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Constructing iterative non-uniform B-spline curve and surface to fit data points 被引量:48
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作者 LINHongwei WANGGuojin DONGChenshi 《Science in China(Series F)》 2004年第3期315-331,共17页
In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that ... In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We startwith a piece of initial non-uniform B-spline curve (surface) which takes the given point setas its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higherprecision. In this paper, using modern matrix theory, we strictly prove that the limit curve(surface) of the iteration interpolates the given point set. The non-uniform B-spline curves(surfaces) generated with the iteration have many advantages, such as satisfying theNURBS standard, having explicit expression, gaining locality, and convexity preserving,etc 展开更多
关键词 FITTING ITERATION non-uniform b-spline curve and surface convexity preserving
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Non-uniform B-spline curves with multiple shape parameters 被引量:5
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作者 Juan CAO Guo-zhao WANG 《Journal of Zhejiang University-Science C(Computers and Electronics)》 SCIE EI 2011年第10期800-808,共9页
We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence.These curves not only have the many valued properties of the usual non-uniform B-spline curves,but also are shape adjustab... We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence.These curves not only have the many valued properties of the usual non-uniform B-spline curves,but also are shape adjustable under fixed control polygons.Our method is based on the degree elevation of B-spline curves,where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline.We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms,which are indispensable from the user's perspective. 展开更多
关键词 non-uniform b-spline Shape parameter Degree elevation
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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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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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Geometry Modeling of Ship Hull Based on Non-uniform B-spline 被引量:4
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作者 王虎 邹早建 《Journal of Shanghai Jiaotong university(Science)》 EI 2008年第2期189-192,共4页
In order to generate the three-dimensional (3-D) hull surface accurately and smoothly,a mixed method which is made up of non-uniform B-spline together with an iterative procedure was developed.By using the iterative m... In order to generate the three-dimensional (3-D) hull surface accurately and smoothly,a mixed method which is made up of non-uniform B-spline together with an iterative procedure was developed.By using the iterative method the data points on each section curve are calculated and the generalized waterlines and transverse section curves are determined.Then using the non-uniform B-spline expression,the control vertex net of the hull is calculated based on the generalized waterlines and section curves.A ship with tunnel stern was taken as test case.The numerical results prove that the proposed approach for geometry modeling of 3-D ship hull surface is accurate and effective. 展开更多
关键词 hull surface geometry modeling non-uniform b-spline iterative procedure
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G^2 Continuity Algorithms between Adjacent NURBS Patches along Common Cubic Boundary Curve 被引量:2
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作者 周西军 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2003年第4期241-246,242-246,共6页
Non-uniform rational B-spline (NURBS) curves and surfaces are becoming increasingly widespread. The author have explored G^1 continuity condition between adjacent NURBS surface patches along common cubic boundary curv... Non-uniform rational B-spline (NURBS) curves and surfaces are becoming increasingly widespread. The author have explored G^1 continuity condition between adjacent NURBS surface patches along common cubic boundary curve. On the basis of the research performed, this paper presents a G^2 continuity condition between adjacent NURBS patches along common cubic boundary curve and deduces a specific algorithm for contro1 points and weights of NURBS patch. For making another NURBS patch and one given NURBS patch to attain G^2, according to algorithm condition, one can adjust another patch control points and weights. It is much more convenient for engineers to apply. 展开更多
关键词 computer aided design geometric continuity non-uniform rational b-spline
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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 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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An Approach to Representing Heterogeneous Non-Uniform Rational B-Spline Objects
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作者 臧婷 徐安平 《Transactions of Tianjin University》 EI CAS 2011年第4期275-279,共5页
The representation method of heterogeneous material information is one of the key technologies of heterogeneous object modeling, but almost all the existing methods cannot represent non-uniform rational B-spline (NU... The representation method of heterogeneous material information is one of the key technologies of heterogeneous 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 heterogene- ous 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 con- trol 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 he obtained by interpolating discrete points and curves with specified material information. Some examples are given to show the effectiveness of the pro- posed methods. 展开更多
关键词 heterogeneous object non-uniform rational b-spline (NURBS) material data structure direct represen- tation method inverse construction method
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Extraction of Feature Points for Non-Uniform Rational B-Splines(NURBS)-Based Modeling of Human Legs
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作者 WANG Xi WU Zongqian LI Qiao 《Journal of Donghua University(English Edition)》 CAS 2022年第4期299-303,共5页
Methods of digital human modeling have been developed and utilized to reflect human shape features.However,most of published works focused on dynamic visualization or fashion design,instead of high-accuracy modeling,w... Methods of digital human modeling have been developed and utilized to reflect human shape features.However,most of published works focused on dynamic visualization or fashion design,instead of high-accuracy modeling,which was strongly demanded by medical or rehabilitation scenarios.Prior to a high-accuracy modeling of human legs based on non-uniform rational B-splines(NURBS),the method of extracting the required quasi-grid network of feature points for human legs is presented in this work.Given the 3 D scanned human body,the leg is firstly segmented and put in standardized position.Then re-sampling of the leg is conducted via a set of equidistant cross sections.Through analysis of leg circumferences and circumferential curvature,the characteristic sections of the leg as well as the characteristic points on the sections are then identified according to the human anatomy and shape features.The obtained collection can be arranged to form a grid of data points for knots calculation and high-accuracy shape reconstruction in future work. 展开更多
关键词 3D scan digital human modeling non-uniform rational b-splines(NURBS) feature extraction
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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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