曲线曲面造型中的变形方法研究与应用
|
摘要
曲线曲面造型是计算机辅助几何设计和计算机图形学等领域的重要研究内容、主要研究在计算机的环境下曲线曲面的表示、设计、显示和分析等.经过近半个世纪的发展、传统的曲线曲面造型技术已经比较成熟。但是,随着人们对图形显示的真实性、实时性要求的日益增强和几何设计对象向多样性、复杂性的靠拢,曲线曲面造型技术又面临着很多新的问题和挑战,比如对于柔性物体的刻画,变形造型方法正是在这样的背景下产生的。本文首先对基于能量的曲线曲面变形方法进行了研究,并将其应用于人体模型的参数化建模以及针织布缩水预测问题中,取得了较好的效果,然后针对点采样曲面的造型问题,给出了一种新的基于物理的造型方法,本文主要工作及贡献如下:
1.本文首先提出了一种基于内在(Intrinsic)表示的折线变形算法.将线段长度与线段之间的角度作为表示参数,既有利于能量函数的构造,又便于处理位移约束和长度内蕴约束条件,利用这一优势,将其应用于三维人体的参数化建模,可以方便地产生具有不同特征尺寸参数的人体模型,由于这种方法只适用于折线变形,具有较大局限性,因此,本文进一步提出一种较通用的离散曲线曲面变形方法,通过分析变形前后的位置关系来构造能量函数,再加上位移约束条件,将变形问题转化为一个凸二次规划问题,并且给出了约束点应满足的必要条件及模型解唯一的充分条件,这种方法还可以与骨架驱动变形的思想相结合,能更好的控制变形。
2.空间曲线是造型中最基本的几何元素之一,对其有效的表示是造型的基础,而特征参数化表示是其中一种包含语义信息的高层次表示,本文对空间自由曲线的特征参数化表示进行研究,建立了一种针织物线圈的特征参数化几何模型,采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系,并将该模型与能量极小化的方法相结合,得到了一种能较好地预测针织物缩水率的新模型,对随机选取的一些针织布缩水预测实验表明了算法的可行性。
3.对点采样曲面的变形问题进行了研究,提出了一种新的基于物理的点采样曲面变形方法一点采样曲面仿真的质点-弹簧模型,采用基于切平面投影和Delaunay三角剖分的方法对点采样曲面进行简化得到仿真点,进一步利用该三角剖分给出仿真点的弹簧结构,从而解决在拓扑信息缺失的情况下弹簧结构的构造问题,最终点采样曲面的变形通过仿真点的变形拟合得到,对一些典型曲面的变形验证了算法的可行性和有效性。
Curve and surface modeling is an important topic in Computer Aided Geometric Design and Computer Graphics, whose major components are the representation, design, display and analysis of curves and surfaces using computer. In the past fifty years, traditional curve and surface modeling techniques have been developed deeply. However, with the enhancement of the demands for reality and real-timeliness in graphics display, and with the trends of variety and complexity of geometrical objects, curve and surface modeling faces many new problems and challenges, such as the description of soft objects. So the researchers began to study deformable modeling methods. In this dissertation, energy based deformation methods for curves and surfaces are studied first, and the proposed methods are applied to parametric modeling of human body and shrinkage predication of knitted fabrics. Then a novel physically-based modeling methods is presented for point-sampled surfaces. The main work and contributions are as follows:
1. A new deformation method for polylines is first presented based on the intrinsic representation of the polylines. Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.
2. Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.
3. Deformation methods for point-sampled surfaces are studied in Chapter 5. A new physically-based method, mass-spring based simulation, is proposed for point-sampled surfaces. A tangent plane projection and Delaunay triangulation based simplification algorithm is applied to the original point-sampled surface to produce the simulation points, and then the mass-spring system for the simulation points is also constructed based on the Delaunay triangulation, which overcomes the lack of connectivity information. Deformation of the original point-sampled surface can be obtained from the deformed simulation surface by fitting. Experiments on some typical point-sampled surfaces indicate the feasibility and effectiveness.
1.本文首先提出了一种基于内在(Intrinsic)表示的折线变形算法.将线段长度与线段之间的角度作为表示参数,既有利于能量函数的构造,又便于处理位移约束和长度内蕴约束条件,利用这一优势,将其应用于三维人体的参数化建模,可以方便地产生具有不同特征尺寸参数的人体模型,由于这种方法只适用于折线变形,具有较大局限性,因此,本文进一步提出一种较通用的离散曲线曲面变形方法,通过分析变形前后的位置关系来构造能量函数,再加上位移约束条件,将变形问题转化为一个凸二次规划问题,并且给出了约束点应满足的必要条件及模型解唯一的充分条件,这种方法还可以与骨架驱动变形的思想相结合,能更好的控制变形。
2.空间曲线是造型中最基本的几何元素之一,对其有效的表示是造型的基础,而特征参数化表示是其中一种包含语义信息的高层次表示,本文对空间自由曲线的特征参数化表示进行研究,建立了一种针织物线圈的特征参数化几何模型,采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系,并将该模型与能量极小化的方法相结合,得到了一种能较好地预测针织物缩水率的新模型,对随机选取的一些针织布缩水预测实验表明了算法的可行性。
3.对点采样曲面的变形问题进行了研究,提出了一种新的基于物理的点采样曲面变形方法一点采样曲面仿真的质点-弹簧模型,采用基于切平面投影和Delaunay三角剖分的方法对点采样曲面进行简化得到仿真点,进一步利用该三角剖分给出仿真点的弹簧结构,从而解决在拓扑信息缺失的情况下弹簧结构的构造问题,最终点采样曲面的变形通过仿真点的变形拟合得到,对一些典型曲面的变形验证了算法的可行性和有效性。
Curve and surface modeling is an important topic in Computer Aided Geometric Design and Computer Graphics, whose major components are the representation, design, display and analysis of curves and surfaces using computer. In the past fifty years, traditional curve and surface modeling techniques have been developed deeply. However, with the enhancement of the demands for reality and real-timeliness in graphics display, and with the trends of variety and complexity of geometrical objects, curve and surface modeling faces many new problems and challenges, such as the description of soft objects. So the researchers began to study deformable modeling methods. In this dissertation, energy based deformation methods for curves and surfaces are studied first, and the proposed methods are applied to parametric modeling of human body and shrinkage predication of knitted fabrics. Then a novel physically-based modeling methods is presented for point-sampled surfaces. The main work and contributions are as follows:
1. A new deformation method for polylines is first presented based on the intrinsic representation of the polylines. Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.
2. Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.
3. Deformation methods for point-sampled surfaces are studied in Chapter 5. A new physically-based method, mass-spring based simulation, is proposed for point-sampled surfaces. A tangent plane projection and Delaunay triangulation based simplification algorithm is applied to the original point-sampled surface to produce the simulation points, and then the mass-spring system for the simulation points is also constructed based on the Delaunay triangulation, which overcomes the lack of connectivity information. Deformation of the original point-sampled surface can be obtained from the deformed simulation surface by fitting. Experiments on some typical point-sampled surfaces indicate the feasibility and effectiveness.
引文
[1]施法中.计算机辅助几何设计与非均匀有理B样条.北京:北京航空航天大学出版社.1994.
[2]王国瑾,汪国昭,郑建民.计算机辅助几何设计.北京:高等教育-施普林格出版社.2001.
[3]朱心雄.自由曲线曲面造型技术.北京:科学出版社,2000.
[4]王仁宏,施锡泉,罗钟铉,苏志勋.多元样条函数及其应用.北京:科学出版社,1994.
[5]苏步青,刘鼎元.计算几何.上海:上海科学技术出版社,1981.
[6]孙家广,陈玉健,辜凯宁.计算机辅助几何造型技术.北京:清华大学出版社,1990.
[7]孙家广,胡事民.计算机图形学基础教程.北京:清华大学出版社,2005.
[8]陈发来.代数曲面的几何连续性、Blending及求交的研究:博士学位论文.中国科技大学.1994.
[9]Bajaj C J,Xu G L.Anisotropic diffusion of subdivision surfaces and functions on surfaces.ACM Transaction on Graphics,2003,22:4-32.
[10]鲍虎军,金小刚,彭群生.计算机动画的算法基础.杭州:浙江大学出版社,2000.
[11]周蕴时,苏志勋,奚勇江等.CAGD中的曲线曲面.长春:吉林大学出版社,1993.
[12]张彩明,杨兴强,李学庆.计算机图形学.北京:科学出版社,2005.
[13]Kass M,Witkin A,Terzopoulos D.Snakes-active contour models.Journal of Computer Vision,1987,1(4):321-331.
[14]Sederberg T W,Parry R.Free-form deformation of solid geometric models.Computer Graphcis,1986,20(4):151-160.
[15]Gibson S F F,Mirtich B.A survey of deformable modeling in computer graphics.TR-97-19.Mitsubishi Electric Research Laboratory,1997.
[16]Montagnat J,Delingette H,Ayache N.A review of deformable surface:topology,geometry and deformation.Image and Vision Computing,2001,19:1023-1040.
[17]Nealen A,Muller M,Keiser R,etal.Physically based deformable models in computer graphics.Proc.Eurographics 2005.Dublin,2005:71-94.
[18]Kobbelt L,Botsch M.A survey of point-based techniques in computer graphics.Computers & Graphics,2004,28:801-814.
[19]Hu S M,Li Y F,Ju T,Zhu X.Modifying the shape of nurbs surface with geometric constrains.Computer Aided Design,2001,33:903-912.
[20]Zhang C M,Zhang F H,Cheng F H.Constrained scaling of trimmed NURBS surfaces based on fix-and stretch approach.Computer Aided Design,2001,33(1):103-112.
[21]王志国.曲线曲面形状修改和变形关键技术研究:博士学位论文.南京航空航天大学.2006.
[22]张国华,杨兴强,张彩明.基于权因子的NURBS曲线形状调整.计算机辅助设计与图形学学报,2004,16(10):1396-1400.
[23]李亚娟.样条曲线曲面的造型与形状调整的研究:博士学位论文.浙江大学,2007.
[24]Barr A.Global and local deformation of solid primitives.Computer Graphics,1984,18(3):21-30.
[25]Watt A,Watt M,eds.Advanced Animation and Rendering Technique.ACM Press,1992.
[26]金小刚,鲍虎军,彭群生.一种新的基于factor curve的变形控制方法.软件学报,1996,7(9):537-541.
[27]Borrel P,Bechmann D.Deformation of n-dimensional objects.International Journal of Computational Geometry Applications,1991,1(4):427-453.
[28]Bechmann D.Space deformation models survey.Computers & Graphics,1994,18(4):571-586.
[29]Aubert F,Bechmann D.Volume-preserving space deformation.Computers &Graphics,1997,21(5):625-639.
[30]孙岩松.带几何约束条件的空间变形方法:硕士学位论文.大连理工大学,2001.
[31]Coquillart S.Extended free-form deformation:a sculpturing tool for 3d geometric modeling.Computer Graphics,1990,24(4):187-196.
[32]Lamousin H J,Waggenspack W N.Nurbs-based free-form deformations.IEEE Transaction on Computer Graphics and Applications,1994,14(6):59-65.
[33]Ruprecht D,Nagel R,Muller H.Spatial free-form deformation with scattered data interpolation methods.Computers & Graphics,1995,19(1):63-71.
[34]Hsu W M,Hughes J F,Kaufman H.Direct manipulation of free-form deformation.Computer Graphics,1992,26(2):177-184.
[35]Kalra P,Mangili A,Thalmann N,Thalmann D.Simulation of facial muscle actions based on rational free-form deformation.Computer Graphics Forum,1992,2(3):59-69.
[36]Rappoport A,Sheffer A,Bercovier M.Volume-preserving free-form solids.IEEE Transactions on Visualization and Computer Graphics,1996,2(1):19-27.
[37]Lazarus F,Coquillart S,Jancene P.Axial deformation:an intuitive technique.Computer-Aided Design,1994,26(8):607-613.
[38]冯结青,马利庄,彭群生.基于弧长参数的轴变形新方法.计算机学报,1996,19:161-170.
[39]Peng Q S,Jin X G,Feng J Q.Arc-length-based axial deformation and length preserving deformation.Proc.Computer Animatemp' 97.Geneva,1997:86-92.
[40]Chang Y K,Rockwood A P.A generalized de casteljau approach to 3d free-form deformation.Computer Graphics,1994,28:257-260.
[41]计忠平,刘利刚,王国瑾.无局部自交的轴变形新方法.计算机学报,2006,29(5):828-834.
[42]Singh K,Fiume E.Wires:A geometric deformation technique.Proc.SIGGRAPH'98.1998:405-414.
[43]冯结青,马利庄,彭群生.一种应用参数曲面的动态自由变形方法.计算机学报,1997,20(7):600-607.
[44]Feng J Q,Ma L Z,Peng Q S.New free-form deformation through the control of parametric surfaces.Computers & Graphics,1996,20(4):531-539.
[45]冯结青,马利庄,彭群生.嵌入参数空间的曲面控制自由变形方法.计算机辅助设计与图形学学报,1998,10(3):208-215.
[46]Alexa M.Differential coordinates for local mesh morphing and deformation.The Visual Computer,2003,19(2):105-114.
[47]Lipman Y,Sorkine O,Cohen-Or D,etal.Differential coordinates for interactive mesh editing.Proc.Shape Modehng International.2004:181-190.
[48]Sorkine O,Lipman Y,Cohen-Or D,etal.Laplacian surface editing.Proc.Eurographics Symposium on Geometry Processing.2004:179-188.
[49]Huang J,Shi X H,Liu X G,etal.Geometrically based potential energy for simulating deformable objects.The Visual Computer,2006,22(9-11):740-748.
[50]Huang J,Shi X H,Liu X G,etal.Subspace gradient domain mesh deformation.ACM Transaction on Graphics,2006,25(3):1126-1134.
[51]Zhou K,Huang J,Snyder J,etal.Large mesh deformation using the volumetric graph laplacian.ACM Transaction on Graphics,2005,24(3):496-503.
[52]王小平,叶正麟,孟雅琴,李红达.参数曲面自由变形新方法.工程图学学报,2002,(1):48-52.
[53]Zwicker M,Pauly M,Knoll O,Gross M.Pointshop3d:An interactive system for point-based surface editing.Proc.SIGGRAPH' 02.2002:322-329.
[54]Pauly M,Keiser R,Kobbelt L,Gross M.Shape modeling with point-sampled geometry.Proc.SIGGRAPH.California,2003:641-650.
[55]Terzopoulos D,Platt J,Barr A.Elastically deformable models.Computer Graphics,1987,21(4):205-214.
[56]宋德军,朱心雄.基于数学规划的曲面造型方法.工程图学学报,1997,18(2-3):78-84.
[57]经玲,席平,唐荣锡.有限元方法在变形曲线曲面造型中的应用.计算机学报,1998,21(3):245-251.
[58]Guan Z D,Jing L,Ning e T.Study and application of physics-based deformable curves and surfaces.Computer & Graphics,1997,21(3):305-313.
[59]席平,经玲,唐荣锡.用可变形模型整体构造b样条曲面方法研究.北京航空航天大学学报,1999,25(4):471-474.
[60]Gelniker G,Gossard D.Deformable curve and surface finite elements for free-form shape design.Computer Graphics,1991,25(4):257-266.
[61]Welch W,Witckin A.Variational surface modeling.Computer Graphics,1992,26(2):157-166.
[62]Wesselink W,Veltkamp R C.Interactive design of constrained variational curves.Computer Aided Geometric Design,1995,13(3):533-546.
[63]Qin H,Terzopoulos D.D-nurbs:a physics-based framework for geometric design.IEEE Transactions on Visualization and Computer Graphics,1996,2(1):85-96.
[64]House D H,Breen D,eds.Cloth Modeling and Animation.Natick,MA:AK Peters,2000.
[65]宋德军,朱心雄.用能量优化方法构造n边域曲面.工程图学学报,1998,19(1):41-47.
[66]刘海峰,王同洋,王启富.约束可变形曲面的交互设计.计算机辅助设计与图形学学报,2000,28(3):7-9.
[67]高成英,刘宁,罗笑南.基于细分优化方法的织物模拟.中山大学学报(自然科学版),2004,43(2):17-20.
[68]满家巨,汪国昭.基于有限元方法的极小曲面造型.计算机学报,2003,26(4):507-510.
[69]成思源,张湘伟.可变形b样条曲线曲面模型及其有限元求解.重庆大学学报,2003,26(2):75-77.
[70]Bro-Nielsen M,Cotin S.Real-time volumetric deformable models for surgery simulation using finite elements and condensation.Computer Graphics Forum,1996,15(3):57-66.
[71]Cotin S,Delingette H,Ayache N.Real-time elastic deformations of soft tissues for surgery simulation.IEEE Transactions on Visualization and Computer Graphics,1999,5(1):62-73.
[72]Wu X,Dowries M S,Goktekin T,Tendick F.Adaptive nonlinear finite elements for deformable body simulation using dynamic progressive meshes.Proc.Eurographics.2001:349-358.
[73]Grinspun E,Krysl P,SchrSder P.Charms:A simple framework for adaptive simulation.Proc.SIGGRAPH 2002.2002:281-290.
[74]Irving G,Teran J,Fedkiw R.Invertible finite elements for robust simulation of large deformation.Proc.2004 ACM SIGGRAPH/Eurographics symposium on Computer animation.2004:131-140.
[75]Georgii J,Westermann R.A multigrid framework for real-time simulation of deformable bodies.Computers & Graphics,2006,30(3):408-415.
[76]Picinbono G,Delingette H,Ayache N.Real-time large displacement elasticity for surgery simulation:Non-linear tensor-mass model.Proc.Third International Conference on Medical Robotics,Imaging And Computer Assisted Surgery:MICCAI 2000.2000:643-652.
[77]Picinbono G,Delingette H,Ayache N.Nonlinear and anisotropic elastic soft tissue models for medical simulation.Proc.2001 IEEE International Conference on Robotics and Automation.Seoul,Korea,2001:21-26.
[78]Rutter C M.Registration of X-ray Mammograms and MR-Volumes of the Female Breast based on Simulated Mammographic Deformation:PhD Thesis.Germany:Universiy of Mannheim,2003.
[79]James D L,Pal D K.Real time simulation of multizone elastokinematic models.Proc.2002 IEEE International Conference on Robotics and Automation.2002:927-932.
[80]James D L,Fatahalian K.Precomputing interactive dynamic deformable scenes.ACM Transactions on Graphics,2003,22(3):879-887.
[81]梅春晖,石教英.基于边界元素法的柔软物体变形模拟.计算机学报,2003,26(12).
[82]张雄.无网格法.北京:清华大学出版社,2004.
[83]Muller M,Keiser R,Nealen A,etal.Point based animation of elastic,plastic and melting objects.Proc.ACM SIGGRAPH/Eurographics Symposium on Computer Animation.2004:141-151.
[84]Guo X.Point-Based Modeling,Animation,and Simulation System for Computer Graphics:PhD Thesis.USA:Stony Brook University,2006.
[85]Terzopoulos D,Waters K.Physically-based facial modeling,analysis,and animation.Journal of Visualization and Computer Animation,1990,1:73-80.
[86]Yu Z,Prakash E C,Sung E.physically-based model with adaptive refinement for facialanimation.Proc.The Fourteenth Conference on Computer Animation.Seoul,South Korea,2001:28-39.
[87]Tu X,Terzopoulos D.Artificial fishes:physics,locomotion,perception,behavior.Proc.SIGGRAPH' 94.1994:43-50.
[88]Provot X.Deformation constrains in a mass spring model to describe rigid cloth behavior.Graphics Interface,1995,33(3):147-155.
[89]Baraff D,Witkin A.Large steps in cloth simulation.Proc.SIGGRAPH' 98.Orlando,1998:43-54.
[90]Coati F,Khatib O,Baur C.Interactive rendering of deformable objects based on a filling sphere modeling approach.Proc.2003 IEEE International Conference on Robotics & Automation.Taipei,2003:14-19.
[91]潘振宽,高波.手术仿真中基于质点—弹簧模型的人体组织变形仿真.青岛大学学报,2003,18(3):9-14.
[92]李基拓,陆国栋.基于边折叠和质点-弹簧模型的网格优化算法.计算机辅助设计与图形学学报,2006,18(3):426-432.
[93]陈功,周来水,安鲁陵等.基于质点-弹簧模型曲面展开的改进算法.计算机辅助设计与图形学学报,2007,19(8):1009-1014.
[94]Eberhardt B,Weber A,Strasser W.A fast,flexible particle-system model for cloth draping.IEEE Computer Graphics and Applications,1996,16(5):52-59.
[95]Etzmuss O,Gross J,Strasser W.Deriving a particle system from continuum mechanics for the animation of deformable objects.IEEE Transactions on Visualization and Computer Graphics,2003,9(4):538-550.
[96]Pentland A,Williams J.Good vibrations:Modal dynamics for graphics and animation.Compter Graphics,1989,23(3):215-222.
[97]Teran J,Blemker S,Hing V N T,Fedkiw R.Finite volume methods for the simulation of skeletal muscle.Proc.Eurographics/SIGGRAPH Symposium on Computer Animation.2003.
[98]Balaniuk R,Salisbury K.Dynamic simulation of deformable objects using the long elements method.Proc.10th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems.Dublin,2002:58-65.
[99]李现民.三角网格简化及等值面抽取技术:博士学位论文.中国科学院计算技术研究所,2001.
[100]Sweldens W,Schroder P.Digital geometry processing.SIGGRAPH' 2001 Course Notes.2001.
[101]寇述舜.凸分析与凸二次规划.天津:天津大学出版社,1994.
[102]袁亚湘,孙文瑜.最优化理论与方法.北京:科学出版社,1997.
[103]Sumner R W,Zwicker M,Gotsman C,Popovic J.Mesh-based inverse kinematics.ACM Transactions on Graphics,2005,24(3):488-495.
[104]王小平,叶正麟,孟雅琴,李红达.基于伸缩因子的参数曲线自由变形.计算机辅助设计与图形学学报,2002,14(1):66-69.
[105]李玲,苏志勋,刘秀平.刚性关节链模型在保弧长曲线变形中的应用.计算机辅助设计与图形学学报,2005,17(5):1002-1007.
[106]李玲.基于细分的保弧长曲线变形:硕士学位论文.大连理工大学,2004.
[121]苟文选.材料力学.北京:科学出版社,2005.
[107]Chen H,Wang W P.On intrinsic representations of 3d polygons for shape blending.Computers & Graphics,2003,27:133-141.
[108]宫可想,周淑秋,常宪平等.三维人体建模技术探讨.首都师范大学学报(自然科学版),2003,24(4):17-20.
[109]Forsey D.A surface model for skeleton-based character animation.Proc.Second Eurographics Workshop on Animation and Simulation.1991:155-170.
[110]Chadwick J E,Haumann D R,Parent R E.Layered construction for deformable animated characters.Computer Graphics,1989,23(3):243-252.
[111]Aubel A,Thalmann D.Realistic deformation of human body shape.Proc.Computer Animation and Simulation.Interlaken,2000:125-135.
[112]曹俊杰.多尺度的参数化人体建模:硕士学位论文.大连理工大学,2003.
[113]Nedel L,Thalmann D.A modeling and deformation of human body using an anatomy-based approach.Proc.Computer Animation.Philadelphia,1998:34-40.
[114]Seo H,Magnenat-Thalmann N.An automatic modehng of human bodies from sizing parameters.Proc.SIGGRAPH 2003 Symposium on Interactive 3D Graphics.2003:19-26.
[115]Brett A,Brian C,Zoran P.Articulated body deformation from range scan data.ACM Transactions on Graphics,2002,21(3):612-619.
[116]秦可,庄越挺,吴飞.服装CAD中三维人体模型的参数化研究.计算机辅助设计与图形学学报,2004,16(7):918-922.
[117]阿尔文R蒂利(朱涛译).人体工程学图解-设计中的人体因素.北京:中国建筑工业出版社.1998.
[118]梁学章,崔利宏.代数曲线上的Lagrange插值.吉林大学自然科学学报,2001,(3):17-20.
[119]崔利宏.多元Lagrange插值与多元Kergin插值:博士学位论文.吉林大学,2003.
[120]王仁宏.数值逼近.北京:高等教育出版社,1999.
[122]Zhou X J,Su Z X,Xia S G.Wave surface reconstruction based on spline.Journal of Dalian University of Technology,2007,47(4):613-617.
[123]Su Z X,Xia S G,Zhou X J.Application of b-spline to 2d wave surface measurement.Journal of Information and Computational Science,2004,1(1):143-150.
[124]Shah J.Assessment of features technology.Computer Aided Design,1991,23(5):331-343.
[125]张鸿志.服装CAD原理与应用.北京:中国纺织出版社,200 5.
[126]Wang C C L,Wang Y,Matthew M Y.Feature-based 3d non-manifold freeform object construction.Engineering with Computers,2003,19(2-3):174-190.
[127]Wang C C L,Wang Y,Matthew M Y.Feature based 3d garment design through 2d sketches.Computer-Aided Design,2003,35(7):659-672.
[128]Wang C C L.Parameterization and parametric,design of mannequins.ComputerAided Design,2005,37(1):83-98.
[129] Postle R. Dimensional stability of plain knitted fabrics. Journal of Textile Institute, 1968, 59:65-77.
[130] Postle R, Munden D. Analysis of the dry relaxed knitted loop configuration. Journal of Textile Institute, 1967, 58:329-365.
[131] Peirce F. Geometrical principles applicable to the design of functional fabrics. Textile Research Journal, 1947, 17:123-147.
[132] Leaf G, Glaskin A. The geometry of the plain knitted loop. Journal of Textile Institute, 1955, 46:587-605.
[133] Choi K, Lo T Y. An energy model of plain knitted fabric. Textile Research Journal, 2003, 73(8):739-748.
134] Demiroz A, Dias T. A study of the graphical representation of plain-knitted structure, part I: stitch model for the graphical representation of plain-knitted structures. Journal of Textile Institute, 2000, 91:463-480.
[135] Shanahan W, Postle R . A theoretical analysis of plain knitted structure. Textile Research Journal, 1970, 40:656-665.
[136] Knapton J, Truter E C, Aziz M. The geometry, dimensional properties and stabilization of the cotton plain jersey structure. Journal of Textile Institute, 1975, 66:413-419.
[137] Lo T. Dimensional Properties of Weft Knitted Fabrics from Blended Yarn: PhD Thesis. UK: Huddersfield Polytechnic, 1981.
[138] Doyle P. Fundamental aspects of the design of knitted fabrics. Journal of Textile Institute, 1953, 44(8):561-578.
[139] Munden D. The geometry and dimensional properties of plain-knit fabric. Journal of Textile Institute, 1959, 50:448-471.
[140] Heap S A, Greenwood P F, Leah R D, Eaton J T. Prediction of finished weight and shrinkage of cotton knits: the starfish project part I: an introduction and general overview. Textile Research Journal, 1983, 53:109-119.
[141] Kass M, Witkin A, Terzopoulos D. Snakes: Active contour models. International Journal of Computer Vision, 1987, 1(4):321-331.
[142]Pauly M.Point Primitives for Interactive Modeling and Processing of 3D Geometry:PhD Thesis.Switzerland:ETH Zurich,2003.
[143]肖春霞.三维点采样模型的数字几何处理技术研究:博士学位论文.浙江大学,2006.
[144]缪永伟.点模型的几何处理和形状编辑:博士学位论文.浙江大学,2007.
[145]Pauly M,Gross M,Kobbelt L.Efficient simplification of point-sampled surfaces.Proc.IEEE Visualization.2002:163-170.
[146]Shinya M.Theories for mass-spring simulation in computer graphics:stability,costs and improvements.IEICE Transactions on Information and Systems,2005,E88-D(4):767-774.
[2]王国瑾,汪国昭,郑建民.计算机辅助几何设计.北京:高等教育-施普林格出版社.2001.
[3]朱心雄.自由曲线曲面造型技术.北京:科学出版社,2000.
[4]王仁宏,施锡泉,罗钟铉,苏志勋.多元样条函数及其应用.北京:科学出版社,1994.
[5]苏步青,刘鼎元.计算几何.上海:上海科学技术出版社,1981.
[6]孙家广,陈玉健,辜凯宁.计算机辅助几何造型技术.北京:清华大学出版社,1990.
[7]孙家广,胡事民.计算机图形学基础教程.北京:清华大学出版社,2005.
[8]陈发来.代数曲面的几何连续性、Blending及求交的研究:博士学位论文.中国科技大学.1994.
[9]Bajaj C J,Xu G L.Anisotropic diffusion of subdivision surfaces and functions on surfaces.ACM Transaction on Graphics,2003,22:4-32.
[10]鲍虎军,金小刚,彭群生.计算机动画的算法基础.杭州:浙江大学出版社,2000.
[11]周蕴时,苏志勋,奚勇江等.CAGD中的曲线曲面.长春:吉林大学出版社,1993.
[12]张彩明,杨兴强,李学庆.计算机图形学.北京:科学出版社,2005.
[13]Kass M,Witkin A,Terzopoulos D.Snakes-active contour models.Journal of Computer Vision,1987,1(4):321-331.
[14]Sederberg T W,Parry R.Free-form deformation of solid geometric models.Computer Graphcis,1986,20(4):151-160.
[15]Gibson S F F,Mirtich B.A survey of deformable modeling in computer graphics.TR-97-19.Mitsubishi Electric Research Laboratory,1997.
[16]Montagnat J,Delingette H,Ayache N.A review of deformable surface:topology,geometry and deformation.Image and Vision Computing,2001,19:1023-1040.
[17]Nealen A,Muller M,Keiser R,etal.Physically based deformable models in computer graphics.Proc.Eurographics 2005.Dublin,2005:71-94.
[18]Kobbelt L,Botsch M.A survey of point-based techniques in computer graphics.Computers & Graphics,2004,28:801-814.
[19]Hu S M,Li Y F,Ju T,Zhu X.Modifying the shape of nurbs surface with geometric constrains.Computer Aided Design,2001,33:903-912.
[20]Zhang C M,Zhang F H,Cheng F H.Constrained scaling of trimmed NURBS surfaces based on fix-and stretch approach.Computer Aided Design,2001,33(1):103-112.
[21]王志国.曲线曲面形状修改和变形关键技术研究:博士学位论文.南京航空航天大学.2006.
[22]张国华,杨兴强,张彩明.基于权因子的NURBS曲线形状调整.计算机辅助设计与图形学学报,2004,16(10):1396-1400.
[23]李亚娟.样条曲线曲面的造型与形状调整的研究:博士学位论文.浙江大学,2007.
[24]Barr A.Global and local deformation of solid primitives.Computer Graphics,1984,18(3):21-30.
[25]Watt A,Watt M,eds.Advanced Animation and Rendering Technique.ACM Press,1992.
[26]金小刚,鲍虎军,彭群生.一种新的基于factor curve的变形控制方法.软件学报,1996,7(9):537-541.
[27]Borrel P,Bechmann D.Deformation of n-dimensional objects.International Journal of Computational Geometry Applications,1991,1(4):427-453.
[28]Bechmann D.Space deformation models survey.Computers & Graphics,1994,18(4):571-586.
[29]Aubert F,Bechmann D.Volume-preserving space deformation.Computers &Graphics,1997,21(5):625-639.
[30]孙岩松.带几何约束条件的空间变形方法:硕士学位论文.大连理工大学,2001.
[31]Coquillart S.Extended free-form deformation:a sculpturing tool for 3d geometric modeling.Computer Graphics,1990,24(4):187-196.
[32]Lamousin H J,Waggenspack W N.Nurbs-based free-form deformations.IEEE Transaction on Computer Graphics and Applications,1994,14(6):59-65.
[33]Ruprecht D,Nagel R,Muller H.Spatial free-form deformation with scattered data interpolation methods.Computers & Graphics,1995,19(1):63-71.
[34]Hsu W M,Hughes J F,Kaufman H.Direct manipulation of free-form deformation.Computer Graphics,1992,26(2):177-184.
[35]Kalra P,Mangili A,Thalmann N,Thalmann D.Simulation of facial muscle actions based on rational free-form deformation.Computer Graphics Forum,1992,2(3):59-69.
[36]Rappoport A,Sheffer A,Bercovier M.Volume-preserving free-form solids.IEEE Transactions on Visualization and Computer Graphics,1996,2(1):19-27.
[37]Lazarus F,Coquillart S,Jancene P.Axial deformation:an intuitive technique.Computer-Aided Design,1994,26(8):607-613.
[38]冯结青,马利庄,彭群生.基于弧长参数的轴变形新方法.计算机学报,1996,19:161-170.
[39]Peng Q S,Jin X G,Feng J Q.Arc-length-based axial deformation and length preserving deformation.Proc.Computer Animatemp' 97.Geneva,1997:86-92.
[40]Chang Y K,Rockwood A P.A generalized de casteljau approach to 3d free-form deformation.Computer Graphics,1994,28:257-260.
[41]计忠平,刘利刚,王国瑾.无局部自交的轴变形新方法.计算机学报,2006,29(5):828-834.
[42]Singh K,Fiume E.Wires:A geometric deformation technique.Proc.SIGGRAPH'98.1998:405-414.
[43]冯结青,马利庄,彭群生.一种应用参数曲面的动态自由变形方法.计算机学报,1997,20(7):600-607.
[44]Feng J Q,Ma L Z,Peng Q S.New free-form deformation through the control of parametric surfaces.Computers & Graphics,1996,20(4):531-539.
[45]冯结青,马利庄,彭群生.嵌入参数空间的曲面控制自由变形方法.计算机辅助设计与图形学学报,1998,10(3):208-215.
[46]Alexa M.Differential coordinates for local mesh morphing and deformation.The Visual Computer,2003,19(2):105-114.
[47]Lipman Y,Sorkine O,Cohen-Or D,etal.Differential coordinates for interactive mesh editing.Proc.Shape Modehng International.2004:181-190.
[48]Sorkine O,Lipman Y,Cohen-Or D,etal.Laplacian surface editing.Proc.Eurographics Symposium on Geometry Processing.2004:179-188.
[49]Huang J,Shi X H,Liu X G,etal.Geometrically based potential energy for simulating deformable objects.The Visual Computer,2006,22(9-11):740-748.
[50]Huang J,Shi X H,Liu X G,etal.Subspace gradient domain mesh deformation.ACM Transaction on Graphics,2006,25(3):1126-1134.
[51]Zhou K,Huang J,Snyder J,etal.Large mesh deformation using the volumetric graph laplacian.ACM Transaction on Graphics,2005,24(3):496-503.
[52]王小平,叶正麟,孟雅琴,李红达.参数曲面自由变形新方法.工程图学学报,2002,(1):48-52.
[53]Zwicker M,Pauly M,Knoll O,Gross M.Pointshop3d:An interactive system for point-based surface editing.Proc.SIGGRAPH' 02.2002:322-329.
[54]Pauly M,Keiser R,Kobbelt L,Gross M.Shape modeling with point-sampled geometry.Proc.SIGGRAPH.California,2003:641-650.
[55]Terzopoulos D,Platt J,Barr A.Elastically deformable models.Computer Graphics,1987,21(4):205-214.
[56]宋德军,朱心雄.基于数学规划的曲面造型方法.工程图学学报,1997,18(2-3):78-84.
[57]经玲,席平,唐荣锡.有限元方法在变形曲线曲面造型中的应用.计算机学报,1998,21(3):245-251.
[58]Guan Z D,Jing L,Ning e T.Study and application of physics-based deformable curves and surfaces.Computer & Graphics,1997,21(3):305-313.
[59]席平,经玲,唐荣锡.用可变形模型整体构造b样条曲面方法研究.北京航空航天大学学报,1999,25(4):471-474.
[60]Gelniker G,Gossard D.Deformable curve and surface finite elements for free-form shape design.Computer Graphics,1991,25(4):257-266.
[61]Welch W,Witckin A.Variational surface modeling.Computer Graphics,1992,26(2):157-166.
[62]Wesselink W,Veltkamp R C.Interactive design of constrained variational curves.Computer Aided Geometric Design,1995,13(3):533-546.
[63]Qin H,Terzopoulos D.D-nurbs:a physics-based framework for geometric design.IEEE Transactions on Visualization and Computer Graphics,1996,2(1):85-96.
[64]House D H,Breen D,eds.Cloth Modeling and Animation.Natick,MA:AK Peters,2000.
[65]宋德军,朱心雄.用能量优化方法构造n边域曲面.工程图学学报,1998,19(1):41-47.
[66]刘海峰,王同洋,王启富.约束可变形曲面的交互设计.计算机辅助设计与图形学学报,2000,28(3):7-9.
[67]高成英,刘宁,罗笑南.基于细分优化方法的织物模拟.中山大学学报(自然科学版),2004,43(2):17-20.
[68]满家巨,汪国昭.基于有限元方法的极小曲面造型.计算机学报,2003,26(4):507-510.
[69]成思源,张湘伟.可变形b样条曲线曲面模型及其有限元求解.重庆大学学报,2003,26(2):75-77.
[70]Bro-Nielsen M,Cotin S.Real-time volumetric deformable models for surgery simulation using finite elements and condensation.Computer Graphics Forum,1996,15(3):57-66.
[71]Cotin S,Delingette H,Ayache N.Real-time elastic deformations of soft tissues for surgery simulation.IEEE Transactions on Visualization and Computer Graphics,1999,5(1):62-73.
[72]Wu X,Dowries M S,Goktekin T,Tendick F.Adaptive nonlinear finite elements for deformable body simulation using dynamic progressive meshes.Proc.Eurographics.2001:349-358.
[73]Grinspun E,Krysl P,SchrSder P.Charms:A simple framework for adaptive simulation.Proc.SIGGRAPH 2002.2002:281-290.
[74]Irving G,Teran J,Fedkiw R.Invertible finite elements for robust simulation of large deformation.Proc.2004 ACM SIGGRAPH/Eurographics symposium on Computer animation.2004:131-140.
[75]Georgii J,Westermann R.A multigrid framework for real-time simulation of deformable bodies.Computers & Graphics,2006,30(3):408-415.
[76]Picinbono G,Delingette H,Ayache N.Real-time large displacement elasticity for surgery simulation:Non-linear tensor-mass model.Proc.Third International Conference on Medical Robotics,Imaging And Computer Assisted Surgery:MICCAI 2000.2000:643-652.
[77]Picinbono G,Delingette H,Ayache N.Nonlinear and anisotropic elastic soft tissue models for medical simulation.Proc.2001 IEEE International Conference on Robotics and Automation.Seoul,Korea,2001:21-26.
[78]Rutter C M.Registration of X-ray Mammograms and MR-Volumes of the Female Breast based on Simulated Mammographic Deformation:PhD Thesis.Germany:Universiy of Mannheim,2003.
[79]James D L,Pal D K.Real time simulation of multizone elastokinematic models.Proc.2002 IEEE International Conference on Robotics and Automation.2002:927-932.
[80]James D L,Fatahalian K.Precomputing interactive dynamic deformable scenes.ACM Transactions on Graphics,2003,22(3):879-887.
[81]梅春晖,石教英.基于边界元素法的柔软物体变形模拟.计算机学报,2003,26(12).
[82]张雄.无网格法.北京:清华大学出版社,2004.
[83]Muller M,Keiser R,Nealen A,etal.Point based animation of elastic,plastic and melting objects.Proc.ACM SIGGRAPH/Eurographics Symposium on Computer Animation.2004:141-151.
[84]Guo X.Point-Based Modeling,Animation,and Simulation System for Computer Graphics:PhD Thesis.USA:Stony Brook University,2006.
[85]Terzopoulos D,Waters K.Physically-based facial modeling,analysis,and animation.Journal of Visualization and Computer Animation,1990,1:73-80.
[86]Yu Z,Prakash E C,Sung E.physically-based model with adaptive refinement for facialanimation.Proc.The Fourteenth Conference on Computer Animation.Seoul,South Korea,2001:28-39.
[87]Tu X,Terzopoulos D.Artificial fishes:physics,locomotion,perception,behavior.Proc.SIGGRAPH' 94.1994:43-50.
[88]Provot X.Deformation constrains in a mass spring model to describe rigid cloth behavior.Graphics Interface,1995,33(3):147-155.
[89]Baraff D,Witkin A.Large steps in cloth simulation.Proc.SIGGRAPH' 98.Orlando,1998:43-54.
[90]Coati F,Khatib O,Baur C.Interactive rendering of deformable objects based on a filling sphere modeling approach.Proc.2003 IEEE International Conference on Robotics & Automation.Taipei,2003:14-19.
[91]潘振宽,高波.手术仿真中基于质点—弹簧模型的人体组织变形仿真.青岛大学学报,2003,18(3):9-14.
[92]李基拓,陆国栋.基于边折叠和质点-弹簧模型的网格优化算法.计算机辅助设计与图形学学报,2006,18(3):426-432.
[93]陈功,周来水,安鲁陵等.基于质点-弹簧模型曲面展开的改进算法.计算机辅助设计与图形学学报,2007,19(8):1009-1014.
[94]Eberhardt B,Weber A,Strasser W.A fast,flexible particle-system model for cloth draping.IEEE Computer Graphics and Applications,1996,16(5):52-59.
[95]Etzmuss O,Gross J,Strasser W.Deriving a particle system from continuum mechanics for the animation of deformable objects.IEEE Transactions on Visualization and Computer Graphics,2003,9(4):538-550.
[96]Pentland A,Williams J.Good vibrations:Modal dynamics for graphics and animation.Compter Graphics,1989,23(3):215-222.
[97]Teran J,Blemker S,Hing V N T,Fedkiw R.Finite volume methods for the simulation of skeletal muscle.Proc.Eurographics/SIGGRAPH Symposium on Computer Animation.2003.
[98]Balaniuk R,Salisbury K.Dynamic simulation of deformable objects using the long elements method.Proc.10th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems.Dublin,2002:58-65.
[99]李现民.三角网格简化及等值面抽取技术:博士学位论文.中国科学院计算技术研究所,2001.
[100]Sweldens W,Schroder P.Digital geometry processing.SIGGRAPH' 2001 Course Notes.2001.
[101]寇述舜.凸分析与凸二次规划.天津:天津大学出版社,1994.
[102]袁亚湘,孙文瑜.最优化理论与方法.北京:科学出版社,1997.
[103]Sumner R W,Zwicker M,Gotsman C,Popovic J.Mesh-based inverse kinematics.ACM Transactions on Graphics,2005,24(3):488-495.
[104]王小平,叶正麟,孟雅琴,李红达.基于伸缩因子的参数曲线自由变形.计算机辅助设计与图形学学报,2002,14(1):66-69.
[105]李玲,苏志勋,刘秀平.刚性关节链模型在保弧长曲线变形中的应用.计算机辅助设计与图形学学报,2005,17(5):1002-1007.
[106]李玲.基于细分的保弧长曲线变形:硕士学位论文.大连理工大学,2004.
[121]苟文选.材料力学.北京:科学出版社,2005.
[107]Chen H,Wang W P.On intrinsic representations of 3d polygons for shape blending.Computers & Graphics,2003,27:133-141.
[108]宫可想,周淑秋,常宪平等.三维人体建模技术探讨.首都师范大学学报(自然科学版),2003,24(4):17-20.
[109]Forsey D.A surface model for skeleton-based character animation.Proc.Second Eurographics Workshop on Animation and Simulation.1991:155-170.
[110]Chadwick J E,Haumann D R,Parent R E.Layered construction for deformable animated characters.Computer Graphics,1989,23(3):243-252.
[111]Aubel A,Thalmann D.Realistic deformation of human body shape.Proc.Computer Animation and Simulation.Interlaken,2000:125-135.
[112]曹俊杰.多尺度的参数化人体建模:硕士学位论文.大连理工大学,2003.
[113]Nedel L,Thalmann D.A modeling and deformation of human body using an anatomy-based approach.Proc.Computer Animation.Philadelphia,1998:34-40.
[114]Seo H,Magnenat-Thalmann N.An automatic modehng of human bodies from sizing parameters.Proc.SIGGRAPH 2003 Symposium on Interactive 3D Graphics.2003:19-26.
[115]Brett A,Brian C,Zoran P.Articulated body deformation from range scan data.ACM Transactions on Graphics,2002,21(3):612-619.
[116]秦可,庄越挺,吴飞.服装CAD中三维人体模型的参数化研究.计算机辅助设计与图形学学报,2004,16(7):918-922.
[117]阿尔文R蒂利(朱涛译).人体工程学图解-设计中的人体因素.北京:中国建筑工业出版社.1998.
[118]梁学章,崔利宏.代数曲线上的Lagrange插值.吉林大学自然科学学报,2001,(3):17-20.
[119]崔利宏.多元Lagrange插值与多元Kergin插值:博士学位论文.吉林大学,2003.
[120]王仁宏.数值逼近.北京:高等教育出版社,1999.
[122]Zhou X J,Su Z X,Xia S G.Wave surface reconstruction based on spline.Journal of Dalian University of Technology,2007,47(4):613-617.
[123]Su Z X,Xia S G,Zhou X J.Application of b-spline to 2d wave surface measurement.Journal of Information and Computational Science,2004,1(1):143-150.
[124]Shah J.Assessment of features technology.Computer Aided Design,1991,23(5):331-343.
[125]张鸿志.服装CAD原理与应用.北京:中国纺织出版社,200 5.
[126]Wang C C L,Wang Y,Matthew M Y.Feature-based 3d non-manifold freeform object construction.Engineering with Computers,2003,19(2-3):174-190.
[127]Wang C C L,Wang Y,Matthew M Y.Feature based 3d garment design through 2d sketches.Computer-Aided Design,2003,35(7):659-672.
[128]Wang C C L.Parameterization and parametric,design of mannequins.ComputerAided Design,2005,37(1):83-98.
[129] Postle R. Dimensional stability of plain knitted fabrics. Journal of Textile Institute, 1968, 59:65-77.
[130] Postle R, Munden D. Analysis of the dry relaxed knitted loop configuration. Journal of Textile Institute, 1967, 58:329-365.
[131] Peirce F. Geometrical principles applicable to the design of functional fabrics. Textile Research Journal, 1947, 17:123-147.
[132] Leaf G, Glaskin A. The geometry of the plain knitted loop. Journal of Textile Institute, 1955, 46:587-605.
[133] Choi K, Lo T Y. An energy model of plain knitted fabric. Textile Research Journal, 2003, 73(8):739-748.
134] Demiroz A, Dias T. A study of the graphical representation of plain-knitted structure, part I: stitch model for the graphical representation of plain-knitted structures. Journal of Textile Institute, 2000, 91:463-480.
[135] Shanahan W, Postle R . A theoretical analysis of plain knitted structure. Textile Research Journal, 1970, 40:656-665.
[136] Knapton J, Truter E C, Aziz M. The geometry, dimensional properties and stabilization of the cotton plain jersey structure. Journal of Textile Institute, 1975, 66:413-419.
[137] Lo T. Dimensional Properties of Weft Knitted Fabrics from Blended Yarn: PhD Thesis. UK: Huddersfield Polytechnic, 1981.
[138] Doyle P. Fundamental aspects of the design of knitted fabrics. Journal of Textile Institute, 1953, 44(8):561-578.
[139] Munden D. The geometry and dimensional properties of plain-knit fabric. Journal of Textile Institute, 1959, 50:448-471.
[140] Heap S A, Greenwood P F, Leah R D, Eaton J T. Prediction of finished weight and shrinkage of cotton knits: the starfish project part I: an introduction and general overview. Textile Research Journal, 1983, 53:109-119.
[141] Kass M, Witkin A, Terzopoulos D. Snakes: Active contour models. International Journal of Computer Vision, 1987, 1(4):321-331.
[142]Pauly M.Point Primitives for Interactive Modeling and Processing of 3D Geometry:PhD Thesis.Switzerland:ETH Zurich,2003.
[143]肖春霞.三维点采样模型的数字几何处理技术研究:博士学位论文.浙江大学,2006.
[144]缪永伟.点模型的几何处理和形状编辑:博士学位论文.浙江大学,2007.
[145]Pauly M,Gross M,Kobbelt L.Efficient simplification of point-sampled surfaces.Proc.IEEE Visualization.2002:163-170.
[146]Shinya M.Theories for mass-spring simulation in computer graphics:stability,costs and improvements.IEICE Transactions on Information and Systems,2005,E88-D(4):767-774.