S的充分条件. 相似文献
14.
题目:在图1中,平面镜MN竖直放置,发光点经平面镜所成的像为S′.保持S不动,使MN在竖直面内绕O点按顺时针方向转过α的过程中,试确定S的虚像S′的运动轨迹.图1图2解:建立如图2所示的坐标系.各位置坐标为O(0,0),S(m,0),S′(x,y).MN与x轴的夹角为θ.所以,镜MN的方程为y=xtanθ.S与S′关于MN对称,所以直线SS′的斜率为k=-ta1nθ.(1)设SS′的中点为C,所以,C(x 2m,2y).因为C∈MN,所以y2=x 2mtanθ.(2)tanθ=-x-ym.(3)代入(2)式得y=-(x m)y(x-m).化简得x2 y2=m2.所以S′(x,y)的轨迹为以O为圆心,m为半径的一段圆弧.用数学方法解一道竞赛… 相似文献
15.
16.
A family of quasi-cubic blended splines and applications 总被引：4，自引：0，他引：4
SU Ben-yue TAN Jie-qing 《浙江大学学报(A卷英文版)》2006,7(9):1550-1560
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… 相似文献
17.
在f(t,x),fx(t,x)α（t),α′（t),β（t)连续,fx(t,x)≥-β（t）,β（t）≤π^2 [α^2(t)-2α′(t)]/4,且β(t)≠π^2 [α^2(t)-2α′(t)]/4条件下,证明了拟线性两点边值问题x″=α(t)x′ f(t,x),x(0=a,x(1)=b,对于任给实数a,b都有唯一解。 相似文献
18.
“对称”是解析几何中的常见问题 ,也是一种重要的思想方法 .本文旨在对解析几何中的点对称、轴对称问题进行整理 ,以供学生参考 .1 关于点的对称(1)点关于点的对称问题 ,通常我们是将其化为中点问题来解决 .例如 ,求点P(x ,y)关于点M (x0 ,y0 )的对称点P′的坐标 .设P′(x′ ,y′) ,由M为｜PP′｜的中点 ,得 x+x′2 =x0y+ y′2 =y0 x′ =2x0 -x ,y′=2 y0 - y ,即所求对称点的坐标为P′(2x0 -x ,2 y0 - y) .(2 )曲线关于点的对称问题 ,利用对称定义 ,结合求轨迹方程的代入法即可解决 .例如 ,求曲线C :f(x ,y) =0关于M (x0 ,y0 )对… 相似文献
19.
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
20.
讨论了偏差变元微分方程x′(t) a(t)x(t) p(t)f[x(g_1(t)),x(g_2(t),…x(g_(?)(t))]=0的振动性,改进了文[1]的结果. 相似文献