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The quadratic B-spline curve fitting for the shape of log cross sections 被引量:2
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作者 任洪娥 吴妍 朱哓明 《Journal of Forestry Research》 SCIE CAS CSCD 2006年第2期150-152,共3页
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... 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. 展开更多
关键词 Quadratic b-spline curve Cross section shape LOG Computer simulation Optimum saw cutting
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Efficient Construction of B-Spline Curves with Minimal Internal Energy 被引量:6
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作者 Gang Xu Yufan Zhu +3 位作者 Lishan Deng Guozhao Wang Bojian Li Kin-chuen Hui 《Computers, Materials & Continua》 SCIE EI 2019年第3期879-892,共14页
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-minimizati... 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. 展开更多
关键词 Minimal energy b-spline curves geometric construction discrete mask method sparse linear system.
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A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves
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作者 Nihat Arslan Kali Gurkahraman 《Computers, Materials & Continua》 SCIE EI 2023年第4期331-350,共20页
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... 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. 展开更多
关键词 Contour tracing algorithm bézier curve b-spline curve object shape reconstruction
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Approximate merging of B-spline curves and surfaces 被引量:2
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作者 CHEN Jun: WANG Guo-jin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第4期429-436,共8页
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 curv... 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. 展开更多
关键词 Computer aided geometric design approximate merging b-spline curves and surfaces.
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One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation 被引量:1
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作者 ZHANG Li YANG Yan +1 位作者 LI Yuan-yuan TAN Jieqing 《Computer Aided Drafting,Design and Manufacturing》 2014年第1期36-41,共6页
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:... 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. 展开更多
关键词 b-spline curves FAIRING WPIA
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B-spline curve-based routing in ad hoc networks
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作者 黄林 《High Technology Letters》 EI CAS 2012年第4期428-432,共5页
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 trajectorie... 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. 展开更多
关键词 ROUTING quality of service (QoS) b-spline curve
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RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES
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作者 ZHU Weidong KE Yinglin 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2007年第4期112-116,共5页
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 par... 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. 展开更多
关键词 Reconstruction Symmetry Freeform curve Freeform surface b-spline
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THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES
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作者 HAN XI’AN AND HUANG XILI 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1998年第4期445-450,共6页
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 f... 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. 展开更多
关键词 Computer aided geometric design rational b-spline curve cross ratio weight
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An adaptive generation method for free curve trajectory based on NURBS
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作者 朱昊 刘京南 +1 位作者 杨安康 汪木兰 《Journal of Southeast University(English Edition)》 EI CAS 2014年第3期296-301,共6页
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,... 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. 展开更多
关键词 free curve NURBS (non-uniform rational b-spline sigmoid function Adams algorithm
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COMPLEX RATIONAL TYPE INTERPOLATION AT DISTURBED FEJR POINTS ON A CURVE 被引量:1
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作者 涂天亮 莫烔 《Acta Mathematica Scientia》 SCIE CSCD 2012年第2期441-454,共14页
The results of accurate order of uniform approximation and simultaneous approximation in the early work "Jackson Type Theorems on Complex Curves" are improved from Fejer points to disturbed Fejer points in this arti... The results of accurate order of uniform approximation and simultaneous approximation in the early work "Jackson Type Theorems on Complex Curves" are improved from Fejer points to disturbed Fejer points in this article. Furthermore, the stability of convergence of Tn,∈(f,z) with disturbed sample values f(z^*) + Sk are also proved in this article. 展开更多
关键词 Disturbed Fejer points complex interpolation order of approximation closed Jordan curve uniform convergence
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Study on Real-time Look-ahead and Adaptive Parametric Curve Interpolator 被引量:2
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作者 郭伟 杜道山 +1 位作者 徐荣珍 李从心 《Journal of Shanghai Jiaotong university(Science)》 EI 2007年第3期388-393,共6页
The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpol... The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpolation, which considering the maximum acceleration/deceleration of the machine tool. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, the look-ahead function was designed and illustrated. It can detect and adjust the feedrate adaptively. With the help of real-time look-ahead, the acceleration/deceleration can be limited to the range of the machine tool capacity. Thus, feedrate fluctuation is reduced. A NURBS curve interpolation experiment was provided to verify the feasibility and advantages of the proposed interpolator with a real-time look-ahead function. 展开更多
关键词 adaptive interpolator LOOK-AHEAD non-uniform rational b-spline curves feedrate sensitive corner chord error
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Adaptive B-snake for planar curve approximation 被引量:1
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作者 成思源 《Journal of Chongqing University》 CAS 2005年第4期185-188,共4页
An adaptive B-spline active contour model for planar curve approximation is proposed. Starting with an initial B-spline curve, the finite element method is adopted to make the active B-spline curve converge towards th... An adaptive B-spline active contour model for planar curve approximation is proposed. Starting with an initial B-spline curve, the finite element method is adopted to make the active B-spline curve converge towards the target curve without the need of data points parameterization. A strategy of automatic control point insertion during the B-spline active contour deformation, adaptive to the shape of the planar curve, is also given. Experimental results show that this method is efficient and accurate in planar curve approximation. 展开更多
关键词 active contour model b-spline curve approximation
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On the Parametric Modeling of Turbine Blade Section Curve 被引量:1
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作者 ZHU Jian SONG Yu-wang XI Ping 《Computer Aided Drafting,Design and Manufacturing》 2007年第2期1-7,共7页
Geometric parameters of the turbine blade are classified according to their destined functions, and the mathematical definition of those parameters in the section curve is introduced in detail. Some parts of the secti... Geometric parameters of the turbine blade are classified according to their destined functions, and the mathematical definition of those parameters in the section curve is introduced in detail. Some parts of the section curve shape can be adjusted freely, offering more flexibility to designers. 展开更多
关键词 blade section curve parametric modeling parametric modification b-spline
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A SPACE THEORY BASIS FOR CURVE FITTING PROBLEMS
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作者 韩维信 《Transactions of Tianjin University》 EI CAS 1995年第2期194+192-194,共4页
itherto, a precision Concept for curve fitting problems has not been set. By using the theory of functional analysis, the author of this paper established a space theory basis for curve fitting problems. Also given in... itherto, a precision Concept for curve fitting problems has not been set. By using the theory of functional analysis, the author of this paper established a space theory basis for curve fitting problems. Also given in the paper is the precision concept of the curve fitting problems and the method for constructing the fitting of a curve satisfying given precision requirements. 展开更多
关键词 fitted space fitted curve uniform convergence least square approximation norm equivalence principle
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A Methodology for Curve and Surface Fitting with Adaptive Fairing for Digitized Points
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作者 李大永 彭颖红 +1 位作者 尹忠慰 李建新 《Journal of Shanghai Jiaotong university(Science)》 EI 2006年第4期460-464,共5页
A new approach for NURBS(Non-uniform rational B-spline) curve and surface fitting for measured points was presented which employs a fairing method applied to digitized point data with discrete curvature. If measured p... A new approach for NURBS(Non-uniform rational B-spline) curve and surface fitting for measured points was presented which employs a fairing method applied to digitized point data with discrete curvature. If measured points are used as control points to construct an NURBS curve, then the curvature of each data point corresponding to control point of the constructed curve can be computed. According to the convex hull and local properties of NURBS, based on the curvatures obtained, the measured points can be faired. If faired measured points are used as target points to modify, the constructed curve passing through these faired points can produce a smooth NURBS curve. This paper also presented the justification for utilizing the curvatures of constructed NURBS curve instead of the conventional interpolated curve to fair the measured points. Based on the presented algorithms, some qualities of the constructed curves can be improved. 展开更多
关键词 NON-uniform rational B-splihe (NURBS) FAIR curvATURE CONSTRUCTED curve
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Multiresolution for Closed Curves and Surfaces Using Wavelets
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作者 ZHAO Gang BAI Jie WANG Chao YAO Fu-sheng 《Computer Aided Drafting,Design and Manufacturing》 2005年第2期1-13,共13页
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... 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. 展开更多
关键词 closed b-spline curves closed b-spline surfaces WAVELETS multiresolution representation analysis multiresolution representation multiresolution editing
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CURVE AND SURFACE INTERPOLATIONBY SUBDIVISION ALGORITHMS 被引量:1
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作者 Ruibin Qu 《Computer Aided Drafting,Design and Manufacturing》 1994年第2期28-39,共2页
Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference... Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17. 展开更多
关键词 curve and surface interpolation subdivision algorithm divided difference generationpolynomial uniform triangulation WAVELET
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挖掘机时间最优与脉动最优轨迹规划
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作者 孙志毅 刘松 +1 位作者 王银 李虹 《机械设计与制造》 北大核心 2024年第1期304-307,313,共5页
为了在提高挖掘机工作效率的同时减小各个关节的振动,提出了一种使挖掘机关节运行时间和关节脉动达到某种综合最优的轨迹规划方法,在同时考虑挖掘机动臂、斗杆、铲斗的运动学约束以及动作时间约束条件的前提下,采用五次非均匀B样条曲线... 为了在提高挖掘机工作效率的同时减小各个关节的振动,提出了一种使挖掘机关节运行时间和关节脉动达到某种综合最优的轨迹规划方法,在同时考虑挖掘机动臂、斗杆、铲斗的运动学约束以及动作时间约束条件的前提下,采用五次非均匀B样条曲线对离散序列点进行插值,然后运用自适应粒子群优化算法(ASPO)对目标函数进行优化求解得到一条动作时间较短且脉动连续关节轨迹,最后对优化后得到的关节轨迹进行仿真实验,结果表明,该方法最终可以得到比较理想的运动轨迹,从而验证了该方法的有效性。 展开更多
关键词 挖掘机 轨迹规划 非均匀B样条曲线 自适应粒子群
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基于广义波阻抗理论的SHPB试验中弹性压缩阶段试件应力-应变曲线的应力波效应及其影响机理
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作者 高光发 《爆炸与冲击》 EI CAS CSCD 北大核心 2024年第9期98-111,共14页
定量研究分离式霍普金森压杆(split Hopkinson pressure bar,SHPB)试验中弹性压缩阶段试件中的应力波效应是解耦准确材料弹性曲线的基础。在满足平面波假设的基础上,基于广义波阻抗理论,对杆与试件面积不匹配时试件弹性压缩阶段应力波... 定量研究分离式霍普金森压杆(split Hopkinson pressure bar,SHPB)试验中弹性压缩阶段试件中的应力波效应是解耦准确材料弹性曲线的基础。在满足平面波假设的基础上,基于广义波阻抗理论,对杆与试件面积不匹配时试件弹性压缩阶段应力波演化造成的结构效应开展了定量理论研究,分析了不同情况下弹性阶段内试件唯象工程及实际材料应力-应变曲线的偏差特征与主要因素,并揭示了影响这种偏差的影响规律及其机理。研究表明:对于线性入射加载波,当无量纲时间为0.5的倍数时,即使其他参数改变,试件唯象与材料实际的应力-应变曲线仍对应相等;试件两端的应力差较大时,若应力差的变化趋于稳定,则试件唯象与材料实际的应力-应变曲线差异较小。计算了不同波动区间内试件的最大应力偏离值及其变化趋势和对应的无量纲时间,研究了入射波是双线性组合波时试件的应力-应变曲线。研究表明:双线性波入射时,2个线性区间可以独立分析,无论如何组合线性区间或应力差如何变化,只要试件两端应力差为近似恒定曲线,对应的试件唯象工程应力-应变曲线都是相对准确的。 展开更多
关键词 分离式霍普金森压杆 应力波效应 应力均匀性假设 动态应力-应变曲线
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眼镜镜片尖边轮廓的五轴数控加工
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作者 李宏涛 项华中 +5 位作者 郑泽希 丁琦慧 张欣 王彭 张大伟 庄松林 《光学精密工程》 EI CAS CSCD 北大核心 2024年第5期704-713,共10页
为了改善和优化眼镜镜片的加工流程,避免镜片尖边加工过程中刀轴矢量变化剧烈、影响工件表面的加工质量,提出了一种基于UG NX的五轴数控加工路径。利用智能镜框扫描仪对镜框边缘进行扫描,获得镜框凹槽点云数据文件,编写相应程序对符合... 为了改善和优化眼镜镜片的加工流程,避免镜片尖边加工过程中刀轴矢量变化剧烈、影响工件表面的加工质量,提出了一种基于UG NX的五轴数控加工路径。利用智能镜框扫描仪对镜框边缘进行扫描,获得镜框凹槽点云数据文件,编写相应程序对符合眼镜片加工标准的OMA文件中的球坐标数据进行坐标及格式转换等处理。基于NURBS曲线拟合算法,实现刀路轨迹的连续性并保证拟合曲线的精度。设计和建立一种控制刀轴矢量平滑变化的刀轴驱动约束方法,依靠曲线驱动刀轴及镜片曲面法向量约束刀轴使刀头平滑进给,并将刀轨文件经过后处理转换为NC文件。最后,对加工后的镜片进行误差测量,结果表明,通过点云数据拟合刀路曲线的方法提高了加工面的精确度和光滑性,有效缩减了加工流程,提高了加工效率。 展开更多
关键词 光学加工 数控系统 非均匀有理B样条 曲线拟合 刀具路径
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