Multiresolution for Closed Curves and Surfaces Using Wavelets

Multiresolution modeling is becoming a powerful tool for fast display, and geometric data compression and transmission of complex shapes. Most of the existing literatures investigating the multiresolution for B-spline curves and surfaces are concentrated on open ones. In this paper, we focus on the multiresolution representations and editing of closed B-spline curves and surfaces using wavelets. A repetition approach is adopted for the multiresolution analysis of closed B-spline curves and surfaces. Since the closed curve or surface itself is periodic, it can overcome the drawback brought by the repetition method, i.e. introducing the discontinuities at the boundaries. Based on the models at different multiresolution levels, the multiresolution editing methods of closed curves and surfaces are introduced. Users can edit the overall shape of a closed one while preserving its details, or change its details without affecting its overall shape.

Efficient Construction of B-Spline Curves with Minimal Internal Energy

In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.

A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an image,including different translations, scales, and orientations, can be performedusing these parametric curves. For this, Bézier and B-spline curves can be generatedusing a point set that belongs to the outer boundary of the object. Theresulting object shape can be used in computer vision fields, such as searchingand segmentation methods and training machine learning algorithms. Theprerequisite for reconstructing the shape with parametric curves is to obtainsequentially the points in the point set. In this study, a novel algorithm hasbeen developed that sequentially obtains the pixel locations constituting theouter boundary of the object. The proposed algorithm, unlike the methods inthe literature, is implemented using a filter containing weights and an outercircle surrounding the object. In a binary format image, the starting point ofthe tracing is determined using the outer circle, and the next tracing movementand the pixel to be labeled as the boundary point is found by the filter weights.Then, control points that define the curve shape are selected by reducing thenumber of sequential points. Thus, the Bézier and B-spline curve equationsdescribing the shape are obtained using these points. In addition, differenttranslations, scales, and rotations of the object shape are easily provided bychanging the positions of the control points. It has also been shown that themissing part of the object can be completed thanks to the parametric curves.

DOUBLE-MOMENT OF SPACIAL CURVED BARS WITH CLOSED THIN- WALL CROSS-SECTION

In this paper, the double_moment of thin_wall cross_section spacial curved bars of anisotropic materials is discussed, and a general solving method for this type of problems as well as the concrete double_moment formula of planary curved bars subjected to action of vertical loads are given out.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation

A new method to the problem of fairing planar cubic B-spline curves is introduced in this paper. The method is based on weighted progressive iterative approximation （WPIA for short） and consists of following steps： finding the bad point which needs to fair, deleting the bad point, re-inserting a new data point to keep the structm-e of the curve and applying WPIA method with the new set of the data points to obtain the faired curve. The new set of the data points is formed by the rest of the original data points and the new inserted point. The method can be used for shape design and data processing. Numerical examples are provided to demonstrate the effectiveness of the method.

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

Abstract For two rational quadratic B spline curves with same control vertexes, the cross ratio of four collinear points are represented: which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the two curves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Bézier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray's location is showed. Also another cross ratio of the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initial vertex intersects respectively with the curve segment, the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only with the ray's location, but not with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.

The quadratic B-spline curve fitting for the shape of log cross sections

This paper describes a new method for simulation of the cross section shape of log. The self-developed MQK3102 log shape recognizing machine was used to acquire the finite discrete sampling points on the cross section of log and those points were fitted with the quadratic B-spline parametric curve. This method can clearly stimulate the real shape of the log cross section and is characterized by limited sampling points and high speed computing. The computed result of the previous curve does not affect the next one, which may avoid the graphic distortion caused by the accumulative error. The method can be used to simulate the whole body shape of log approximately by sampling the cross sections along the length direction of log, thus providing a reference model for optimum saw cutting of log.

B-spline curve-based routing in ad hoc networks

Routing algorithms capable of providing quality of service （QoS） will play an important role in future communication networks. For the trajectory-based routing （ TBR）, An effective method of en- coding trajectories into packets is proposed. The method uses a B-spline curve, which provides a lot of flexibility. The simulation results show that the performance of the proposed algorithms is im- proved significantly compared with the existing algorithm.

对FETKOVICH(费特科维奇)典型曲线的质疑与评论

FETKOVICH(费特科维奇,以下简称为费氏)于1971年和1980年,分别提出的有限水域水侵量方程和定压典型曲线,受到国内外专家的重视和引用。由于费氏典型曲线可以通过实际数据的拟合,确定井的驱动半径和驱动面积,因此,受到业内专家的青睐。通过推导表明,费氏有限水域水侵量方程,是一个指数递减方程。费氏将该方程直接应用于定容封闭边界油井的产量递减分析,并基于初始递减率的关系式,得到了费氏典型曲线的无因次时间。费氏利用无因次压力的倒数作为无因次产量,得到了典型曲线的无因次产量。然而,由于费氏典型曲线的无因次时间和无因次产量之间没有直接的函数关系,无法建立费氏的无因次典型曲线,因此,对费氏的有限水域水侵量方程和典型曲线的无因次时间和无因次产量进行了推导,并对存在的问题提出了质疑和评论。

山丘区自压输水管道水锤计算与模拟方法

为了准确预测和防护山丘区自压输水管道的水锤破坏,提高管道输水的安全性和可靠性,针对山丘区自压输水管道落差大、距离长和地势起伏的特点,提出将输水管道划分为弯曲段和带倾斜角度的直管段,利用极限思想将弯曲管段基于切线的曲线拟合矢量化方法,拟合为沿管道中心线具有相同过流断面的多段等效短管;采用拟合等效短管和倾斜直管相结合的方法进行水锤计算,建立了自压输水管道的数值计算模型.以陕西省千阳县一自压管道输水工程为例进行了验证分析,通过模拟管道末端阀门不同关阀时间的水锤压力变化规律,得出最优关阀时间为50 s≤T≤120 s,提出了相应的水锤防护方案.结果表明该方法的计算和模拟精度高,可为山丘区长距离自压管道输水工程建设与管理提供参考.

时间旅行的量子门

量子计算可以解决经典计算难于求解的问题,在物理原理允许范围内扩大了可有效计算的问题范围,对经典计算的扩展丘奇图灵论题提出了挑战.这里我们讨论一个有趣的问题:通过突破物理原理限制来实现更强大的计算机,进一步扩展量子计算机的能力.我们考虑一种全新的操纵能力,让量子计算可以实现时间穿梭旅行的量子控制门.这是量子门线路图形语言的一个符合直觉的扩展,作为例子,我们展示了一个可以有效求解SAT难题的扩展量子算法.我们的结果有助于更深刻地理解计算和物理原理之间的关系.

An adaptive generation method for free curve trajectory based on NURBS

To realize the high precision and real-time interpolation of the NURBS （non-uniform rational B-spline） curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.

真空断路器弹簧操动机构的优化

真空断路器触头弹簧压力增大会导致断路器无法可靠合闸,四连杆结构在一定程度上会影响机构的出力特性和机械效益,进而影响断路器合闸的可靠与稳定。文中分析了真空断路器的动作原理,建立弹簧操动机构的数学模型;对机构中的凸轮轮廓、传动拐臂的角度和尺寸、连板与合闸滚子的尺寸参数进行优化,建立弹簧操动机构的仿真模型。动力学仿真表明,优化后的触头弹簧压力增大了58%(从1 700 N提升到2 686 N),仍能保证断路器操动机构可靠合闸。试验结果显示,触头弹簧压力为2 500 N时断路器触头能够可靠吸合,平均合闸速度降至0.68 m/s,弹跳时间缩短了18.4%,整体优化后的方案满足设计要求并具有良好的可靠性与稳定性。

微型种植体支抗钉结合滑动法与关闭曲法治疗安氏Ⅱ类1分类错[牙合]畸形的效果

目的分析微型种植体支抗钉结合滑动法与关闭曲法治疗安氏Ⅱ类1分类错[牙合]畸形的效果。方法选取2020年1月至12月我院收治的80例安氏Ⅱ类1分类错[牙合]畸形患者为研究对象,按照随机法将其分为关闭曲组(微型种植体支抗钉结合关闭曲法治疗)和滑动组(微型种植体支抗钉结合滑动法治疗),每组40例。比较两组的治疗效果。结果治疗后,滑动组的ANB角、Wits值、FMA角、IMPA角小于关闭曲组,Z角、FMIA角大于关闭曲组(P<0.05)。治疗后,滑动组的牙龈指数(GI)、龈沟出血指数(SBI)、菌斑指数(PLI)评分及牙周探诊深度(PD)、附着丧失(AL)低于关闭曲组(P<0.05)。滑动组的不良事件总发生率低于关闭曲组(P<0.05);两组的前后牙消耗支抗比较,差异无统计学意义(P>0.05)。结论相较于微型种植体支抗钉结合关闭曲法,微型种植体支抗钉结合滑动法治疗安氏Ⅱ类1分类错[牙合]畸形可改善错[牙合]畸形与牙周指标,取得显著的正畸治疗效果,且不良事件发生率低。

轮式移动机器人沿相同目标轨迹的编队运动控制

为使轮式移动机器人编队能在某些特殊地形中沿着狭长路线顺利地执行任务,需要通过控制实现所有移动机器人沿着相同的路径运动。为了实现这一编队运动控制任务,本研究采用了领航跟随法的控制策略。首先,将目标路径曲线设计成动态跟踪目标的形式,通过动态跟踪目标中的相对曲率实现领航者对目标曲线精确跟踪。然后,找出领航机器人与跟随机器人的相对角度和目标轨迹曲线之间的关系,采用双闭环控制器设计思路实现领航者和跟随者沿相同轨迹运动。在双闭环控制器中,外环采用直接Lyapunov函数方法构造姿态控制器,内环使用时变障碍Lyapunov函数法构造力矩控制器。最后,基于Matlab进行数值仿真,验证所提控制策略的有效性和鲁棒性。

电子液压线控制动压力控制开发

为了克服电子液压线控制动系统(EHB)死区、摩擦及系统不确定性对压力控制的响应和精度的影响,文章提出一种新的闭环-前馈相结合的压力控制策略。该策略首先建立电子液压线控制动系统的动力学模型,并分析压力与活塞位移和速度相互关系,根据试验台架获取主缸压力与活塞位移的关系曲线;同时提出以压力-速度-电流为主的主控制回路,并以主缸活塞位置为辅助量的压力补偿控制策略;最后在斜坡和正弦工况下进行测试,结果表明该方法能够保证压力跟踪的快速响应和稳态跟踪性能。

On the Mean Absolute Geodesic Curvature of Closed Curves in 2-Dimensional Space Forms

In this paper, we establish some formulas on closed curves in 2-dimensionalspace forms. Mean absolute geodesic curvature is introduced to describe the average curving of aclosed curve. In this sense, a closed curve could be compared with a geodesic circle that is theboundary of a convex geodesic circular disk containing the closed curve. The comparison can be usedto show some properties of space forms only on themselves.

Finite difference modeling of sinking stage curved beam based on revised Vlasov equations

For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.